TRM Instruments: Processing And Calculations Instrument Guide

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Wall Street Systems – Empowering Treasury Trade and Settlement

Wallstreet Suite
Transaction & Risk Management Module (TRM)
Instruments: Processing and Calculations
Version 7.3.14

Information in this document is subject to change without notice and does not represent a commitment on the part
of Wall Street Systems. The software and documentation, which includes information contained in any databases,
described in this document is furnished under a license agreement or nondisclosure agreement and may only be
used or copied in accordance with the terms of the agreement. It is against the law to copy the software or
documentation except as specially allowed in the license or nondisclosure agreement. No part of this publication
may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without the prior written permission of Wall Street Systems.
Although Wall Street Systems has tested the software and reviewed the documentation, Wall Street Systems
makes herein no warranty or representation, either expressed or implied, with respect to software or
documentation, its quality, performance, marketability, or fitness for a particular purpose. As a result, this
software is provided "as is", and in no event will Wall Street Systems be liable for direct, indirect, special,
incidental, or consequential damages from any defect in the software or by virtue of providing this
documentation, even if advised of the possibility of such damages. The documentation may contain technical
inaccuracies and omissions.
The mention of an activity or instrument in this publication does not imply that all matters relating to that activity or
instrument are supported by Wallstreet Suite, nor does it imply that processing of or by that activity or instrument is
carried out in any particular way, even if such processing is customary in some or all parts of the industry.
The windows and screen images shown herein were obtained from prototypes during software development. The
actual windows and screen images in the software may differ.
© Copyright 2011 Wall Street Systems IPH AB. All rights reserved.
Second Edition (May 2011)
This edition applies to Wallstreet Suite version 7.3.14 and to all later releases and versions until indicated in new
editions or Wall Street Systems communications. Make sure you are using the latest edition for the release level of
the Wall Street Systems product.

Wall Street Systems, WSS, WALLSTREET, WALLSTREET SUITE and the Wall Street Systems logos are
trademarks of Wall Street Systems Delaware, Inc.
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Incorporated in the United States and/or other countries.
All other products mentioned in this book may be trademarks or service marks of their respective companies or
organizations.
Company names, people names, and data used in examples are fictitious unless otherwise noted.

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Contents

Preface ...........................................................................................................................19
Intended audience ........................................................................................................................ 19
Associated documents ................................................................................................................ 19
Change history ............................................................................................................................. 20

1 Concepts ....................................................................................................................21
1.1 Instruments ............................................................................................................................ 21
1.2 Classes and types ................................................................................................................. 21
1.2.1 Creating types ................................................................................................................. 22
1.2.2 Customizing types ........................................................................................................... 22
1.3 Instrument templates ............................................................................................................ 23
1.4 Groups ................................................................................................................................... 23
1.5 Features ................................................................................................................................. 24
1.5.1 Primary and trading features ........................................................................................... 25
1.5.2 Action features ................................................................................................................ 25
1.5.3 Valuation approach and valuation setup features ........................................................... 25
1.6 Schedules .............................................................................................................................. 25
1.7 Deal capture ........................................................................................................................... 27
1.7.1 Input data ........................................................................................................................ 27
1.7.2 Generated data ............................................................................................................... 27
1.8 Processing ............................................................................................................................. 28
1.8.1 Setup ............................................................................................................................... 28
1.8.2 Execution ........................................................................................................................ 29
1.8.3 Cancellation .................................................................................................................... 29
1.9 Valuation and results ............................................................................................................ 29
1.9.1 Market value ................................................................................................................... 29
1.9.2 Profits and results ........................................................................................................... 29
1.9.3 Valuation modes ............................................................................................................. 30

2 Market standards and calculations .........................................................................33
2.1 Market standards .................................................................................................................. 33
2.1.1 Date basis ....................................................................................................................... 33
2.1.2 Interest types .................................................................................................................. 37
2.1.3 Price types ...................................................................................................................... 38
2.1.4 Yield/price conversions ................................................................................................... 38
2.1.5 Discount Margin .............................................................................................................. 66
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2.1.6 Calculation methods ....................................................................................................... 67
2.2 Yield curves ........................................................................................................................... 81
2.2.1 Yield curve ...................................................................................................................... 81
2.2.2 Basis swaps .................................................................................................................... 91
2.2.3 Yield Curve interpolation ................................................................................................. 98
2.2.4 FX rate interpolation ...................................................................................................... 110
2.3 Key-figures .......................................................................................................................... 112
2.3.1 Valuation ....................................................................................................................... 112
2.3.2 Profit and Loss .............................................................................................................. 113
2.3.3 Option figures ................................................................................................................ 115
2.3.4 Risk ............................................................................................................................... 119
2.3.5 Dual currency ................................................................................................................ 147
2.4 Performance calculations .................................................................................................. 149
2.4.1 Actual basis and all cash basis ..................................................................................... 150
2.4.2 Trade date and value date based performance ............................................................ 150
2.4.3 Time-weighted rate of return (TWR) ............................................................................. 151
2.4.4 Money-weighted return ................................................................................................. 154
2.4.5 Instrument market values for third currency .................................................................. 155
2.4.6 Instrument market values and cashflows ...................................................................... 160
2.4.7 Example portfolio .......................................................................................................... 163
2.4.8 Risk-adjusted returns .................................................................................................... 166
2.4.9 Risk-adjusted return measures ..................................................................................... 175
2.4.10 Performance attribution ............................................................................................... 180
2.4.11 Performance measurement key-figures ...................................................................... 189
2.5 Value-at-Risk calculations .................................................................................................. 200
2.5.1 TRM approach to VaR calculations .............................................................................. 201
2.5.2 RiskMetrics data ........................................................................................................... 201
2.5.3 Market variables ............................................................................................................ 202
2.5.4 Transforming RiskMetrics data ..................................................................................... 204
2.5.5 VaR calculations ........................................................................................................... 207
2.5.6 Incremental VaR ........................................................................................................... 212

3 Debt instruments .....................................................................................................215
3.1 Bond ..................................................................................................................................... 215
3.1.1 Fixed-rate bond ............................................................................................................. 215
3.1.2 Floating rate note .......................................................................................................... 228
3.1.3 Australian floating rate note .......................................................................................... 236
3.1.4 Zero-coupon bond ......................................................................................................... 239
3.1.5 Amortizing bond ............................................................................................................ 241
3.1.6 Step-up bond ................................................................................................................ 243
3.2 Structured bonds ................................................................................................................ 244
3.2.1 Callable bond ................................................................................................................ 244
3.2.2 Dual-currency bond ....................................................................................................... 246
3.2.3 Credit step-up bond ...................................................................................................... 249
3.3 Schuldscheindarlehen ........................................................................................................ 250
3.3.1 Instrument setup ........................................................................................................... 250
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3.3.2 Deal capture .................................................................................................................. 251
3.3.3 Processing .................................................................................................................... 251
3.3.4 Position monitoring ....................................................................................................... 251
3.4 Denominated bond .............................................................................................................. 254
3.4.1 Instrument setup ........................................................................................................... 254
3.4.2 Deal capture .................................................................................................................. 255
3.4.3 Processing .................................................................................................................... 256
3.4.4 Position monitoring ....................................................................................................... 256
3.5 Convertible bond ................................................................................................................. 258
3.5.1 Instrument setup ........................................................................................................... 258
3.5.2 Deal capture .................................................................................................................. 259
3.5.3 Processing .................................................................................................................... 259
3.6 Index-linked bond ............................................................................................................... 260
3.6.1 Instrument setup ........................................................................................................... 260
3.6.2 Deal capture .................................................................................................................. 262
3.6.3 Processing .................................................................................................................... 262
3.6.4 Australian index-linked annuity bond ............................................................................ 263
3.6.5 Australian index-linked bond ......................................................................................... 267
3.6.6 Brazilian (LFT) selic-linked security .............................................................................. 270
3.6.7 Brazilian FX-linked NBC-E/NTN-D ................................................................................ 271
3.6.8 Brazilian inflation-linked NTN ........................................................................................ 272
3.6.9 Canadian real return bond ............................................................................................ 273
3.6.10 French OAT€i .............................................................................................................. 274
3.6.11 Greek index-linked bond ............................................................................................. 277
3.6.12 Israeli index-linked bond ............................................................................................. 279
3.6.13 Italian BTP €i ............................................................................................................... 281
3.6.14 Japanese index-linked bond ....................................................................................... 282
3.6.15 Swedish index-linked bond ......................................................................................... 283
3.6.16 UK index-linked gilt ..................................................................................................... 287
3.6.17 US Tips ....................................................................................................................... 292
3.7 Asset backed security ........................................................................................................ 297
3.7.1 Instrument setup ........................................................................................................... 297
3.7.2 Deal capture .................................................................................................................. 299
3.7.3 Processing .................................................................................................................... 300
3.7.4 Position monitoring ....................................................................................................... 302
3.7.5 Australian MBS ............................................................................................................. 302
3.8 Short term loan .................................................................................................................... 305
3.8.1 Instrument setup ........................................................................................................... 306
3.8.2 Deal capture .................................................................................................................. 307
3.8.3 Processing .................................................................................................................... 308
3.8.4 Position monitoring ....................................................................................................... 311
3.9 Discount paper .................................................................................................................... 316
3.9.1 Instrument setup ........................................................................................................... 316
3.9.2 Deal capture .................................................................................................................. 317
3.9.3 Processing .................................................................................................................... 319
3.9.4 Position monitoring ....................................................................................................... 320

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3.10 Loan .................................................................................................................................... 326
3.10.1 Fixed-rate loan ............................................................................................................ 326
3.10.2 Floating-rate loan ........................................................................................................ 337
3.10.3 Other loan structures .................................................................................................. 340

4 Equities ....................................................................................................................345
4.1 Equity ................................................................................................................................... 345
4.1.1 Instrument setup ........................................................................................................... 345
4.1.2 Deal capture .................................................................................................................. 346
4.1.3 Processing .................................................................................................................... 347
4.1.4 Position monitoring ....................................................................................................... 352

5 Security lending ......................................................................................................355
5.1 Repurchase agreement ...................................................................................................... 355
5.1.1 Repo (classic) ............................................................................................................... 355
5.1.2 Buy/sell back and sell/buy back .................................................................................... 362
5.1.3 Floating Repo ................................................................................................................ 363
5.1.4 Collateral ....................................................................................................................... 365
5.1.5 Substitution ................................................................................................................... 366
5.1.6 Margin movement ......................................................................................................... 370
5.1.7 Cash Collateral ............................................................................................................. 376
5.2 Security loan ........................................................................................................................ 380
5.2.1 Instrument setup ........................................................................................................... 380
5.2.2 Deal capture .................................................................................................................. 380
5.2.3 Processing .................................................................................................................... 381

6 Forex ........................................................................................................................383
6.1 FX spot and FX forward ...................................................................................................... 383
6.1.1 Instrument setup ........................................................................................................... 383
6.1.2 Market information ........................................................................................................ 384
6.1.3 Deal capture .................................................................................................................. 384
6.1.4 Processing .................................................................................................................... 387
6.1.5 Position monitoring ....................................................................................................... 393
6.2 Average FX rate forward ..................................................................................................... 406
6.2.1 Instrument setup ........................................................................................................... 406
6.2.2 Deal capture .................................................................................................................. 406
6.2.3 Processing .................................................................................................................... 408
6.2.4 Position monitoring ....................................................................................................... 409
6.3 Open Window FX Forward (FX Time Option) ................................................................... 409
6.3.1 Instrument setup ........................................................................................................... 410
6.3.2 Deal capture .................................................................................................................. 410
6.3.3 Processing .................................................................................................................... 411
6.3.4 Position monitoring ....................................................................................................... 411
6.4 FX swap ................................................................................................................................ 416
6.4.1 Instrument setup ........................................................................................................... 416
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6.4.2 Market information ........................................................................................................ 418
6.4.3 Deal capture .................................................................................................................. 418
6.4.4 Processing .................................................................................................................... 420
6.4.5 Position monitoring ....................................................................................................... 422
6.5 Cost-of-funding FX swap .................................................................................................... 422
6.5.1 Instrument setup ........................................................................................................... 423
6.5.2 Deal capture .................................................................................................................. 423
6.5.3 Processing .................................................................................................................... 424
6.5.4 Position monitoring ....................................................................................................... 424

7 Index .........................................................................................................................425
7.1 Index types .......................................................................................................................... 425
7.2 Instrument setup ................................................................................................................. 426
7.2.1 Simple Index ................................................................................................................. 426
7.2.2 Composite Index ........................................................................................................... 427
7.2.3 Derived Index ................................................................................................................ 430
7.2.4 Performance averaging index ....................................................................................... 433
7.2.5 Performance totaling index ........................................................................................... 436
7.3 Market information .............................................................................................................. 440
7.4 Processing ........................................................................................................................... 440
7.4.1 Revision ........................................................................................................................ 440
7.4.2 Freezing Index Values .................................................................................................. 440
7.4.3 Updating Factors and Cash .......................................................................................... 441
7.4.4 Rebalancing .................................................................................................................. 441

8 Cash .........................................................................................................................443
8.1 Bank account ....................................................................................................................... 443
8.1.1 Instrument setup ........................................................................................................... 443
8.1.2 Deal capture .................................................................................................................. 444
8.1.3 Processing .................................................................................................................... 445
8.2 Call account ......................................................................................................................... 446
8.2.1 Instrument setup ........................................................................................................... 446
8.2.2 Deal capture .................................................................................................................. 447
8.2.3 Processing .................................................................................................................... 447
8.3 Call money ........................................................................................................................... 450
8.3.1 Instrument setup ........................................................................................................... 450
8.3.2 Deal capture .................................................................................................................. 451
8.3.3 Processing .................................................................................................................... 451
8.3.4 Position monitoring ....................................................................................................... 454
8.4 Cash ..................................................................................................................................... 454
8.4.1 Payment ........................................................................................................................ 454
8.4.2 Transfer ......................................................................................................................... 455
8.4.3 Complex payment ......................................................................................................... 457
8.5 Forecast ............................................................................................................................... 459
8.5.1 Instrument setup ........................................................................................................... 459
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8.5.2 Deal capture .................................................................................................................. 459
8.5.3 Processing .................................................................................................................... 459
8.6 Cost-of-carry ........................................................................................................................ 460
8.6.1 Instrument setup ........................................................................................................... 461
8.6.2 Deal capture .................................................................................................................. 462
8.6.3 Processing .................................................................................................................... 462

9 Futures .....................................................................................................................465
9.1 Forward rate agreement ..................................................................................................... 465
9.1.1 FRA deposit and FRA discount ..................................................................................... 465
9.1.2 Australian FRA .............................................................................................................. 476
9.1.3 Swedish FRA ................................................................................................................ 477
9.2 Bond forward ....................................................................................................................... 479
9.2.1 Bond forward ................................................................................................................. 479
9.2.2 Swedish Bond forward .................................................................................................. 482
9.3 Money market future ........................................................................................................... 485
9.3.1 Money market future (single contract) .......................................................................... 485
9.3.2 Money market future chain ........................................................................................... 503
9.4 Bond future .......................................................................................................................... 506
9.4.1 Bond future ................................................................................................................... 506
9.4.2 CTD future .................................................................................................................... 509
9.4.3 Australian bond future ................................................................................................... 518
9.5 Equity future ........................................................................................................................ 519
9.5.1 Instrument setup ........................................................................................................... 519
9.5.2 Deal capture .................................................................................................................. 521
9.5.3 Processing .................................................................................................................... 521
9.6 FX future .............................................................................................................................. 523
9.6.1 Instrument setup ........................................................................................................... 523
9.6.2 Deal capture .................................................................................................................. 525
9.6.3 Processing .................................................................................................................... 525
9.6.4 Position monitoring ....................................................................................................... 527
9.7 Index future .......................................................................................................................... 529
9.7.1 Instrument setup ........................................................................................................... 530
9.7.2 Deal capture .................................................................................................................. 531
9.7.3 Processing .................................................................................................................... 531

10 Options ...................................................................................................................533
10.1 Cap/floor/collar .................................................................................................................. 533
10.1.1 Vanilla cap/floor/collar ................................................................................................. 533
10.1.2 Exotic cap/floor/collar .................................................................................................. 544
10.2 Swaption ............................................................................................................................ 546
10.2.1 Instrument setup ......................................................................................................... 547
10.2.2 Deal capture ................................................................................................................ 548
10.2.3 Processing .................................................................................................................. 549
10.2.4 Position monitoring ..................................................................................................... 550
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© Wall Street Systems IPH AB - Confidential

10.3 Option on MM future ......................................................................................................... 559
10.3.1 Instrument setup ......................................................................................................... 560
10.3.2 Market information ...................................................................................................... 562
10.3.3 Deal capture ................................................................................................................ 562
10.3.4 Processing .................................................................................................................. 563
10.3.5 Position monitoring ..................................................................................................... 564
10.3.6 Australian MM Future option ....................................................................................... 568
10.4 Bond option ....................................................................................................................... 569
10.4.1 Instrument setup ......................................................................................................... 570
10.4.2 Deal capture ................................................................................................................ 572
10.4.3 Processing .................................................................................................................. 573
10.5 Bond Future Option .......................................................................................................... 574
10.5.1 Instrument setup ......................................................................................................... 574
10.5.2 Australian Bond Future Option .................................................................................... 574
10.6 Equity option ..................................................................................................................... 575
10.6.1 Instrument setup ......................................................................................................... 576
10.6.2 Deal capture ................................................................................................................ 577
10.6.3 Processing .................................................................................................................. 578
10.6.4 Position monitoring ..................................................................................................... 579
10.7 Index option ....................................................................................................................... 582
10.7.1 Instrument setup ......................................................................................................... 582
10.7.2 Deal capture ................................................................................................................ 583
10.7.3 Processing .................................................................................................................. 584
10.8 FX option ............................................................................................................................ 585
10.8.1 Vanilla FX option ......................................................................................................... 585
10.8.2 Digital FX option .......................................................................................................... 593
10.8.3 Barrier FX option ......................................................................................................... 596
10.8.4 Compound FX option .................................................................................................. 601
10.8.5 Average FX rate option ............................................................................................... 605
10.8.6 Position monitoring ..................................................................................................... 610
10.9 Exchange traded FX option .............................................................................................. 628

11 Swaps .....................................................................................................................629
11.1 Interest rate swap .............................................................................................................. 629
11.1.1 Single-currency IR swap ............................................................................................. 629
11.1.2 Asset swap .................................................................................................................. 656
11.1.3 Cross-currency swap .................................................................................................. 656
11.1.4 Brazilian IDxUSD Swap .............................................................................................. 677
11.1.5 Overnight index swap ................................................................................................. 677
11.1.6 Other swap structures ................................................................................................. 682
11.2 Total return swap .............................................................................................................. 682
11.2.1 Instrument setup ......................................................................................................... 683
11.2.2 Deal capture ................................................................................................................ 684
11.2.3 Processing .................................................................................................................. 685
11.3 Credit default swap ........................................................................................................... 688

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11.3.1
11.3.2
11.3.3
11.3.4
11.3.5

Instrument setup ......................................................................................................... 688
Market information ...................................................................................................... 690
Deal capture ................................................................................................................ 690
Processing .................................................................................................................. 692
Position monitoring ..................................................................................................... 694

12 Commodities .........................................................................................................699
12.1 Gold .................................................................................................................................... 699
12.1.1 Gold deposit ................................................................................................................ 699
12.1.2 Gold IR swap .............................................................................................................. 702
12.2 Setting up commodities as currencies ........................................................................... 702
12.3 Commodity futures ........................................................................................................... 703
12.3.1 Setting up instruments ................................................................................................ 703
12.4 Commodity swaps and forwards ..................................................................................... 703
12.4.1 Schedule structure ...................................................................................................... 703
12.4.2 Setting up instruments ................................................................................................ 704
12.4.3 Deal capture ................................................................................................................ 705

13 Funds .....................................................................................................................707
13.1 Fund shares ....................................................................................................................... 707
13.1.1 Instrument setup ......................................................................................................... 707
13.1.2 Deal capture ................................................................................................................ 708
13.2 Fund fees ........................................................................................................................... 708
13.2.1 Instrument setup ......................................................................................................... 708
13.2.2 Deal capture ................................................................................................................ 710
13.2.3 Processing .................................................................................................................. 710

Appendix A: Features ............................................................................................................713
A.1 Categories of features ........................................................................................................ 713
A.2 List of features .................................................................................................................... 713
A.2.1 ABS - Asset Backed Security ....................................................................................... 713
A.2.2 ABS Valuation .............................................................................................................. 714
A.2.3 Accrual Yield Setup ...................................................................................................... 714
A.2.4 Allow Ad-Hoc Instructions ............................................................................................. 715
A.2.5 Allow Ad-Hoc Clients/Instructions ................................................................................. 715
A.2.6 Allow Forcing Type to Spot ........................................................................................... 715
A.2.7 Allow FX Currency Pair Shift ........................................................................................ 716
A.2.8 Allow Manual Classification .......................................................................................... 716
A.2.9 Allow Roll Over ............................................................................................................. 716
A.2.10 Allow Roll Over (Dual Currency) ................................................................................. 717
A.2.11 Allow Roll Over (FX) ................................................................................................... 717
A.2.12 Allow Roll Over (FX - Margin Result) .......................................................................... 718
A.2.13 Allow Roll Over (repo) ................................................................................................ 719
A.2.14 Allow Roll Over (Short Loan) ...................................................................................... 719
A.2.15 Allow Roll Over (Short Loan - Margin Result) ............................................................. 719
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A.2.16
A.2.17
A.2.18
A.2.19
A.2.20
A.2.21
A.2.22
A.2.23
A.2.24
A.2.25
A.2.26
A.2.27
A.2.28
A.2.29
A.2.30
A.2.31
A.2.32
A.2.33
A.2.34
A.2.35
A.2.36
A.2.37
A.2.38
A.2.39
A.2.40
A.2.41
A.2.42
A.2.43
A.2.44
A.2.45
A.2.46
A.2.47
A.2.48
A.2.49
A.2.50
A.2.51
A.2.52
A.2.53
A.2.54
A.2.55
A.2.56
A.2.57
A.2.58
A.2.59
A.2.60
A.2.61
A.2.62
A.2.63

Allow Roll Over (FX - Swap Style) .............................................................................. 720
Allow Roll Over (FX - Swap Style - Margin Result) .................................................... 720
Allow Roll Over (Guarantee) ....................................................................................... 720
Allow Security Loan .................................................................................................... 721
Allow Sight Account Transfer ..................................................................................... 721
Allow Signature Date .................................................................................................. 721
Allow Spread Curves .................................................................................................. 721
Allow Swap ................................................................................................................. 722
Allow Transaction Transfer ......................................................................................... 722
Allow Weight Difference ............................................................................................. 722
Allow Valuation Curves ............................................................................................... 723
Alternative Repayment Estimates .............................................................................. 723
Australian Bond Future Option ................................................................................... 724
Australian CIB ............................................................................................................. 724
Australian FRN ........................................................................................................... 724
Australian FRN Method .............................................................................................. 725
Australian IAB ............................................................................................................. 725
Australian IAB Valuation ............................................................................................. 725
Australian IAB (Round to 3) ........................................................................................ 725
Australian IAB Valuation (Round to 3) ........................................................................ 726
Australian IAB Par Curve Valuation ............................................................................ 726
Australian IAB Par Curve Valuation (Round to 3) ....................................................... 727
Australian Index-Linked Bond Valuation ..................................................................... 727
Australian MBS ........................................................................................................... 727
Australian MBS Valuation ........................................................................................... 728
Average FX Rate Forward .......................................................................................... 728
Average FX Rate Valuation ........................................................................................ 728
Average FX Rate Option ............................................................................................ 729
Average FX Rate Option Valuation ............................................................................ 729
Bank Account Balance ............................................................................................... 729
Bank Account Interest ................................................................................................ 730
Bank Account Valuation ............................................................................................. 732
Base IR Exposure Setup ............................................................................................ 732
Base IR Setup ............................................................................................................ 733
Base Valuation Setup ................................................................................................. 734
Bond ........................................................................................................................... 734
Bond - Brazilian LFT ................................................................................................... 737
Bond - Brazilian LFT Valuation ................................................................................... 737
Bond - Brazilian FX-Linked NBC ................................................................................ 737
Bond - Brazilian FX-Linked NBC Valuation ................................................................ 737
Bond - Brazilian Inflation-Linked NTN ........................................................................ 738
Bond - Brazilian Inflation-Linked NTN Valuation ........................................................ 738
Bond - Canadian RRB ................................................................................................ 738
Bond - Canadian Index-Linked Bond Valuation .......................................................... 738
Bond Denominations Setup ........................................................................................ 739
Bond Forward ............................................................................................................. 739
Bond Forward (Swedish) ............................................................................................ 740
Bond Forward Dates ................................................................................................... 741

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A.2.64 Bond Forward Valuation ............................................................................................. 741
A.2.65 Bond - French OAT€i .................................................................................................. 741
A.2.66 Bond - French Index-Linked Bond Valuation .............................................................. 742
A.2.67 Bond Future ................................................................................................................ 742
A.2.68 Bond Future - Australian ............................................................................................. 743
A.2.69 Bond Future Valuation ................................................................................................ 743
A.2.70 Bond Future Option Valuation .................................................................................... 743
A.2.71 Bond - Greek Index-Linked Bond ............................................................................... 744
A.2.72 Bond - Greek Index-linked Bond Valuation ................................................................ 744
A.2.73 Bond - Israeli Index-Linked Bond ............................................................................... 744
A.2.74 Bond - Israeli Index-Linked Bond Valuation ............................................................... 745
A.2.75 Bond - Italian BTP€i .................................................................................................... 745
A.2.76 Bond - Italian Index-Linked Bond Valuation ............................................................... 745
A.2.77 Bond Option ................................................................................................................ 745
A.2.78 Bond Option Valuation ................................................................................................ 746
A.2.79 Bond Pricing ............................................................................................................... 746
A.2.80 Branch Codes ............................................................................................................. 747
A.2.81 Bootstrap Instrument .................................................................................................. 747
A.2.82 Call Account ............................................................................................................... 747
A.2.83 Call Account Valuation ............................................................................................... 749
A.2.84 Call Money .................................................................................................................. 750
A.2.85 Call Money Valuation .................................................................................................. 750
A.2.86 Cancel Provisional Settlements .................................................................................. 750
A.2.87 Cap/Floor/Collar ......................................................................................................... 751
A.2.88 Cap/Floor/Collar Valuation ......................................................................................... 751
A.2.89 Cashflow Charges ...................................................................................................... 751
A.2.90 Cash Collateral Account ............................................................................................. 752
A.2.91 Cash Payment ............................................................................................................ 754
A.2.92 Choose Coupon .......................................................................................................... 755
A.2.93 Collateral .................................................................................................................... 755
A.2.94 Collateral Delivery ...................................................................................................... 755
A.2.95 Collateral Setup .......................................................................................................... 756
A.2.96 Collateral Transfer ...................................................................................................... 756
A.2.97 Collateral Valuation .................................................................................................... 756
A.2.98 Competitive Premiums ............................................................................................... 756
A.2.99 Competitive Prices ...................................................................................................... 757
A.2.100 Competitive Rates .................................................................................................... 757
A.2.101 Competitive Rates (FX Swap) .................................................................................. 757
A.2.102 Complex Payment (cash) ......................................................................................... 757
A.2.103 Convertible Bond ...................................................................................................... 759
A.2.104 Convertible Bond Valuation ...................................................................................... 759
A.2.105 Convertible Bond Setup ............................................................................................ 759
A.2.106 Cost of Carry Balance .............................................................................................. 760
A.2.107 Cost of Carry Interest ............................................................................................... 760
A.2.108 Cost of Carry Valuation ............................................................................................ 761
A.2.109 Credit Client Setup ................................................................................................... 761
A.2.110 Credit Default Swap .................................................................................................. 762
A.2.111 Credit Default Swap Valuation .................................................................................. 763

12

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A.2.113
A.2.114
A.2.115
A.2.116
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A.2.122
A.2.123
A.2.124
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A.2.151
A.2.152
A.2.153
A.2.154
A.2.155
A.2.156
A.2.157
A.2.158
A.2.159

CreditManager position template .............................................................................. 764
Credit Rating ............................................................................................................. 764
Credit Default Swap Curve Setup ............................................................................. 764
Credit-Step-Up .......................................................................................................... 765
CTD Future ............................................................................................................... 765
Currency Conversion ................................................................................................ 767
Debt Flows Valuation (payment amount extraction) ................................................. 767
Delivery ..................................................................................................................... 767
Denominated Bond ................................................................................................... 767
Discount Paper ......................................................................................................... 768
Discount Paper OTC ................................................................................................ 770
Discount Valuation .................................................................................................... 770
Dividend Estimate ..................................................................................................... 771
Dual Currency ........................................................................................................... 771
Dual Currency Forecast ............................................................................................ 772
Equity ........................................................................................................................ 772
Equity Cash Dividend ............................................................................................... 773
Equity Conversion .................................................................................................... 773
Equity Detachment ................................................................................................... 774
Equity Future ............................................................................................................ 775
Equity Info ................................................................................................................. 776
Equity Option ............................................................................................................ 776
Equity Option Pricing ................................................................................................ 777
Equity Option Setup .................................................................................................. 777
Equity Option Valuation ............................................................................................ 778
Equity Return of Capital ............................................................................................ 778
Equity Split ................................................................................................................ 779
Estimation Curve Setup ............................................................................................ 780
Exotic Structure (Option) .......................................................................................... 780
Expiry Date Setup ..................................................................................................... 781
External Valuation .................................................................................................... 781
Fed Fund Future Chain ............................................................................................ 781
Fed Fund Future Dates ............................................................................................ 782
Fed Fund Future Par Valuation ................................................................................ 782
Fed Fund Future Valuation ....................................................................................... 783
Filtered Valuation ...................................................................................................... 783
Fixed Bond Valuation ............................................................................................... 783
Fixed IR Quote Valuation ......................................................................................... 783
Fixed IR Valuation .................................................................................................... 784
Fixed Quoted Valuation ............................................................................................ 784
Force Trade Date Performance ................................................................................ 784
Forecast .................................................................................................................... 784
Forecast Valuation .................................................................................................... 785
Forward Price Setup ................................................................................................. 785
FRA Dates ................................................................................................................ 785
Forward Rate Agreement (Deposit) .......................................................................... 786
Forward Rate Agreement (Discount) ........................................................................ 787
Forward Rate Agreement (Swedish) ........................................................................ 788

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A.2.160
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A.2.162
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A.2.164
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A.2.202
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A.2.204
A.2.205
A.2.206
A.2.207

14

FRA Valuation .......................................................................................................... 789
FRA Option ............................................................................................................... 790
FRA Option Valuation ............................................................................................... 790
FRA Periods ............................................................................................................. 790
FRN Valuation .......................................................................................................... 791
Fund ......................................................................................................................... 791
Fund Fee Accrual and Realization .......................................................................... 792
Fund Fee Valuation .................................................................................................. 794
Future Dates ............................................................................................................. 795
Future Valuation ....................................................................................................... 795
FX ............................................................................................................................. 795
FX Cross Method ...................................................................................................... 796
FX Estimate (Forward) ............................................................................................. 797
FX Estimate (IR Difference) ...................................................................................... 797
FX Fixing .................................................................................................................. 797
FX Forward ............................................................................................................... 797
FX Future .................................................................................................................. 798
FX Future Netting ..................................................................................................... 798
FX Future Valuation .................................................................................................. 799
FX - Lagged FX Function ......................................................................................... 799
FX Margin Result ...................................................................................................... 800
FX Valuation ............................................................................................................. 800
FX Option ................................................................................................................. 800
FX Option Compound ............................................................................................... 801
FX Option Digital ...................................................................................................... 801
FX Option Listed ....................................................................................................... 802
FX Option Premium .................................................................................................. 803
FX Option Pricing ..................................................................................................... 803
FX Option Setup ....................................................................................................... 804
FX Option Valuation ................................................................................................. 805
FX Pricer (Forward) .................................................................................................. 805
FX Pricer (Option) ..................................................................................................... 806
FX Setup ................................................................................................................... 806
FX Swap ................................................................................................................... 807
FX Swap Cost-of-Funding ........................................................................................ 807
FX Swap Margin Result ............................................................................................ 808
FX Swap Quote Default ............................................................................................ 808
FX Swap Split ........................................................................................................... 810
FX Time Option ........................................................................................................ 810
FX Time Option Valuation ........................................................................................ 811
FX Trading Platform ................................................................................................. 811
Generic IR Valuation ................................................................................................ 811
Generic Loan ............................................................................................................ 812
Index ......................................................................................................................... 813
Index Averaging ........................................................................................................ 813
Index Composite ....................................................................................................... 814
Index Derived ........................................................................................................... 816
Index Estimate .......................................................................................................... 817

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A.2.247
A.2.248
A.2.249
A.2.250
A.2.251
A.2.252
A.2.253
A.2.254
A.2.255

Index Future ............................................................................................................. 818
Index - Lagged Index Function ................................................................................. 818
Index-Linked Bond .................................................................................................... 818
Index Option ............................................................................................................. 818
Index Option Setup ................................................................................................... 819
Index Option Valuation ............................................................................................. 820
Index Rebase (Index-Linked Bond) .......................................................................... 820
Index Totaling ........................................................................................................... 821
Index - UK Index Function ........................................................................................ 822
Index Valuation ......................................................................................................... 822
Instrument Quote Estimate ....................................................................................... 822
Internal Deal Mirroring .............................................................................................. 823
IR Derivative Valuation ............................................................................................. 823
IR Derivative Valuation Setup ................................................................................... 823
IR Pricer (Swap) ....................................................................................................... 824
IR Pricer (Swaption) ................................................................................................. 824
Issue ......................................................................................................................... 825
Japanese JGBi ......................................................................................................... 825
Japanese Index-Linked Bond Valuation ................................................................... 826
Loan Structure .......................................................................................................... 826
Manual Charges ....................................................................................................... 826
Margin Movement ..................................................................................................... 827
Maturity Date Setup .................................................................................................. 827
MM Future ................................................................................................................ 827
MM Future - Australian Bank Bill Future ................................................................... 828
MM Future - Australian 90-Day Bank Bill Future Chain ............................................ 829
MM Future - Money Market Future Chain ................................................................ 830
MM Future - Money Market 1M Future Chain .......................................................... 831
MM Future - Money Market 3M Future Chain .......................................................... 831
MM Future Method - Australian ................................................................................ 832
MM Future Dates ...................................................................................................... 832
MM Future Option ..................................................................................................... 833
MM Future Option - Australian Bank Bill Future Option ........................................... 834
MM Future Option Valuation ..................................................................................... 834
Money Market Future Par Valuation ......................................................................... 834
Money Market Future Valuation ............................................................................... 834
Mode Specific Method .............................................................................................. 835
Mode/Transaction Specific Method .......................................................................... 836
MtoM Instrument Setup ............................................................................................ 836
Netted Instrument ..................................................................................................... 837
Non Deliverable Forward FX Instrument .................................................................. 837
NumeriX Asset Swap Setup ..................................................................................... 838
NumeriX Setup ......................................................................................................... 839
NumeriX Single-Swap Valuation .............................................................................. 840
NumeriX Swap Valuation .......................................................................................... 841
NumeriX Valuation .................................................................................................... 841
Option Dates ............................................................................................................. 841
Option Premium ........................................................................................................ 842

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A.2.256
A.2.257
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A.2.293
A.2.294
A.2.295
A.2.296
A.2.297
A.2.298
A.2.299
A.2.300
A.2.301
A.2.302
A.2.303

16

Option Template Setup ............................................................................................. 842
Payment Agent ......................................................................................................... 842
Performance, Cash In/Out ........................................................................................ 843
Performance, FX Hedge ........................................................................................... 843
Performance, Index .................................................................................................. 843
Per-Leg Cashflow Valuation ..................................................................................... 844
Premium ................................................................................................................... 844
Premium Date Setup ................................................................................................ 844
Price Exposure Setup ............................................................................................... 845
Price Valuation ......................................................................................................... 845
Quote Default ........................................................................................................... 845
Quote Default (Australian FRN) ................................................................................ 846
Quote Default (Australian MBS) ............................................................................... 846
Quote Default (Chain) ............................................................................................... 847
Quote Default (Collateral) ......................................................................................... 847
Quote Default (Discount Paper OTC) ....................................................................... 847
Quote Default (FX) ................................................................................................... 848
Quote Default (Short Loan) ...................................................................................... 849
Quoted ...................................................................................................................... 849
Quoted Chain ........................................................................................................... 851
Range Accrual .......................................................................................................... 852
Repo Cash Delivery .................................................................................................. 853
Repo Cash Delivery (Floating) ................................................................................. 853
Repo Cash Delivery (Substitution) ........................................................................... 853
Repo Rounding ......................................................................................................... 854
Repo Valuation ......................................................................................................... 854
Repo Valuation (Floating) ......................................................................................... 854
Repurchase Agreement ............................................................................................ 854
Repurchase Agreement (Floating) ........................................................................... 856
Result ....................................................................................................................... 856
Result with Classification .......................................................................................... 857
RiskManager position template ................................................................................ 857
Risk Setup (BOND) .................................................................................................. 858
Risk Setup (FRN) ..................................................................................................... 858
Risk Venture Capital ................................................................................................. 859
Risk Yield .................................................................................................................. 859
Schedule Data .......................................................................................................... 859
Schedule Template Setup ........................................................................................ 859
Schuldschein ............................................................................................................ 860
Security Identifiers .................................................................................................... 860
Security Info .............................................................................................................. 861
Security Loan ............................................................................................................ 861
Settlement Setup ...................................................................................................... 861
Short Term Loan ....................................................................................................... 862
Short Term Loan Margin Result ............................................................................... 863
Short Term Loan Valuation ....................................................................................... 863
Single Swap Valuation .............................................................................................. 863
Special Issue ............................................................................................................ 864

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A.2.337
A.2.338
A.2.339
A.2.340
A.2.341
A.2.342
A.2.343

Spot Date Setup ....................................................................................................... 864
Spread Curve Setup ................................................................................................. 865
Substitution ............................................................................................................... 865
Swap ......................................................................................................................... 866
Swap (Book, FX Rate) .............................................................................................. 867
Swap (Deal, FX Rate) ............................................................................................... 867
Swap Valuation ......................................................................................................... 867
Swaption Valuation ................................................................................................... 868
Swaption Pricing ....................................................................................................... 868
Swap Per Leg Valuation ........................................................................................... 868
Swap Pricing ............................................................................................................. 868
Swaption ................................................................................................................... 869
Swap, Upfront ........................................................................................................... 869
Swedish Index-Linked Treasury Bond ...................................................................... 869
Swedish Index-Linked Bond Valuation ..................................................................... 870
Ticks Netting ............................................................................................................. 870
Trading Unit (Derivative) ........................................................................................... 871
Trading Unit (Equity) ................................................................................................. 871
Trading Unit (Index) .................................................................................................. 872
Trading Yield ............................................................................................................ 872
Transaction Charges ................................................................................................ 873
Transaction Conversion ............................................................................................ 873
Transfer (cash) ......................................................................................................... 874
TRS - Total Return Swap ......................................................................................... 875
TRS Deferred ........................................................................................................... 875
UK ILG (3M) ............................................................................................................. 876
UK ILG (8M) ............................................................................................................. 876
UK Index-Linked Bond (3M) Valuation ..................................................................... 876
UK Index-Linked Bond (8M) Valuation ..................................................................... 877
US Index-Linked Bond Valuation .............................................................................. 877
US TIPS .................................................................................................................... 877
US TIPS (with Rounding) ......................................................................................... 877
VaR Mapping Type ................................................................................................... 878
Valuation Curve Setup .............................................................................................. 878
Valuation Setup (Floating) ........................................................................................ 879
Value Date Setup ..................................................................................................... 879
Volatility Surface Setup ............................................................................................ 880
XAU Loan ................................................................................................................. 880
Yield .......................................................................................................................... 881
Z-DM/Spread Setup .................................................................................................. 882

Appendix B: Schedules .........................................................................................................883
B.1 Schedule parameters ......................................................................................................... 883
B.2 Templates ............................................................................................................................ 889
B.2.1 System-defined templates ............................................................................................ 889
B.2.2 User-defined templates ................................................................................................ 909
B.3 Schedule template groups ................................................................................................. 910
Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations

17

Appendix C: Option schedules .............................................................................................911
C.1 Option schedule parameters ............................................................................................. 911
C.2 Templates ............................................................................................................................ 913
C.2.1 System-defined templates ............................................................................................ 913
C.2.2 User-defined templates ................................................................................................ 915
C.3 Option schedule template groups .................................................................................... 915

Appendix D: Expressions......................................................................................................917
D.1 Expression syntax .............................................................................................................. 917
D.2 Market references in expressions ..................................................................................... 917
D.2.1 Using Fixing Quote ....................................................................................................... 917
D.2.2 Not using Fixing Quote ................................................................................................. 918
D.3 Constants in expressions .................................................................................................. 919
D.4 Functions in expressions .................................................................................................. 920
D.4.1 Basic functions ............................................................................................................. 920
D.4.2 Referring functions ....................................................................................................... 921
D.4.3 Special functions .......................................................................................................... 922
D.4.4 Special characters ........................................................................................................ 929

18

© Wall Street Systems IPH AB - Confidential

Preface

Welcome to the Transaction & Risk Management Module (TRM) Instruments: Processing and
Calculations guide. This guide describes the following for TRM:

•

The financial instruments that TRM supports and their required setup.

•

The calculations that TRM performs to produce the key-figures–market value, risk exposure, and
profit/loss–used to analyze a position.

Intended audience
This guide is intended for TRM users who require information to support the following tasks:

•

Set up and customize instruments: For users with back office and middle office experience
who have a good understanding of TRM.

•

Valuation: For experienced TRM users who need to understand how calculations are performed
in TRM.

Associated documents
Associated documents can be accessed from the Help menu of the Wallstreet Suite’s applications.

•

TRM User Guide

•

TRM System Administration Guide

•

ACM User Guide

•

CLM User Guide

•

WebSuite User Guide.

Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations

19

Change history
Edition

Date

Changes

Updated By

0.1

April 2011

Initial release 7.3.14.
Features: Positive spread, Negative spread
Bonds: Asset swap (minor changes)
Dual currency: FX Fixing and Generic IR Valuation
Risk profiles: Output (replaced the description)
AI method: Australian Floater (3 decimals)
Bond Futures: Position monitoring setup, Risk Setup (BOND)
Yield/price conversion: Malaysian government bonds
Bank Account, Cost of Carry, and Funds: Update Realization
Date

TRM Dev Team

0.2

May 2011

Israeli Index-Linked Bonds: time-dependent, Index Rebase

TRM Dev Team

20

© Wall Street Systems IPH AB - Confidential

Chapter 1

Concepts

In the Wallstreet Suite Transaction & Risk Management Module (TRM), all instruments rely on the
same key concepts. It is important to be familiar with these concepts to understand how the system
works and to be able to use it effectively.
TRM’s concepts are referred to frequently throughout this guide. Each one is explained in more
detail in the relevant section.

1.1 Instruments
In TRM, all instruments share several main characteristics:

•

Unique ID (and an optional Name)

•

Instrument Type (mandatory) (see 1.2 Classes and types on page 21 for more information)

•

Active From / Active To period (from/to dates inclusive) to restrict the period in which the

•

Instrument Group for use in rules, monitoring, and reporting

•

Labeling for Buy/Sell transactions (optional Buy Label and Sell Label naming) to override the
default settings.

instrument can be traded in TRM (optional)

The following information is also available for each instrument:

•

History of all modifications made to an instrument since it was defined in the system

•

Links to documents or Web pages attached to the instrument which can be opened through the
editor

•

User-defined properties that can be added to the instrument.

Finally, an instrument is made up of features. Features are the most important of the key concepts.
They are the building blocks of an instrument and are responsible for driving the processes in TRM.
Features are explained in a later section of this chapter.
First however, it is important to understand the concepts of instrument classes and types.

1.2 Classes and types
The notion of instrument class is specific to TRM. Instrument classes denote the different categories
of instruments which are supported by TRM. They are pre-defined in the system and cannot be
changed by the user.
An instrument class is only used as a basis on which to define an instrument type. Once the types
have been defined, the instrument classes are no longer used.

Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations

21

1 Concepts
1.2 Classes and types

1.2.1 Creating types
The first step in defining instruments involves creating all the instrument types that are necessary to
use the system. It is possible to create an infinite number of types with each class.
However, it is not recommended to create instrument types that are based on an instrument class
that you do not need.
In contrast, you may wish to create more than one instrument type based on the same class to
create more specific instrument definitions. For example, the Bond instrument class is used to define
many different types of bonds instruments, such as fixed-rate bonds, floating-rate bonds,
dual-currency bonds, and so on. Creating and customizing an instrument type for each type of bond
makes it easier to define the instruments. Nevertheless, it is still possible to have only one
instrument type, and differentiate the setup later, when the instrument is created.

1.2.2 Customizing types
As mentioned in the earlier section, features are the most important of the key concepts. Features
drive the behavior of an instrument in TRM. Each instrument class contains a set of available
features: some features are mandatory, some are assigned by default, and others are optional. An
instrument type is derived from an instrument class. The type inherits all the features contained in
the instrument class automatically.
Apart from mandatory features, which cannot be changed or removed, the default and optional
features within the list can be modified as follows:

•

Default features can be made mandatory, optional, or be removed completely

•

Optional features can be made mandatory, default, or be removed completely.

When the instrument type is assigned to an instrument, the instrument inherits the features as
follows:

•

Mandatory features from the instrument type are assigned to the instrument and cannot be
removed

•

Default features from the instrument type are assigned to the instrument but may be removed

•

Optional features from the instrument type can be manually applied to the instrument if
required.

For example, assume you need to define some fixed-rate bonds, some FRNs, and some
dual-currency bonds in your system. You could simply create one Bond instrument type that exactly
replicates the Bond instrument class. It will then be possible to set up any kind of bond instrument
using this type.
However, you may prefer to simplify the setup of bond instruments by creating three different
instrument types based on the same instrument class. You could modify the set of features in the
instrument class by selecting only the relevant features for each type of bond:

•

For the fixed-rate bond, you remove the features related to dual-currency, and everything
related to floating-rates

•

For the FRN instrument, you assign as mandatory the FRN valuation method, and remove all
features related to dual-currency, and anything else not related to an FRN

•

For the dual-currency bond, you assign as mandatory the Dual Currency feature, and remove
anything else not related to the instrument you want to set up.

By customizing an instrument type to correspond to a particular category of instrument, a significant
part of the set up is done at type level making the task of setting up instruments much easier. It is
important to keep in mind that the instrument type is a visible attribute of the instrument. Its
definition is an important step in the process of instrument setup and therefore must be made with
care.

22

© Wall Street Systems IPH AB - Confidential

1 Concepts
1.3 Instrument templates

1.3 Instrument templates
Instrument templates use the framework of static data template editors. In the context of
instrument setup, templates can be used to define more closely the characteristics of instruments
that can be set up using a given instrument type, as follows:

•

The selected optional and default features of the given type can be modified to reflect more
accurately the nature of instruments for which the template is designed.

•

Subentities and individual fields can be identified as mandatory or frozen in the instrument setup
in a similar way to the features. Thus, you can control the instrument at the field level.

•

Values for default or frozen setup of the instrument can be already defined in the template.
Thus, instruments based on a template, already inherits these configured values.

As in with other static data templates, when you select a template in Instrument Editor, the
template will automatically load all configured information, so that you only have to provide a
limited set of values when you create the new instrument.
For information about using the Instrument Template Editor, see TRM User Guide.

1.4 Groups
Instrument groups facilitate reporting and monitoring of instruments and their subsequent
transactions. They are also used in the setting up of rules as a means to identify individual cashflows
in order to direct them to the correct place in the transaction flow. Each instrument is assigned to an
instrument group during the setup process.
Instrument groups are arranged into a simple hierarchy, where each group is assigned one parent.
Instruments can only be assigned to a single instrument group in the hierarchy.
Default instrument groups for the first level in the hierarchy are pre-defined in the system, but can
be modified at implementation according to your organization’s requirements. You then create
further instrument groups for the lower levels of the hierarchy to reflect the requirements of your
organization.
The first level of the hierarchy could typically represent the class of instruments in which you trade;
such as Debt Instrument, Foreign Exchange, and Equity. Instrument groups in the second level
could correspond to different types of instruments traded in these markets, and any lower levels
would usually be created for instruments, which are derived from the same instrument type, but
have different characteristics.
Instrument groups from any level in the hierarchy can be used as a parameter when setting up
reports or rules, and when monitoring instruments. The instrument group you use depends on how
specific the rule, report, or position needs to be.

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1 Concepts
1.5 Features

Consider the following example which illustrates how an instrument group hierarchy may be set up
and used.

Level 1
Level 2
Level 3
Level 4

In the example hierarchy, if the Government instrument group in level 4 is used as one of the
parameters to run a report, the generated report will only contain data resulting from any
Government Bonds assigned to this instrument group. Alternatively, if the Fixed-Rate Bond
instrument group in level 3 is used as the start-up parameter, the resulting report will include data
from both Corporate and Government Bonds. If an overview of all debt instruments is required in
the report, the Debt Instrument group in level 1 should be selected.

1.5 Features
The notion of the Instrument Class/Feature association is specific to TRM. Features are an integral
part of setting up instruments.
Features are system-defined entities used to give instruments their distinctive functionality and
enable deal capture, transaction processing, and position monitoring.
A feature is a combination of Setup and Process:

•

Setup refers to the number of database tables that are attached to a feature. It is only possible
to populate the information related to these tables in the editor if the feature is attached to the
instrument.

•

Process refers to the number of units of processing that are attached to a feature. The code that
is linked to the feature is triggered only when the feature is attached to the instrument.

The major benefits of this architecture are two-fold:

•

Setting up instruments becomes much easier because the system only proposes the necessary
information according to the behavior required by the user for the instrument.

•

Processing is completely modular. This means that many independent units of code are triggered
in sequence to handle the processing of the deals. This very low level dependency ensures an

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1.6 Schedules

improved stability of the system should any modifications be made, and also an improved
capacity for the addition of new processing features.
Features are organized into the following categories: Primary, Trading, Action, Valuation, and
Valuation Setup. These categories are pre-defined in the system and cannot be modified by the
user.
Features are frequently referred to throughout this guide. The combination of features associated
with an instrument completely defines the instrument’s characteristics. Any parameters that need to
be defined for the set up and processing of the features and their related actions are explained in
more detail in the relevant section.

Note: In Appendix A Features on page 713 you can find a list of the available features together
with an explanation of how they are used.

1.5.1 Primary and trading features
Primary features are responsible for the core deal generation (such as, transaction and cashflows),
and core instrument setup. There can be only one primary feature associated with an instrument.
Primary features contain the largest part of the business logic. They are used during instrument
setup and throughout deal-entry.
For example, the primary feature Bond enables the setup of the main characteristics of a bond and
its associated cashflows. It also manages the creation and modification of a bond deal by calculating
amounts and generating the cashflows.
Trading features introduce additional setup possibilities and some additional rules for deal
management. More than one trading feature can be applied to an instrument, and some trading
features can be used for several different classes of instrument.
For example, the trading feature Trading Unit enables the setup of a denomination size, a minimum
bid size, and a minimum price unit for an instrument. It also ensures that this setup is verified when
a deal is entered and will adjust the deal accordingly if the deal does not correspond to the setup.
The processing units of primary and trading features are assigned with a priority number. This
number ensures that the processes are executed in the correct order.

1.5.2 Action features
Action features enable deal processing, some of which are also linked to a setup. The parameters
defined in the setup are used when the action is performed. Action features are called each time the
user wants to execute a business process.
For example, the action feature Allow Roll Over (FX) enables roll over of FX forwards and FX swaps.

1.5.3 Valuation approach and valuation setup features
Valuation Approach and Valuation Setup features work together: they determine which valuation
approach is used for the instrument. With these features, it is possible to specify the market
variables used in the valuation, such as yield curves, date basis, and discounting methods.
Valuation can still be performed on an instrument even without any specific setup. In this case, the
default settings for valuation are employed to find the market variables used to value the
instrument.
Note that, in TRM, as well as being responsible for calculating market value, the valuation approach
is also responsible for calculating other figures, such as unrealized results and risk figures.

1.6 Schedules
The concept of Schedules is used in several places in TRM.

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1 Concepts
1.6 Schedules

There are two types of schedules; Schedules and Option Schedules:

•

Schedules are used for most debt instruments (and their derivatives):
Asset Backed Securities, Bonds, Caps, Floors, and Collars, Loans, and Commercial Loans,
Swaps, Total Return Swaps, and Swaptions.

•

Option Schedules are used for Exotic FX Options.
Option schedules are a simplified version of schedules. They are used to enable the definition of
option events, such as barriers or Bermudan exercise periods.

In TRM, schedules and option schedules drive the generation of a set of cashflows.
When the cashflow structure is frozen for an instrument, as is the case for Asset Backed Securities
and Bonds, schedules are linked to the instrument itself, together with the generated cashflows.
When the cashflow structure is not frozen (for example, with instruments such as Caps, Floors, and
Collars, Loans, FX Options with Barriers, and so on), schedules can be associated with the deal
instead of with the instrument. The cashflows are then generated at deal entry.
Schedules contain a number of values that determine how a set of cashflows are generated. The
information that can be defined in a schedule is explained in the appendices.
TRM provides a number of Schedule Templates and Option Schedule Templates. A template groups
together the prepackaged set of individual schedules that are necessary to set up a deal or type of
instrument. Some of the characteristics of the deal or instrument are then used to automatically
update many of the values in the schedule.
When a template is applied, the schedules included in the template are simply copied onto the deal
or instrument. Consequently, there is not a dynamic link between the deal or instrument and the
schedule template. If any changes are subsequently made to a template, they are not reflected in
the characteristics of the deal or instrument to which it had previously been applied.
Many templates are provided by the system and users can use these as a basis on which to create
their own.
The following simple example illustrates the concept of schedules in TRM:

•

A 3-year fixed-rate loan paying 5% interest per annum with a bullet repayment of the principal
amount

A deal involving this instrument has two distinct types of cashflow: interest cashflows, and the
principal payback cashflow. Two schedules need to be associated to the deal: one schedule to drive
the creation of the interest cashflows, and another schedule to drive the creation of the principal
payback cashflow.
The following information is required for the interest schedule:

26

Type:

Interest

Category:

Payback

Start Date:

Value date of the deal

End Date:

Maturity date of the deal

Currency:

Currency of the deal

Method:

Times/Year

Frequency:

1

Rate Type:

Interest Rate

Rate:

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1 Concepts
1.7 Deal capture

The following information is required for the principal schedule:
Type:

Principal

Category:

Payback

Start Date:

Value date of the deal

End Date:

Maturity date of the deal

Currency:

Currency of the deal

Method:

Bullet

TRM provides a system template (called Fixed, Bullet Repayment) which contains both these
schedules. The template also contains some defaulting rules. As a result, when the schedule is
applied to the instrument most of the information relating to the cashflow structure is defaulted
automatically by TRM.

Note: For more details about system templates and how they can be grouped or specialized into
user templates, see Appendix B Schedules on page 883 and Appendix C Option schedules
on page 911.)

1.7 Deal capture
In TRM, dealing is carried out in Transaction Manager or in Enter Board.

1.7.1 Input data
Some deal information that needs to be input is common to all transaction types, no matter what
type of instrument is involved.
This generic input data includes the following:

•

Instrument to be used in the deal

•

Opening Date of the deal when it is taken into account in the system

•

Portfolio that is impacted by the deal

•

Counterparty, that is, the other party involved in the deal.

Other required input data is specific to an instrument type, for example, premium flow parameters
for option transactions. Some input data can be defined either in the instrument definition or it can
be specified at deal entry.

1.7.2 Generated data
Some information is automatically set by the system on a new deal when the deal has been saved,
such as:

•

Transaction Number which identifies the deal in the system

•

State which shows the transaction’s position in the workflow

•

Status, which gives additional information about the status of the deal.

The deal’s associated cashflows, for example, interest flows, settlement or premium amounts, and
position flows are generated, according to the instrument and its setup.

Note: Deal capture information that is specific to an instrument type is explained in the relevant

Deal capture section of this guide. For information about entering deals that is common to
all instruments: see the TRM User Guide.

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1 Concepts
1.8 Processing

1.8 Processing
Processing deals in TRM is mainly done through Transaction Manager; although some back office
operations are performed using activities.
There are a number of commands that can be performed on all deals. These commands are used to
save, reject, or cancel a deal and move the deal through TRM’s process flow, and include:

•

Apply, Commit, Accept, Reject, Re-Open, and so on
These commands are used to move a transaction to a different state in the workflow. The new
state of the transaction when one of these actions is performed depends on how the transaction
flow has been defined for the system.

•

Reset
The Reset command resets all changes made to a deal since the last time it was saved in the
system. If the reset command is performed on a new deal, the deal is removed.

•

Cancel
Using this command, it is possible to cancel a deal which has been entered in error.

Another of the concepts on which TRM is based is that of actions. An action is something you can
execute on a deal (or several deals) in order to perform a business task.
Some actions are available for all instruments, either by default, or through the addition of a
feature:

•

Duplicate
This action creates a new deal with the same characteristics as the initial transaction, apart from
Transaction Number and State. After the deal has been duplicated, it is possible to change some
of the characteristics of the new deal. This is a useful function when you need to create many
deals with similar characteristics using the same instrument.

•

Package
The Package action assigns a deal to a package. Packaging several deals together creates a link
between them. Packages can be used as criteria in position monitoring or reports.

•

Add Transaction Charge or Cashflow Charge
These actions allow you to add one or more charges to a deal. They are available when the
respective feature is applied to the instrument. The charges are stored as separate cashflows.

Many actions are specific to certain instruments, and details of these can be found in the relevant
Processing section of this guide.
Examples of instrument-specific actions in TRM are: Early Expiration of a loan; Exercise of an option;
Fixing of a cashflow; and the Netting of a future. These actions are often only available once the deal
has reached a certain stage in the process flow.

Note: See the TRM User Guide for more information about executing actions on deals and
processing deals through the transaction flow.

1.8.1 Setup
The ability to execute certain actions on an instrument can either be linked to the presence of
instrument-specific features applied to the instrument definition, or for other instruments, the
execution is automatically included in the instrument setup.
In all cases, the availability of an action can be made dependent on the state of the transaction. For
example, it is possible to allow a tax to be added for newly entered transactions, but not for
confirmed ones.

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1.8.2 Execution
The availability of the action is also often driven by certain conditions that are built into the action
itself. The exercise of an option for example, recognizes that it can only be executed during the
exercise period. The exercise action is unavailable outside the exercise period.
Many frequently performed actions can be automated through batch activities. It is important to
note that the batch activity executes exactly the same code as the user for the execution of the
action.

1.8.3 Cancellation
Sometimes, it is necessary to cancel the execution of an action. In TRM, all actions can be canceled
or reversed.

1.9 Valuation and results
1.9.1 Market value
In TRM, market value can be calculated using two different valuation methods:

•

Quoted valuation method which is a direct mark-to-market quote of an instrument

•

Theoretical valuation method which is a theoretical valuation model defined in the system.

Generally, quotes can be obtained from the market for exchange-traded (listed) instruments and
can be applied directly to establish the market value of a position, whereas over-the-counter (OTC)
transactions need to be valued using a theoretical model. Theoretical models are set up in TRM and
can range from models used for simple discounting of cashflows to complex multi-factor option
valuation models.
Regardless of the approach taken, users have two additional decisions to make that will have a
minor impact on the market value of each position. More specifically, for each instrument, the
following needs to be defined:

•

•

Market value calculation period

–

If market value is calculated to the spot date (as of the valuation date) of the instrument

–

If market value is discounted from the spot date to the valuation date of the instrument.

Market value calculation of foreign currency positions (into the base currency of the portfolio or
another currency)

–

If market value is calculated using the spot rate between the two currencies

–

If the spot rate is further adjusted by O/N and T/N points

–

If the spot rate is adjusted by the interest rate differential between the two currencies from
valuation date to spot date.

1.9.2 Profits and results
The market value is used when calculating the total profit of a position.
In TRM, the term profit refers to the profit/loss on a position at a given point in time since its
inception or since a subsequent realization (for example, the payment of interest).
The term result refers to the profit/loss over a specific period of time (for example, from January 1
to January 31).

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1.9 Valuation and results

In general terms, the market value of a position is compared to capital invested, and the difference
is the total profit of the position. Total profit is further split into the following components (the exact
description of each component may vary slightly according to the instrument):
Profit

Description

Accrued Interest

Interest accrued since the value date of the transaction or the previous coupon date
until the valuation date.

Accrued Profit

Accrued/amortized discount/premium, accrued fees, or amortized option premiums
since the value date of the transaction or the payment date of the premium/fee, until
the valuation date.

MtoM Profit

Profit/loss resulting from the difference between market valuation (excluding accrued
interest and accrued profit) and capital invested.
For example, for instruments with a market quotation, MtoM profit is generally the
difference between the market price and the deal price.However, when accruals and
fees need to be taken into account, the calculation of MtoM Profit becomes more
complex.
MtoM profit is calculated to the spot date of the instrument, and not discounted to the
valuation date.
Note: For details of the MtoM Profit calculation for a particular type of instrument, see
the relevant section of this guide.

FX Profit

Profit/loss resulting from the change in FX rates, between the value (or trade) date
and the valuation date, calculated on the invested amount.

Other Profit

The residual profit/loss after the above components are separated from total profit.
This residual is usually the end-product when total result is calculated correctly
theoretically, but the other components are calculated according to general
accounting practices.
For example, the market value for a bond includes the accrued interest calculated
until the spot date of the instrument (that is, the amount which would be received if
the bond was sold today), while accrued interest includes the interest accrued until
the valuation date.

1.9.3 Valuation modes
Sometimes, it is necessary to calculate market value and results in different ways. For example,
even if market value can be obtained from market quotes, occasionally it may be useful to run the
valuation using a theoretical model. Furthermore, for accounting purposes, it may also be necessary
to do the valuation using specific benchmark yield curves, and to apply specific accounting
treatment for the difference between normal and benchmark valuation.
Valuation modes allow users to define different valuation methods and models and to use different
market parameters to value the same instrument. Every time valuation is requested by a user, the
user specifies the valuation mode, and the system performs the valuation using the setup applicable
to that mode.
The standard system provides three different valuation modes:

•

Default

•

Theoretical

•

Benchmark.

The valuation modes themselves are simply identifiers. Users need to specify the type of valuation
that is to be carried out at instrument level. For example, if the Theoretical valuation mode is
selected, the system will not switch automatically to a theoretical model. Rather, the user needs to
link the appropriate valuation methods and models for each instrument, which are then called each
time theoretical valuation is requested.

Valuation Mode can be used as a start-up parameter for monitoring the treasury position, for running
profit/loss reports, and for closing-the books. If no mode is specified, the system’s Default valuation
mode is used.

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1.9 Valuation and results

New valuation modes can be added during implementation according to your organization’s
requirements.

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1.9 Valuation and results

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Chapter 2

Market standards and calculations

2.1 Market standards
2.1.1 Date basis
Date bases are used to calculate the length, in years, of the period between two dates. The formula
for this calculation is t=d/B, where d is the number of days in the period, and B is the basis
denominator. Both d and B depend on the date basis used. Different date bases may result in
different values for d and B for the same period and, consequently, in different period lengths.
TRM uses date bases when an interest rate is defined over a period. The definition of the rate must
include how the length of the period is calculated.

•

360 date bases
In these date bases, the denominator B is always 360, but the calculation of the numerator
varies. However, there is a difference in the way the 31st day at the beginning and at the end of
the period under consideration is handled.
The formulas used show how the period d between date1 (y1, m1, d1) and date2 (y2, m2, d2) is
calculated: yi, mi, and di represent the year, month, and day, respectively; and min is the
minimum value in the set. For example, min(d2, 30) means "use the lesser value of d2 and 30."

•

Actual date bases
Actual date bases allow for different lengths of months and are, therefore, more accurate than
the 360 date bases. The Actual date bases generally differ in the way that they handle leap
years.

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2.1 Market standards

Example period 1991-06-30 to 1996-01-31
The period 1991-06-30 to 1996-01-31 is used in some of the following examples to show how the
various date bases calculate the number of days between two dates.
Name

Description

30E/360

Any 31st day of the month is considered to be the 30th of the month. The formal
definition is:
d = min(d2,30) - min (d1,30) + 30(m2 - m1) + 360(y2 - y1)
For the example period:
d = min(31,30) - min(30,30) + 30*(1 - 6) + 360*(1996 -1991) = 1650
The length of the period in years is 1650/360 = 4.583

30E/360 EOM

This is a variation of the 30E/360 basis, with the month of February having an
invariable 30 days.
Example: For the 2003-08-31 through 2004-02-29:
d = min(30,30)

min (31,30 + 30*(2 - 8

360*(2004 - 2003 = 180

The length of the period in years is 180/360 = 0.5
30/360

This is a variation of the 30E/360 basis. The difference occurs when d1 < 30. In this
case, no rounding of the date occurs, and the above equation is replaced by:
d = d2, - d1 + 30(m2 - m1) + 360(y2 - y1)
For the example period:
d1 = 30, so the 30E/360 formula is used and d = 1650
However, if the beginning of the period was the 29th instead of the 30th, the result
would be:
d = 31 - 29 + 30*(1 - 6) + 360*(1996 - 1991) = 1652
The length of the period in years would then be 1652/360 = 4.589.

30E+/360

This is a variation of the 30E/360 basis. The difference is that rounding is applied only
to the earlier date. The equation is then:
d = d2 - min(d1,30) + 30(m2 - m1) + 360(y2 - y1)
For the example period:
d = 31 - min(31,30) + 30*(1 - 6) + 360*(1996 -1991) = 1651
The length of the period in years is 1651/360 = 4.586

Actual/Actual ISDA

If no leap year is involved in the calculation, then t = d/B where d = the actual
number of days and B = 365.
If there is a leap year, then t = d1/B1 + d2/B2, where
d1 = the actual number of days in the leap year and B1 = 366
d2 = the actual number of days in the non-leap year and B2 = 365

Actual+/Actual ISDA
Actual-/365

This is a variation on Actual/Actual ISDA, for which the first day is excluded for the
day count.
d = the actual number of days excluding all leap days (29th of February).
B = 365 days.
For the example period:
The number of days between 1991-06-30 and 1996-01-31 is 1676, but since there is
one leap day within that period, d = 1675.
The length of the period in years, t, is 1675/365 = 4.589

Actual-/365+

d = the actual number of days excluding all leap days (29th of February).
B = the number of days in the year in which the coupon value date falls.

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2.1 Market standards

Name

Description

Actual-/365L

d = the actual number of days excluding all leap days (29th of February).
B = 366 if the last partial year of the period contains a leap day; otherwise, B = 365.
The last partial year is the remaining period when the maximum number of full years
have been counted off, starting from the beginning of the period.
For the example period:
The last partial year is the period from 1995-06-30 to 1996-01-31, which does not
contain a leap day, so B = 365. The number of days between 1991-06-30 and
1996-01-31 is 1676, but since there is one leap day within that period, d = 1675.
The length of the period in years, t, is 1675/365 = 4.589.
If, instead, the end of the period were on 1996-02-29, the number of days would be
1675+29-1=1703 (the leap day is not counted), and the last partial year would
contain a leap day, so that t would be 1703/366 = 4.653.

Actual/360

d = the actual number of days.
B = 360 days.
For the example period:
d = 1676 and B = 360, so t = 1676/360 = 4.656

Actual/365

d = the actual number of days.
B = 365 days.
For the example period:
d = 1676 and B = 365 so t = 1676/365 = 4.592

Actual/365+

d = the actual number of days.
B = 366 if the end of the period falls on a leap year; otherwise, B = 365.
For the example period:
The number of days between 1991-06-30 and 1996-01-31 is 1676. B = 366 since
1996 is a leap year. So t = 1675/366 = 4.577

Actual/365L

d = the actual number of days.
B = 366 if the last partial year of the period contains a leap day; otherwise B = 365.
The last partial year is the remaining period when the maximum number of full years
have been counted off, starting from the beginning of the period.
For the example period:
The last partial year is the period from 1995-06-30 to 1996-01-31, which does not
contain a leap day, so B = 365 and t = 1676/365 = 4.592

Actual/Actual ISDA

If no leap year is involved in the calculation, then t = d/B where d = the actual
number of days and B = 365.
If there is a leap year, then t = d1/B1 + d2/B2, where
d1 = the actual number of days in the leap year and B1 = 366
d2 = the actual number of days in the non-leap year and B2 = 365.

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2.1 Market standards

Name

Description

Actual/Actual (n)

The variable n is 1, 2, or 4, specifying the frequency of coupons. The corresponding
coupon periods are 12, 6, and 3 months (= 12 / n), respectively. The time between
the dates d1 and d2 is calculated by first calculating the number (p) of the whole
periods that fit into the interval (d1, d2), from the date (d2) backwards, and then by
adding the length of the first fractional period.
The end and start dates of the periods are generated by repeatedly subtracting 12, 6,
or 3 from the month number of d2. If the month thus generated has fewer days than
the day of month of the end date (d2), the period end date is the end date of the
month in question. That is, if d2 = 2008-05-31 and n = 4, then the start date of the
last period is 2008-02-29.
If the date (d1) is a start date of a whole period, then the time in years between d1
and d2 is simply the number of whole periods:
Equation 2-1 Actual/Actual (n): number of whole periods

t = p⁄n

Otherwise, let ds and de be the start and end dates of the whole period wherein the
date (d1) falls. Then the time in years between d1 and d2 is:
Equation 2-2 Actual/Actual (n): time in years between d1 and d2

de – d1
t = p ⁄ n + -----------------------n ( de – ds )
Example
Let the start and end dates be d1 = 2008-03-31 and d2 = 2009-09-30, and the
frequency be n = 2. Then, the dates generated are as follows:
•

2009-09-30

•

2009-03-30

•

2008-09-30 = de

•

2008-03-30 = ds

There are two (2) whole periods, and the time between d1 and d2 is:
Equation 2-3 Actual/Actual (n): Example with 2 whole periods

Actual/Actual (n) EOM

Note: The Actual/Actual (n) EOM data basis is TRM-specific, i.e. non-market standard.
This date basis is similar to Actual/Actual (n) except that the period end and start
dates are moved to the last date of the month in question. That is, all the whole
periods begin and end at the last day of the month.
Example
Let the start and end dates be d1 = 2008-03-31 and d2 = 2009-09-30,
and frequency be n = 2. Then the dates generated are as follows:
•

2009-09-30

•

2009-03-31

•

2008-09-30 = de

•

2008-03-31 = ds

That is, the dates in March have been moved to the end of March. There are three (3)
whole periods, and no fractional part. Therefore, time in years is as follows:
Equation 2-4 Actual/Actual (n) EOM: Example with 3 whole periods

t = 3 ⁄ 2 = 1.5

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2.1 Market standards

Name

Description

BRL/252

This date basis calculates time as business days according to the Brazilian (BRL)
calendar divided by 252.
Example
Take the period between 2003/12/16 and 2004/02/02. For this period, the BRL
calendar is set up with the following public holidays: 2003/12/25, 2003/12/26, and
2004/01/01, as well as 14 weekend days.
Therefore, there are 31 business days in the period, and so, using this date basis, the
resulting time is: 31/252 = 0.123015873
(instead of 48/365 = 0.131506849 if the Actual/365 date basis was used).

2.1.2 Interest types
Name

Discount factor in terms of
interest rate

Annually Compounded Rate

Semi-Annually Compounded
Rate

Quarterly Compounded Rate

Monthly Compounded Rate

Daily Compounded Yield
(B = denominator of date basis)

r –t
D = ⎛ 1 + ---------⎞
⎝
100⎠

r = 100 ( D

r – 2t
D = ⎛ 1 + ---------⎞
⎝
200⎠

r = 200 ( D

– 1 ⁄ ( 2t )

– 1)

r – 4t
D = ⎛ 1 + ---------⎞
⎝
400⎠

r = 400 ( D

– 1 ⁄ ( 4t )

– 1)

r –12t
D = ⎛ 1 + ------------⎞
⎝
1200⎠

r = 1200 ( D

r –Bt
D = ⎛ 1 + -------------⎞
⎝
100B⎠

r = 100B ( D

Continuous Yield

D = e
Discount Rate

Interest Rate

Periodic Rate

Interest rate in terms of discount
factor

r
– --------- t
100

r
D = 1 – --------- t
100

–1 ⁄ t

– 1)

– 1 ⁄ ( 12t )

– 1)

– 1 ⁄ ( Bt )

– 1)

100
r = – --------- log D
t
1–D
r = 100 ------------t

Depending on time:
•

Periodic Rate for maturities less than one year

•

Continuous Yield for maturities equal to or over one year.

1
D = -------------------r
1 + --------- t
100

100 1
r = --------- ⎛ ---- – 1⎞
t ⎝D ⎠

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Name

Discount factor in terms of
interest rate

Semi-Annual/Periodic Rate

These interest types work in a similar way to interest type Interest Rate:

Quarterly/Periodic Rate

•

If time is shorter than six months/three months/month, then the
discount factor is periodic:

•

If time is longer than six months/three months/month, then the
discount factor is compounded with frequency of 2, 4, or 12:

Monthly/Periodic Rate

Interest rate in terms of discount
factor

1 / (1 + rate/100 * time)

(1 + rate / (frequency * 100))^(-frequency * time)
("^" means to the power)

Note: The number of months is calculated as calendar months. For
example, from 15 February to 15 March is one month, regardless
of date basis.
This interest type works in a similar way to interest type Periodic Rate
except that the last coupon period is one day longer, i.e. it includes both
first and last date.

ISDA CDS

2.1.3 Price types
2.1.3.1 Trading Margin
The conversion of the quotation (trading margin) into the price is handled by specific quote handlers
for Australian FRNs and MBS. The formula used to convert the trading margin (market quote) to the
instruments price is described in 3.1.3 Australian floating rate note on page 236 and 3.7.5
Australian MBS on page 302 respectively.

2.1.4 Yield/price conversions
Bonds are traded on either yield or price depending on the market conventions. At deal entry, the
user can enter either the yield or the price of the bond, the missing value is then calculated from the
entered one. For example, if you enter the price then the yield is calculated, and vice versa.
The yield/price conversion of a bond is set by including the Trading Yield feature and associating the
relevant yield convention with the instrument in the Instrument Editor. The convention determines
which price and yield method are used for the conversion.
When no convention is selected at the instrument level, the default convention for calculating the
yield (deal rate) is ISMA with Actual/Actual date basis and Annually Compounded yield.
The following information is provided in this section for each convention:
Field

Description

Name

The name of the convention as it appears in TRM.

Description

General description of the method and standard calculations.

Usage

Describes with which instrument this method is typically used.

2.1.4.1 Price/yield conversion
The yield y is in most cases converted from the clean price Pc of a fixed rate bond by using either
the ISMA or the Simple Yield formula. This section describes these two calculations.

38

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2.1.4.1.1 ISMA (financial/instrument/isma@yield)
Information

Description

Name

ISMA

Description

The ISMA yield uses a goal seeker method id in the system seeks for the yield which gives
the input price.
The algorithm iterates the yield y until the equation equals zero:
Equation 2-5 ISMA method

where

Usage

•

p c is the clean market price

•

c i and d i represent the ith cashflow and its date (coupon date)

•

D

•

I a is the accrued interest

is the discount factor for that cashflow

This method applies to all bonds except Japanese government bonds, which use the simple
yield. See 2.1.4.2 Yield/price conversion on page 40.

2.1.4.1.2 Simple Yield (financial/instrument/simple-yield@yield)
Information

Description

Name

Simple Yield

Description

The simple yield calculates the yield from the clean market price as follows:
Equation 2-6 Simple Yield

where
•

r is the coupon rate

•

p c is the clean market price

•

t m is the time in years from the valuation date to maturity

From this, the conversion equation for simple yield is:
Equation 2-7 Simple Yield: conversion equation

Usage

This method applies only to Japanese government bonds (GOVT-JP). See 2.1.4.2.29
GOVT-JP (financial/instrument/simple-yield@price) on page 59.

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2.1.4.2 Yield/price conversion
The clean price Pc of a fixed rate bond is in most cases converted from the yield y by the formula:
Equation 2-8 Yield/price conversion: clean price

where
• p c is the clean market price
• c i and d i represent the ith cashflow and its date (coupon date)

•

D

•

I a is the accrued interest.

is the discount factor for that cashflow

If the dirty price is used, then accrued interest in the above equation is dropped.
The methods of calculating the discount factor and the accrued interest may depend on market
conventions as explained in the following sections.

Hint:

For the following bond conventions, when the yield is not specifically mentioned then the
convention uses ISMA.

2.1.4.2.1 *ISMA-30/360-BIMONTHLY (financial/instrument/isma@price)
Field

Description

Name

*ISMA-30/360-BIMONTHLY

Description

*ISMA-30/360-BIMONTHLY bonds are regular fixed coupon securities with bi-monthly coupons
and 30/360 date basis. With *ISMA-30/360-BIMONTHLY, the coupons for the ith cashflow on date
di are discounted using the following formula:
Equation 2-9 European bonds before the Euro

t

D ( y, d i ) = ( 1 + y ⁄ 6 ) i
where
•
Usage

t i is the time in years between the value date and the coupon date di .

Convention used for australian bonds.

2.1.4.2.2 *ISMA-30E360-ANNUAL (financial/instrument/isma@price)
Field

Description

Name

*ISMA-30E360-ANNUAL

Description

*ISMA-30E360-ANNUAL bonds are regular fixed coupon securities with annual coupons and
30E/360 date basis. With *ISMA-30E360-ANNUAL, the coupons for the ith cashflow on date di
are discounted using the following formula:

Equation 2-10 European bonds before the Euro

t

D ( y, d i ) = ( 1 + y ) i
where
•

40

t i is the time in years between the value date and the coupon date di .

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2 Market standards and calculations
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Field

Description

Usage

Convention used for European bonds (Belgium, Finland, and Germany) issued before the
introduction of the Euro.

2.1.4.2.3 *ISMA-30E360-SEMI-ANNUAL (financial/instrument/isma@price)
Field

Description

Name

*ISMA-30E360-SEMI-ANNUAL

Description

*ISMA-30E360-SEMI-ANNUAL bonds are regular fixed coupon securities with semi-annual
coupons and 30E/360 date basis. With *ISMA-30E360-SEMI-ANNUAL, the coupons for the ith
cashflow on date di are discounted using the following formula:
Equation 2-11 Sovereign and corporate bonds

t

D ( y, d i ) = ( 1 + y ⁄ 2 ) i
where
•
Usage

t i is the time in years between the value date and the coupon date di .

Convention used for some sovereign or corporate bonds.

2.1.4.2.4 *ISMA-30E360-QUARTERLY (financial/instrument/isma@price)
Field

Description

Name

*ISMA-30E360-QUARTERLY

Description

*ISMA-30E360-QUARTERLY bonds are regular fixed coupon securities with quarterly
coupons and 30E/360 date basis.
With *ISMA-30E360-QUARTERLY, the coupons for the ith cashflow on date di are discounted
using the following formula:
Equation 2-12 ISMA 30E360 Quarterly bonds

y ti
D ( y, d i ) = ⎛ 1 + ---⎞
⎝
4⎠
where
•
Usage

t i is the time in years between the value date and the coupon date d .
i

Supranational or regional bond issuer, for example, German Landesbank.

2.1.4.2.5 *ISMA-ACTACT-ANNUAL (financial/instrument/isma@price)
Field

Description

Name

*ISMA-ACTACT-ANNUAL

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Field

Description

Description

This yield convention is used according to the Eurozone. With *ISMA-ACTACT-ANNUAL, the
coupons for the ith cashflow on date di are discounted using the following formula:
•

If t m > 1
Equation 2-13 Standard Eurozone: when time in years is more than 1

•

If t m ≤ 1
Equation 2-14 Standard Eurozone: when time in years is less than or equal to 1

where

Usage

•

t i is the time in years between the value date and the coupon date d
i

•

t m is the time in years from the valuation date to the maturity of the bond.

Standard Euro Zone convention that can be applied to other corporate bonds.

2.1.4.2.6 *ISMA-ACTACT-QUARTERLY (financial/instrument/isma@price)
Field

Description

Name

*ISMA-ACTACT-QUARTERLY

Description

*ISMA-ACTACT-QUARTERLY bonds are regular fixed coupon securities with quarterly coupons

and Act/Act date basis.

With *ISMA-ACTACT-QUARTERLY the coupons for the ith cashflow on date di are discounted
using the following formula:
Equation 2-15 ISMA Act/Act Quarterly bonds

y ti
D ( y, d i ) = ⎛⎝ 1 + ---⎞⎠
4
where
•
Usage

t i is the time in years between the value date and the coupon date d .
i

Supranational or regional bond issuer, for example, EIB.

2.1.4.2.7 *ISMA-ACTACT-SEMI-ANNUAL (financial/instrument/isma@price)
Field

Description

Name

*ISMA-ACTACT-SEMI-ANNUAL

42

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Field

Description

Description

ISMA-ACTACT-SEMI-ANNUAL bonds are regular fixed coupon securities with semi-annual
coupons and Act/Act date basis. With *ISMA-ACTACT-SEMI-ANNUAL, the coupons for the ith
cashflow on date di are discounted using the following formula:
Equation 2-16 Standard UK government bondS

where
•
Usage

t i is the time in years between the value date and the coupon date d
i

Standard UK government bond convention that can be applied by other corporate bonds.

2.1.4.2.8 *ISMA-ACT360-ANNUAL (financial/instrument/isma@price)
Field

Description

Name

*ISMA-ACT360-ANNUAL

Description

ISMA-ACT360-ANNUAL bonds are regular fixed coupon securities with annual coupons and
Act/360 date basis.
ISMA-ACT360-ANNUAL bonds are calculated using the same formula as
ISMA-30E360-ANNUAL, see 2.1.4.2.2 *ISMA-30E360-ANNUAL
(financial/instrument/isma@price) on page 40.

Usage

This convention is used for bond instruments bonds (Interest FIXBIS) issued by sovereign
issuers such as the Bank for International Settlement (BIS).

2.1.4.2.9 *ISMA-ACT365-ANNUAL (financial/instrument/isma@price)
Field

Description

Name

*ISMA-ACT365-ANNUAL

Description

*ISMA-ACT365-ANNUAL bonds are regular fixed coupon securities with annual coupons and
Act/365 date basis.
ISMA-ACT360-ANNUAL bonds are calculated using the same formula as
ISMA-30E360-ANNUAL, see 2.1.4.2.2 *ISMA-30E360-ANNUAL
(financial/instrument/isma@price) on page 40.

Usage

This convention is used for some sovereign bond instruments.

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2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price)
Field

Description

Name

*U.S.STREET-ACT365-SEMIANNUAL

Description

U.S.STREET-ACT365-SEMIANNUAL bonds are regular or irregular securities with Act/365
date basis. With *U.S.STREET-ACT365-SEMIANNUAL, the coupons for the ith cashflow on date
di are discounted using the following formula:
Equation 2-17 U.S. Treasury Notes

where
•

k is the compounding frequency of the yield. For example, k = 2 for semi-annual yield)

•

t0

is the time in years from the value date to d 0 the first coupon date.

t 0 is calculated using the following formula:
Equation 2-18 U.S. Treasury Notes: time in years

where
-

t v, 0

is the period in years between the valuation date and the first coupon date

t p, 0 is the period in years between the previous and the next coupon date,
calculated using the date basis Act/365.

•

n is the number of coupon periods between d 0 and d i , the ith coupon date.
n is calculated using:
Equation 2-19 U.S. Treasury Notes: number of coupon periods

n = round ( k × t i )

where
Usage

44

t i is the time (in years) between d 0 and d i .

U.S. Treasury Notes market convention on the secondary market.

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2.1.4.2.11 *U.S.STREET-ACTACT-SEMIANNUAL (financial/instrument/us-street@price)
Field

Description

Name

*U.S.STREET-ACTACT-SEMIANNUAL

Description

U.S.STREET-ACTACT-SEMIANNUAL bonds are based on the same formula as
U.S.STREET-ACT365-SEMIANNUAL, but have Act/Act date basis.
See 2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price)
on page 44.

Usage

Zero-coupon markets, such as, the U.S. and the UK strips.

2.1.4.2.12 *U.S.STREET-ACTACT-ANNUAL (financial/instrument/us-street@price-1)
Field

Description

Name

*U.S.STREET-ACTACT-ANNUAL

Description

U.S.STREET-ACTACT-ANNUAL bonds are based on the same formula as
U.S.STREET-ACT365-SEMIANNUAL, but have annual coupon and Act/Act date basis.
See 2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price)
on page 44.

Usage

Some sovereign bonds, for example, on the Euro Dollar market.

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2.1.4.2.13 *U.S. Treasury (financial/instrument/us-treasury@price)
Field

Description

Name

*U.S.TREASURY

Description

U.S.TREASURY bonds are regular and irregular fixed coupon securities with semi-annual
coupons and Act/365 date basis.
With *U.S.TREASURY, a periodic rather than compound rate is used for discounting over the
partial period from the value date to the next coupon date di :
Equation 2-20 U.S. Treasury notes and bonds

where
•

t 0 is the time in years from the value date to the next coupon date (calculated as in
*U.S.STREET-ACT365-SEMIANNUAL, see 2.1.4.2.10 on page 44)

•

t i is time in years from the value date to the coupon date.

U.S. Treasury notes and bonds may have an odd first coupon, that is, the length of the first
coupon period may be longer or shorter than the normal coupon period:
•

If the first coupon period is shorter, the coupon amount is calculated as:
Equation 2-21 U.S. Treasury notes and bonds: shorter first coupon period

c 1 = rt 1
where

•

-

r is the nominal interest rate as a percentage of the par value

-

t 1 is the time (in years) between the value date of the interest accrual (i.e.
beginning of interest accrual) and the first coupon date.

If first coupon periods longer than the regular coupon period, the first coupon amount is
given by:
Equation 2-22 U.S. Treasury notes and bonds: longer first coupon period

where
-

r is the nominal interest rate as a percentage of the par value

-

t 0 is time (in years) between the value date of the interest accrual and the date six
months before the first coupon date.

Note: If the first coupon period is exactly half a year, both equations give the same result.
Usage

46

Standard U.S. Treasury Notes and bonds convention that can be applied to other corporate
bonds.

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2.1.4.2.14 BOND-BR-LFT (financial/instrument/isma@price)
Information

Description

ID

BOND-BR-LFT

Name

Brazilian LFT

Description

BOND-BR-LFT bonds are Brazilian Zero Coupon Bonds linked to the O/N-SELIC-interest
rate. The maturities can be over 2 years. They are traded and quoted in 1000's (Dirty Price,
Date basis: Business Days/252) and have a unique security ID (ISIN number), issue date and
maturity date.
The price is derived from the traded yield according to the following equation:
Equation 2-23 Brazilian zero coupon bond

where

Usage

•

P is the price (as a percentage of the par value)

•

y is the annual yield-to-maturity (as a percentage)

•

d denotes the number of business dates from settlement date to maturity date.

Brazilian Zero Coupon Bonds

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2.1.4.2.15 BOND-BR-NBC (financial/instrument/isma@price)

Information

Description

ID

BOND-BR-NBC

Name

Brazilian NBC

Description

BOND-BR-NBC bonds are fixed rate bonds linked to the PTAX-index (FX-rate). The
maturities are 2Y, 3Y and 5Y. The fixed rate is 12% p.a. They are traded and quoted in
1000’s and have a unique security ID (ISIN number), issue date and maturity date.
The price is calculated as a dirty price and is derived from the traded market rate quoted as
a semiannual yield according to the following equation:
Equation 2-24 Brazilian NBC bonds

where

Usage

•

P is the price (as a percentage of the par value)

•

y is the annual yield-to-maturity (as a percentage)

•

d360(k) is the number of days between settlement date and cashflow value date
according to 30/360 date basis

•

c is the coupon rate (12%)

•

L is the number of future coupons

•

PTAX(t-1) is the PTAX-index rate valid at time t-1, and ID is the issue date

•

PTAX(ID-1) is the PTAX-index rate valid at Issue Date-1.

Brazilian NBC Bonds

2.1.4.2.16 BOND-BR-NTN (financial/instrument/isma@price)
Information

Description

ID

BOND-BR-NTN

Name

Brazilian NTN

48

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Information

Description

Description

BOND-BR-NTN bonds are bonds linked to the IGPM-index (NTN-C) and the ICPA-index
(NTN-B). The maturities are 2Y, 3Y and 5Y. The fixed rate is 12% p.a. or 6% p.a. They are
traded and quoted in 1000’s and have a unique security ID (ISIN number), issue date and
maturity date.
The price is calculated as a dirty price and is derived from the traded market rate quoted as
a compound yield according to the following equation:
Equation 2-25 Brazilian NTN bonds

where
•

P is the price (as a percentage of the par value)

•

y is the annual yield-to-maturity (as a percentage)

•

bd(k) is the number of business days between settlement date and cashflow value date

•

L is the number of future coupons.

•

c is the coupon rate (12% or 6%)

The nominal value is 1 000 at issue date for both NTN-B and NTN-C instruments. The
nominal value is then adjusted by the IGPM-rates (NTN-C) and IPCA-rates (NTN-B)
respectively. These rates are inflation rates published every month as a monthly (p.m.)
rate.
Usage

Brazilian NTN Bonds

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2.1.4.2.17 GOVT-AU (financial/instrument/australian@price)
Information

Description

ID

GOVT-AU

Name

Australian Government bond

Description

GOVT-AU bonds are medium to long-term debt securities with a fixed coupon paid
semi-annually in arrears, redeemable at face value on the maturity date. Treasury Bonds
are traded on a yield to maturity basis with the price per $100 face value calculated using
the following pricing formulae:
•

Basic formula
Equation 2-26 Australian government bond: Basic formula

•

Ex interest bonds
Equation 2-27 Australian government bond: Ex interest bonds

•

Near-maturity bonds: Specifically, those entitling a purchaser to only the final coupon
payment and repayment of principal.
Equation 2-28 Australian government bond: Near-maturity bonds

where
•

P is the price per $100 face value (the computed price is rounded to 3 decimal spaces)

•

v is 1 + i

•

i is the annual percentage yield to maturity divided by 200 in Equation 2-26 on page 50
and Equation 2-27 on page 50, or the annual percentage yield to maturity divided by
100 in Equation 2-28 on page 50

•

f is the number of days from the date of settlement to the next interest payment date
in Equation 2-26 on page 50 and Equation 2-27 on page 50 or to the maturity date in
Equation 2-28 on page 50.

•

If the next interest payment date or maturity date falls on a non-business day, the next
good business day (a day on which banks are open for business in Melbourne or Sydney,
i.e. not a Saturday or Sunday) is used in the calculation of f.

•

d is the number of days in the half year ending on the next interest payment date

•

g is the half-yearly rate of coupon payment per $100 face value

•

n is the term in half years from the next interest-payment date to maturity

1
-----------

Settlement amounts are rounded to the nearest cent (0.50 cent is rounded up). That is, the
pricing formula used for computing the price from the yield is the ISMA method. But in the
case of near maturing bonds, i.e. when the bond is settled six months plus seven days
before maturity, it is treated as a special case, using the pricing of Treasury Notes.
Equation 2-29 Treasury Notes equation

50

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Information

Description

Usage

Australian government bond

2.1.4.2.18 GOVT-CA (financial/instrument/canadian@price)
Information

Description

ID

GOVT-CA

Name

Canadian Government bond

Description

GOVT-CA bonds are regular, fixed-coupon securities with equal, semi-annual coupon
payments and Act/365 date basis. These bonds are traded on a clean price basis.
Although Canadian government bonds share similarities with U.S. Treasury bonds, they
differ in the accrued interest calculation. The accrued interest on Canadian Government
bonds is calculated as follows:
Equation 2-30 Canadian government bonds

where
•

AI is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

PAI is the number of accrued interest days computed in the following way:
where
-

coupon days (pc) is the actual number of days in the current coupon period,
calculated as coupon value date minus the start of the current coupon period

-

p AI is the actual number of days in the period over which the accrued interest is

act

calculated (calculated as accrued interest date minus the start of the current
coupon period).
Then:

Usage

act

act

-

if p AI is less than or equal to 182, then p AI = p AI , or

-

if p AI is greater than 182, then p AI = ( 182.5 – ( p c – p AI ) )

act

act

Canadian government bond

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Information

Description

Yield

The following algorithm is used to calculate the yield (Y) based on the price of Canadian
Government bonds:
•

If one coupon payment remains, then the following algorithm is used to calculate the
yield (Y) based on the price of Canadian Government bonds:
Equation 2-31 Canadian government bonds: one coupon payment remains

where
•

y is the annual yield-to-maturity (as a percentage)
r is the nominal interest rate (to be paid at time i) as a percentage of the par value
P is the clean price (as a percentage of the par value)
DSM is the days from settlement date to maturity date
AI is the accrued interest calculated as described in Equation 2-30 on page 51.

If the first coupon is a short coupon, then the Yield formula of Canadian Bond (yield
convention GOVT-CA) takes into account the first coupon as follows:
Equation 2-32 Canadian government bonds: if first coupon is a short coupon

Where
- r is the nominal interest rate
- t1 is the time (in years) between the beginning of the interest accrual and the first
coupon date
and then applies to the following Yield/Price formula:
Equation 2-33 Canadian government bonds: Yield/Price formula

Where
- P is the clean price (as a percentage) of the Par value
- y is the annual Yield-to-Maturity (as a percentage)
- p1 is the number of days from the settlement date to the first coupon date
-

is the number of days in the quasi-coupon period ending on the first coupon
payment date
r is the nominal interest rate

-

n is the number of coupon payments remaining

•

52

is the number of days from interest accrual date to first payment date

is the number of days from the interest accrual date to the settlement date.

If more than one coupon payment remains, the US Treasury bond market conventions
(i.e. US Street calculation method) are used for the price/yield calculations. See
2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price)
on page 44.

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2.1.4.2.19 GOVT-CH (financial/instrument/isma@price)
Information

Description

ID

GOVT-CH

Name

Swiss Government bond

Description

GOVT-CH bonds are regular, fixed-coupon securities with equal, annual coupon payments
and 30E/360 date basis (the date basis where the 31st of the month is treated as the 30th.)
With GOVT-CH, the coupons for the ith cashflow on date d i are discounted using the
following formula:
Equation 2-34 Swiss government bonds

where
•
Usage

t i is the time in years between the value date and the coupon date d i

Swiss government bond.

2.1.4.2.20 GOVT-DK-OLD-30E360 (financial/instrument/isma@price)
Information

Description

ID

GOVT-DK-OLD-30E360

Name

Danish Government 30E360 before 8 February 2001

Description

GOVT-DK-OLD-30E360 bonds are regular, fixed-coupon securities with annual coupon
payments and 30E/360 date basis (the date basis where the 31st of the month is treated as
the 30th).
With GOVT-DK-OLD-30E360, the coupons for the ith cashflow on date d i are discounted
using the following formula:
Equation 2-35 Danish government bond issued before 8 February 2001

where
•

t i is the time in years between the value date and the coupon date

With GOVT-DK-OLD-30E360, the Accrued Interest calculation is calculated using a 30E/360
date basis:
Equation 2-36

where
•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the number of calendar days between the previous coupon payment (inclusive)
and the settlement date (exclusive).

•

t i equals 360. It represents the number of days between the last and next coupon
dates. 360 is also used for leap years.

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Information

Description

Usage

Danish government bond issued before 8 February 2001.

2.1.4.2.21 GOVT-DK (financial/instrument/isma@price)
Information

Description

ID

GOVT-DK

Name

Danish Government bond issued after 8 February 2001.

Description

GOVT-DK bonds are regular, fixed-coupon securities with equal, annual coupon payments
and Act/Act date basis.
With GOVT-DK, the coupons for the ith cashflow on date d i are discounted using the
following formula:
•

If t m > 1 , then
Equation 2-37

•

If t m ≤ 1 , then
Equation 2-38

where

Usage

54

•

t i is the time in years between the value date and the coupon date d i

•

t m is the time in years from the valuation date to maturity of the bond.

Danish government bond. This corresponds to the standard Euro Zone convention. From 8
February 2001 the Danish Government bonds follow the Euro Zone convention. See
2.1.4.2.22 GOVT-EUROZONE (financial/instrument/isma@price) on page 55

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2.1.4.2.22 GOVT-EUROZONE (financial/instrument/isma@price)
Field

Description

Name

GOVT-EUROZONE

Description

Euro Zone government bonds are regular, fixed-coupon securities with equal, annual
coupon payments and a bullet redemption using Act/Act date basis. These bonds are traded
on a clean-price basis.
With GOVT-EUROZONE, the coupons for the ith cashflow on date di are discounted using the
following formula:
•

If t m > 1
Equation 2-39 GOVT-EUROZONE: time in years is more than 1

•

If t m ≤ 1
Equation 2-40 EGOVT-EUROZONE: time in years is less than or equal to 1

where
-

t i is the time in years between the value date and the coupon date d
i

-

t m is the time in years from the valuation date to the maturity of the bond.

With GOVT-EUROZONE, the Accrued Interest is calculated as follows according to ISMA Rule
251:
Equation 2-41 GOVT-EUROZONE: Accrued Interest

where
•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the actual number of days between the last coupon payment date (inclusive) and
the current value date (exclusive)

•

t i is the actual number of days in the coupon period between the last (inclusive) and
next (exclusive) coupon dates multiplied by the number of coupon periods in the year.
However, the denominator calculation is subject to exceptions in relation to irregular
coupon periods (see below)

•
Usage

n c is the number of coupon periods in the year.

This is the standard Euro Zone convention. This convention applies to the following
government bonds: Austria, Belgium, Cyprus, Finland, France (BTAN), German, Greece,
Ireland, Luxembourg, Malta, Netherlands, Portugal, Slovakia, Slovenia, Spain.

Note: France (OAT) and Italy also belong to the Eurozone, but apply small variants to the
Euro Zone convention.

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2.1.4.2.23 GOVT-FR-OAT-OLD-AIR3 (financial/instrument/isma@price)
Information

Description

ID

GOVT-FR-OAT-OLD-AIR3

Name

French Government OAT Old.

Description

GOVT-FR-OAT-OLD-AIR3 bonds are regular, fixed-coupon securities with equal, annual
coupon payments, and Act/Act date basis. These bonds are traded on a clean price basis.
With GOVT-FR-OAT-OLD-AIR3, the accrued interest calculation is rounded to 3 decimals
using an Actual/Actual date basis:
Equation 2-42 Old French OAT convention

where
•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis,

•

Usage

t i is the time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/Actual date basis.

Old French OAT convention for bonds issued before 18 April 2005, where the convention
required an Accrued Interest calculation rounded to 3 decimals using an Actual/Actual date
basis. This convention has been replaced by a rounding to 7 decimals. The old 3-decimal
rounding is still accepted.

2.1.4.2.24 GOVT-FR-OAT (financial/instrument/isma@price)
Information

Description

ID

GOVT-FR-OAT

Name

French Government OAT

Description

French government OATs follow the Euro Zone standard convention. However, in the
GOVT-FR-OAT method the accrued interest calculation is rounded to 7 decimals using an
Actual/Actual date basis:
Equation 2-43 French government OAT

where
•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis

•

Usage

56

t i is the time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/Actual date basis.

French OAT convention for bonds issued after 18 April 2005

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2.1.4.2.25 GOVT-GR-OLD-30E360 (financial/instrument/isma@price)
Information

Description

ID

GOVT-GR-OLD-30E360

Name

Greek Government 30E360 before 1 January 2001

Description

GOVT-GR-OLD-30E360 bonds are fixed-coupon securities with annual coupon payments,
and 30E/360 date basis (the date basis where the 31st of the month is treated as the 30th).
These bonds are traded on a clean price basis.
With GOVT-GR-OLD-30E360, the coupons for the ith cashflow on date d i are discounted
using the following formula:
Equation 2-44 Greek government bond

where
•
Usage

t i is the time in years between the value date and the coupon date d i .

Greek government bond issued before 1 January 2001.

2.1.4.2.26 GOVT-HU (financial/instrument/isma@price)
Field

Description

ID

GOVT-HU

Name

Hungarian Government

Description

With this yield convention, the coupons for the ith cashflow on date di are discounted using
the following formula:
•

If t m > 1
Equation 2-45 Hungarian government bonds: when time in years is more than 1

•

If t m ≤ 1

Equation 2-46 Hungarian government bonds: when time in years is less than or equal to 1

where

Usage

•

t i is the time in years between the value date and the coupon date d
i

•

t m is the time in years from the valuation date to the maturity of the bond.

Hungarian government bonds. This convention uses the accrued interest method Hungarian
(4 decimals), see Hungarian (4 decimals) on page 75.

2.1.4.2.27 GOVT-IT (financial/instrument/isma@price)
Information

Description

ID

GOVT-IT

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Information

Description

Name

Italian Government

Description

GOVT-IT bonds are regular, fixed-coupon securities with equal, semi-annual coupon
payments, and Actual/Actual date basis.
With GOVT-IT, the coupons for the ith cashflow on date d i are discounted using the
following formula:
Equation 2-47 Italian government bonds

where
•

t i is the time in years between the value date and the coupon date d i
Equation 2-48 Italian government bonds: time in years

-

d i is the number of days between the value date and the coupon date d

-

n is the number of coupons i.e. 2.

-

d c is the number of days during the coupon period

With GOVT-IT, the accrued interest calculation is rounded to 5 decimals using an

Actual/Actual date basis:

Equation 2-49 Italian government bonds: accrued interest calculation

•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis

•
Usage

t i is the time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/Actual date basis.

Italian government bonds.

2.1.4.2.28 GOVT-IT-ZC (financial/instrument/isma@price)
Field

Description

ID

GOVT-IT-ZC

Name

Italian Government Zero Coupon

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Field

Description

Description

This yield convention is used for the Italian Government Bond with Zero Coupon. The date
basis is Actual-/365 and the discount factor is calculated according to the following formula:
•

If t m > 1
Equation 2-50 Italian ZC government bonds: when time in years is more than 1

•

If t m ≤ 1
Equation 2-51 Italian ZC government bonds: when time in years is less than or equal to 1

where

Usage

•

t i is the time in years between the value date and the coupon date d
i

•

t m is the time in years from the valuation date to the maturity of the bond.

Italian Government Bond with Zero Coupon

2.1.4.2.29 GOVT-JP (financial/instrument/simple-yield@price)
Information

Description

ID

GOVT-JP

Name

Japanese Government

Description

GOVT-JP bonds are regular, fixed-coupon securities with equal, annual coupon payments,
and Actual-/365 date basis. These bonds are traded on a clean price basis.
With GOVT-JP, the Accrued Interest calculation is truncated to 7 decimals using Actual/365
date basis:
Equation 2-52 Japanese government bonds

•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis

•

t i is the time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/365 date basis.

Usage

Japanese government bonds

Yield

Simple Yield

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2.1.4.2.30 GOVT-MALAYSIA (financial/instrument/isma@price)
Information

Description

Name

GOVT-MALAYSIA

Usage

Used to support Malaysian Government bonds. These bonds have semi-annual
coupon payments with Act/2Act date basis.

2.1.4.2.31 GOVT-NO (financial/instrument/norwegian@price)
Information

Description

Name

GOVT-NO

Description

Norwegian government bonds are regular, fixed-coupon securities with equal, annual
coupon payments and a bullet redemption on an Act/365 date basis. These bonds are
traded on a clean-price basis.
With GOVT-NO, the coupons for the ith cashflow on date di are discounted using the
following formula:
Equation 2-53 Norwegian government bonds

where
•

t i is the time in years between the value date and the coupon date calculated using the
date basis Actual/365

With GOVT-NO, the Accrued Interest calculation is calculated using date basis Actual/365:
Equation 2-54 Norwegian government bonds: Accrued Interest

where
•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the actual number of calendar days between the previous coupon payment and the
settlement date. The actual number of calendar days include leap years

•

t i is equal to 365 and represents the number of days between the last and next coupon
dates.

Note: 365 is also used for leap years.
Usage

Norwegian government bonds

2.1.4.2.32 GOVT-NZ (financial/instrument/isma@price)
Information

Description

ID

GOVT-NZ

Name

New Zealand Government Bond

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Information

Description

Description

GOVT-NZ bonds are regular, fixed-coupon securities with semi-annual coupon payments,
and Actual/Actual date basis. These bonds are traded on a clean price basis.
With GOVT-NZ, the coupons for the ith cashflow on date d i are discounted using the
following formula:
Equation 2-55 New Zealand government bonds

where
•

Usage

t i is the time in years between the value date and the coupon date d i calculated using
the date basis Actual/Actual.

New Zealand government bonds

2.1.4.2.33 GOVT-SE (financial/instrument/isma@price)
Information

Description

ID

GOVT-SE

Name

Swedish Government Bond

Description

GOVT-SE bonds are regular, fixed-coupon securities with equal, annual coupon payments,
and 30E/360 date basis (the date basis whereby the 31st of the month is treated as the
30th). These bonds are traded on a clean price basis. With GOVT-SE, the coupons for the
ith cashflow on date d i are discounted using the following formula:
Equation 2-56 Swedish government bonds

where
•

t i is the time in years between the value date and the coupon date d i

With GOVT-SE, the accrued interest calculation is calculated using an 30E/360 date basis:
Equation 2-57

where

Usage

•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the number of calendar days between the previous coupon payment (inclusive)
and the settlement date (exclusive)

•

t i equals 360. It represents the number of days between the last and next coupon
dates. 360 is also used for leap years.

Swedish government bonds.

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2.1.4.2.34 GOVT-SG (financial/instrument/us-street@price)
Field

Description

Name

GOVT-SG

Description

Singaporean Government Bonds are based on the same formula as
U.S.STREET-ACTACT-SEMIANNUAL.
See 2.1.4.2.11 *U.S.STREET-ACTACT-SEMIANNUAL (financial/instrument/us-street@price)
on page 45.

Usage

Singaporean government bond convention. This convention uses the accrued interest
method Singaporean (8 decimals), see Singaporean (8 decimals) on page 77.

2.1.4.2.35 GOVT-UK (financial/instrument/isma@price)
Information

Description

ID

GOVT-UK

Name

UK Government Bond

Description

GOVT-UK bonds are regular, fixed-coupon securities with equal, semi-annual coupon
payments, and Actual/Actual date basis. These bonds are traded on a clean price basis.
With GOVT-UK, the coupons for the ith cashflow on date d i are discounted using the
following formula:
Equation 2-58

where
•

t i is the time in years between the value date and the coupon date d i
Equation 2-59

where

Usage

-

d i is the number of days between the value date and the coupon date d

-

n is the number of coupons i.e. 2.

-

d c is the number of days during the coupon period

UK government bond convention.

2.1.4.2.36 GOVT-US (financial/instrument/us-street@price)
Information

Description

ID

GOVT-US

Name

United States Government

62

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2 Market standards and calculations
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Information

Description

Description

U.S. Treasury government bonds are regular and irregular fixed-coupon securities with
semi-annual coupon payments and Actual/365 date basis. These bonds are traded on a clean
price basis.
With GOVT-US, a periodic rather than compound rate is used for discounting over the
partial period from the value date to the next coupon date d i :
Equation 2-60 U.S Treasury government bonds

where
•

t 0 is the time in years from the value date to the next coupon date (calculated as in the
U.S. Street method)

•

t i is the time in years from the value date to d i .

U.S. Treasury notes and bonds may have a first coupon of an unequal length. That is, the
length of the first coupon period may be longer or shorter than the normal coupon period.
•

If the first coupon period is shorter, the coupon amount is calculated as follows:
Equation 2-61 First coupon period shorter

c 1 = rt 1
where
-

r is the nominal interest rate

-

t 1 is the time (in years) between the dated date (the beginning of interest accrual)
and the first coupon date.

•

If the first coupon period is longer, the first coupon amount is calculated as follows:
Equation 2-62 First coupon period longer

c 1 = r ⁄ 2 + rt 0
where
-

t 0 is time (in years) between the dated date and the date six months before the
first coupon date.

•
Usage

If the first coupon period is exactly half a year, both equations give the same result.

This is the US government bond convention based on U.S. Street

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2.1.4.2.37 GOVT-USAGENCY (financial/instrument/isma@price)
Information

Description

ID

GOVT-USAGENCY

Name

United States Government Agency

Description

GOVT- USAGENCY bonds are fixed-coupon securities with annual coupon payments, and

30/360 date basis. These bonds are traded on a clean price basis.

With GOVT-USAGENCY, the accrued interest is calculated as follows using a 30/360 date
basis:
Equation 2-63 United States Government Agency

where
•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t i is the length of the coupon period calculated using the accrual date basis of 30/360
(or coupon date basis if the former is missing)

•
Usage

64

t r is the length of the remaining accrual period (i.e. the time between the accrual date
and the end date of the coupon).

US government Agencies bond convention

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2.1.4.2.38 GOVT-ZA (financial/instrument/south-african@price)
Information

Description

ID

GOVT-ZA

Name

South African Government bond

Description

GOVT-ZA bonds are regular, fixed-coupon securities with semi-annual coupon payments,
and Actual/365 date basis. These bonds are traded on a clean price basis.
With GOVT-ZA, the Accrued Interest calculation is rounded to 5 decimals using an Actual/365
date basis:
Equation 2-64 South African Government bond

where
•

I a is the accrued interest

•

r is the nominal interest rate (to be paid at time i) as a percentage of the par value

•

t a is the time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis

•

t i is the time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/365 date basis.

With GOVT-ZA, the coupons for the ith cashflow on date d i are discounted using the
following formula:
Equation 2-65

where
•

k is the compounding frequency of the yield (for example, k=2 for semi-annual yield)

•

t 0 is time in years from the value date to d 0 , the first coupon date. t 0 is calculated
using the following formula:
Equation 2-66 Time in years from value date to first coupon date

t v, 0
t 0 = --------t p, 0
where
-

t v, 0 and t p, 0 are the periods in years between the valuation date and the first
coupon date, and between the previous and the next coupon date, respectively,
calculated using the date basis Act/365

-

n is the number of coupon periods between d 0 and d i , the ith coupon date.
The number of coupon periods is calculated using:

n = round ( kxt i )

where t i is the time (in years) from the next coupon date to the maturity of the
bond, and round rounds the number to the nearest integer.
Usage

South African Government bond convention

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2.1.4.2.39 INDEX-UK (function/index-uk@price)
ID

INDEX-UK

Name

Index-linked UK Government bond

Description

The prevailing market conventions for price/yield calculations in the UK index-linked market
are different from the conventions used for the Swedish and US index-linked markets.
The market practice is to assume that all future semi-annual coupon periods have the same
length as the present accrued period. Therefore, the overall period T si between settlement
and the ith coupon, in the date basis actual/365, is given by:
Equation 2-67 Index-linked UK Government bond

The market quoted clean price and the semi-annual nominal yield to maturity Y nominal are
calculated by the following price/yield formula:
Equation 2-68 Price/yield equation

where
•

C IndexAdj is the index adjusted coupons

•

R IndexAdj (prolonged RPI index figures) is the redemption.

Given the price, the nominal yield is obtained by numerical methods.
The real yield to maturity y Real is derived from the nominal yield and the assumed inflation
rate using the Fisher equation:
Equation 2-69 Fisher equation

Usage

Index-linked UK Government bonds

2.1.5 Discount Margin
Discount margin is the spread that, when added to the discounting zero curve, will equate the
theoretical value of a floating rate note (see 3.1.2 Floating rate note on page 228) to the quoted
price. Discount Margin is calculated at instrument level and shown in Rate Monitor or in Transaction
Manager (Figure Discount Margin). In this calculation, the day count method and yield type specified
in Discount Margin page are used, and the spread is added to the discounting curve defined in this
page.
When discount margin is used in the valuation, it is added to the valuation curve specified for the
instrument, and the day count method and yield type used are taken from the interpolation method
of this valuation curve. For the results to be consistent, the day count method and yield type
specified in Discount Margin page should match these. Also, the instrument's valuation curve should

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2 Market standards and calculations
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be used for discount margin calculation. Discount margin valuation is enabled by the feature FRN
Valuation, see A.2.164 FRN Valuation on page 791.
At instrument level, discount margin m is calculated by solving the equation:
Equation 2-70 Discount margin

Where:

–

Pd The dirty price (at spot) of the bond, based on the market quote.

–

d i The coupon dates.

–

ci The fixed or estimated coupons.
y
D i The discount factors (from spot) from the discounting curve on dates d i .

–

Note: Coupons have to be fixed in Instrument Editor for the fixing to have an effect on the
discount margin calculation.

–

and
are the rate-to-discount-factor and discount-factor-to-rate conversions
(from spot date) using the day count method and yield type specified in the discount margin
setup.

2.1.6 Calculation methods
2.1.6.1 Accrued interest calculations
The generic formula for accrued interest AI is:
Equation 2-71 Accrued interest (generic formula)

t
AI = --- × C
T
where C is the coupon amount, T is the length of the coupon period (in years, calculated with the
appropriate date basis), and t is the length of the accrual period (in years).
There are many variations of this basic formula.

Note: For bonds, the method used for the accrued interest calculation is specified in the AI Method
field in Instrument Editor’s Bond page. The date basis used for period length calculations is
specified in the Cashflow page (Accrual Date Basis field). If the accrual date basis is not
defined, then the date basis of the cashflow is used. Both these pages are available in the
editor when the Bond feature is present in the instrument definition (see A.2.51 Bond on
page 734).

Some AI methods use neither the accrual nor the cashflow’s date basis. This is because the day
count method is built in the method.
The following table lists the symbols used in the accrued interest calculations:
Symbol

Description

P

Principal on which the coupon amount and accrued interest are calculated.

C

Coupon amount.

r

Coupon interest rate (as a decimal number).

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Symbol

Description

T

Coupon period in years.

t

Accrual period in years.

D

Coupon period in days.

d

Accrual period in days.

2.1.6.1.1 Generic methods
The following sections describe the generic methods for calculating accrued interest in TRM.

Linear
Equation 2-72 Accrued Interest: Linear

t
AI = --- × C
T
Linear 30/360 EOM
The Linear 30/360 EOM method ensures that the calculation of accrued interest follows the same
month-end behavior as accrued interest used in the calculation of accrued profit.
This method is used when defining the Result IR setup for a result treatment (in Result Editor). It
achieves a constant yield when a 30E/360 EOM date basis is selected (in Result Editor’s Accrual Yield
page).
See the TRM User Guide for more information about setting up result treatments.

Linear (Closing)
The Linear (Closing) method ensures that in closing the books, February is considered as having 30
days when 30-day date bases (such as, the 30/360 and 30E/360 date bases) are used.
This means that in accounting, these date bases result in equal interest accrual amount postings in
each month.

Actual/Actual
Equation 2-73 Accrued Interest: Actual/Actual

d
AI = ---- × C
D
where D is the interest period length in actual days, and d is the length of the accrual period in
actual days.
This method will ignore any date basis conventions associated with the coupon.

Actual/Actual (Inclusive)
This method accrues interest linearly over the interest period, including the first day and excluding
the last day of the period.

Actual/Actual Annually
In the following methods, Actual/Actual Annually, Actual/Actual Semi-Annually, and Actual/Actual
Quarterly, the basic formula is used, but the period length calculation is more complicated, as
follows:

•

68

The coupon period is divided into 12/N -month segments, starting from the end of the coupon
period.

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2 Market standards and calculations
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•

The number of months in each segment, 12/N, may be 12, 6, or 3, depending on the method
chosen (respectively, Annually, Semi-Annually, or Quarterly).

•

The segments are created by moving the coupon end date back in 12/N -month steps.

•

If a date created by such a move does not exist (that is, it falls after the end of month), the
end-of-the-month date is substituted for it.

Let ith such segment span dis days, and the part of the period within the segment contain dip days;
then the total period length in years is:
Equation 2-74 Accrued Interest: Actual/Actual Annually - total period length

i

dp
t = ∑ -------i
d
N
i s
Note: If the period extends over an entire segment, then dip = dis and the contribution to the
total period length of that segment is simply 1/N years.

This calculation is repeated for the coupon period (T) and for the accrual period (t), and finally the
accrued interest is:
Equation 2-75 Accrued Interest: Actual/Actual Annually

t
AI = --- × C
T
These methods will ignore any date basis conventions associated with the coupon.

Actual/Actual Annually (5 decimals)
Non-government Italian bonds are based on annual coupon and Actual/Actual accrual date basis
with a rounding to the fifth decimal. This method can be used for more generic purposes as well as
for non-government Italian bonds.
Accrued Interest is calculated as follows:
Equation 2-76 Actual/Actual Annually (5 decimals): accrued interest

AI = R 7 [ r × d ⁄ D ] × P
Where
AI

Accrued interest

r

Nominal interest rate (to be paid at time i) as a real number.

d

Time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis.

D

Time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/Actual date basis.

P

Principal

Index ratio:
Equation 2-77 Actual/Actual Annually (5 decimals): index ratio

Index
IndexRatio = R 5 ⎛⎝ -----------------------------⎞⎠
IssueIndex

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Index Accrued Interest:
Equation 2-78 Actual/Actual Annually (5 decimals): index accrued interest

IndexAI = IndexRatio × AI
Coupon % methods
With the Coupon % methods, the accrued interest is calculated directly from the principal (P) and
the coupon rate (r). It may happen that the accrued interest thus calculated is larger than the actual
coupon amount (for example, if the date basis used in the AI calculation is different from the date
basis used for the calculation of the coupon amount). In this case, accrued interest is capped at the
coupon amount, and the daily accrual towards the end of the coupon period may be zero.

•

Coupon %
Equation 2-79 Accrued Interest: Coupon %

AI = min [ r × t × P ,C ]
•

Coupon % Relative Semi-Annually
Equation 2-80 Accrued Interest: Coupon % Relative Semi-Annually

r×t×P
AI = min ------------------- ,C
2T
Here T is calculated using the date basis of the cashflow, not the accrual date basis.

•

Coupon % Relative Quarterly
Equation 2-81 Accrued interest: Coupon % Relative Quarterly

r×t×P
AI = min ------------------- ,C
4T
Here T is calculated using the date basis of the cashflow, not the accrual date basis.

•

Coupon % Compound Annually
Equation 2-82 Accrued interest: Coupon % Compound Annually

t

AI = min [ ( 1 + r ) – 1 ,C ]
•

Coupon % Compound Semi-Annually
Equation 2-83 Accrued interest: Coupon % Compound Semi-Annually

2t

AI = min [ ( 1 + r ⁄ 2 ) – 1 ,C ]
•

Coupon % Compound Quarterly
Equation 2-84 Accrued interest: Coupon % Compound Quarterly

4t

AI = min [ ( 1 + r ⁄ 4 ) – 1 ,C ]
Expression
If the coupon is fixed in arrears, the fixing rate is not known when figure accrued interest is
calculated. As an estimate, the system uses the current market rate for the fixing period.

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The formula for accrued interest is then:
Equation 2-85 Accrued interest: Coupon % Expression

t
AI = A × --T
where:

–

t is the time in years between the start of the coupon period and the valuation date

–

T is the length in years of the coupon period

–

A is the coupon amount calculated using the expression defined for the coupon cashflow.

Dual currency
•

Dual-Currency Estimated
The settlement amount is calculated using the forward FX rates.

•

Dual-Currency Last
The settlement amount is calculated using the FX rate of the previous FX fixing.

Note: Both methods round the figure value in the cashflow currency before converting it into the
settlement currency.

Range
For range accrual transactions, several specific accrued interest calculation methods exist. They are
all based on the principle that the interest (coupon) rate has to be scaled down by a factor
depending on the number of days the market variable being observed has been within the range.
Once the interest rate has been scaled down, the accrued interest is calculated linearly based on the
time spent until valuation date, the total interest period and the date basis of the cashflow.
The accrued interest methods and the corresponding factors are:

•

Range Proportional
Days In Range / Observation Days until valuation date

•

Range So Far In
Days In Range / Total Interest Period

•

Range So Far Out
(Total Interest Period - Days Out of Range) / Total Interest Period

•

Range Fixing
Assumes the variable observed will remain in the same state as on valuation date, i.e. So Far In
if it is out of range and So Far Out otherwise.

Note that the default observation period includes the first date of the interest period and excludes
the last date (i.e payment date) of the interest period.
For example:
Let us consider the interest period from 01/06/2003 until 01/12/2003 with the interest calculation
expression as:
max[0, 4.85 * range(Euribor/6M, 0, 4.00, up-in/down-in, 2, EUR, ACT/365)]
Valuation date is 30/06/2003, i.e. there have been 30 observation days, and 29 days on interest
accrual.
The total interest period is 183 days.

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Assume that the 6M Euribor rate was in the range 20 times.
The accrued interest would be (using date basis Act/365):

•

Range Proportional method:
4.85% * 20/30 * 29/365 * Nominal Amount

•

So-Far-In method:
4.85% * 20/183 * 29/365 * Nominal Amount

•

So-Far-Out method:
4.85% * (183 - 10)/183 * 29/365 * Nominal Amount, i.e.
4.85% * 173/183 * 29/365 * Nominal Amount

Yield Accrued Interest
This yield based method is used only for the yield accrual of discount/premium – it is not to be used
for actual accrued interest calculation. It converts the coupon rate to the same basis as with which
yield to maturity is calculated (in a manner that the total coupon remains the same, but the rate of
accrual changes). Yield accrual is then based on the coupon accruing with this rate.

ISDA CDS
The ISDA CDS method is used with credit default swap. This AI method is based on the Linear AI
method except that the last period coupon is one day longer, i.e. it includes both the first and last
dates in the AI calculation.

2.1.6.1.2 Market-specific methods
The following sections describe the market-specific methods for calculating accrued interest in TRM.

Note: With regards to rounding, we use the symbol Rn to indicate the rounding to n decimal

places. In the applications the interest rate r is given as a % (e.g. r = 3.85 is treated as
3.85% = 0.0385). In the calculation, the system uses the real number. This means that an
AI Method (3 decimals) corresponds to a rounding (R5) of the real number to 5 decimals.

Australian (3 decimals)
This is the AI method rounded to 3 decimals using the Actual/Actual date basis:
Equation 2-86 Accrued interest: Australian (3 decimals)

AI = R 5 [ ( r ⁄ 2 ) × d ⁄ D ] × P
where d is the length of the accrual period in actual days and D is the interest period length in actual
days.

Australian Floater (3 decimals)
This is the method used for australian domestic floating rate note, rounded to 3 decimals using
instrument date basis.
Equation 2-87 Accrued interest: Australian Floater (3 decimals)

AI = R 5 [ r × t ] × P
where

72

–

r is the fixing rate of the current coupon

–

P is the Principal

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–

t is the length of the accrual period in years, calculated using the coupon date basis.

Moreover, during the ex coupon period, accrued interest is based directly on the number of
remaining days to the next coupon using the following equation:
Equation 2-88 Accrued interest: Australian Floater (3 decimals): ex coupon period

AI = R 5 [ r × t ] × P
Where

–

P is the principal

–

t is the length of the remaining period (to the next coupon) in years, calculated using the
coupon date basis.

Australian Index Linked
These are the Australian Index Linked (IAB) or Australian Index Linked (CIB) AI methods used for Australian
index-linked bonds or Australian capital indexed bonds respectively.

Note: For three decimal places rounding, use AI method Australian Index Linked (IAB) (3 dec).
Belgian
The following calculation applies for all coupon lengths (except short coupons); see Equation 2-74
on page 69 for more details:

For short coupons, the calculation is the following; see Equation 2-79 on page 70 for more details:

Canadian
The Actual/365 (Canadian Bond) date basis considers a year to have 365 days, whereas the length
of a coupon period is represented by 365 divided by the number of coupon periods in a year. For the
most common Canadian domestic bond structures, which pay a semi-annual coupon, this implies
the length of a coupon period is 365/2 = 182.5 days.
Where f is the annual payment frequency (or number of coupon periods per year), the Actual/365
Canadian Bond measures the fraction of a coupon period represented by a given number of days as
follows:

•

If the number of days of interest accrual is less than the actual number of days in the coupon
period:
Equation 2-89 Accrued Interest: Canadian

{ frac }

pc

d×f
= ----------365

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Which, for semi-annual pay bonds where f = 2 , reduces to:
Equation 2-90 Accrued Interest: Canadian semi annual pay bonds

{ frac }

pc

d
= ------------182.5

Then
Equation 2-91 Canadian AI calculation

{ frac }

AI = A c × p c
•

If the number of days of interest accrual exceeds 365/f, or 182.5 days for a semi-annual pay
bond:
Equation 2-92 Accrued Interest: Canadian when interest accrual exceeds 365/f or 182.5 days

{ frac }

pc

df × f
= 1 – ------------365

Where

–

d f is the actual number of days from the valuation date to the next coupon date.

Then
Equation 2-93 Canadian AI calculation when interest accrual exceeds 365/f or 182.5 days

{ frac }

AI = A c × p c
French (3 decimals)

Equation 2-94 Accrued interest: French (3 decimals)

AI = max [ ( R 5 [ 1 + rt ] – 1 ) × P ,C ]
where t is the length of the accrual period in years, calculated using the accrual date basis, operator
R5 signifies the rounding, and Tc and t are the length of the coupon period calculated using the
coupon date basis and the accrual date basis, respectively.

French (4 decimals)
This method is the same as French (3 decimals) except that the rounding operator = R6.

French (7 decimals)
This method is the same as French (3 decimals) except that the rounding operator = R9.

Greek (3 decimals)
Greek index-linked bonds are based on the annual coupon and Actual/Actual Accrual date basis with a
rounding to the third decimal. This method is used for Greek index-linked bonds.
Accrued Interest is calculated as follows:
Equation 2-95 Accrued interest: Greeks (3 decimals)

AI = R 5 [ r × d ⁄ D ] × P

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Where
AI

Accrued interest

r

Nominal interest rate (to be paid at time i) as a real number.

d

Time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis.

D

Time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/Actual date basis.

P

Principal

Index ratio:
Equation 2-96 Accrued interest: Greeks (3 decimals) - index ratio

Index
IndexRatio = R 3 ⎛⎝ -----------------------------⎞⎠
IssueIndex
Index Accrued Interest:
Equation 2-97 Accrued interest: Greeks (3 decimals) - index accrued interest

IndexAI = IndexRatio × AI
Hungarian (4 decimals)
This is the AI method rounded to 4 decimals using the Actual/Actual accrual date basis:
Equation 2-98 Accrued interest: Hungarian (4 decimals)

AI = max [ ( R 6 [ 1 + rt ] – 1 ) × P ,C ]
where t is the length of the accrual period in years, calculated using the accrual date basis, the
operator R6 signifies the rounding, and Tc and t are the length of the coupon period calculated using
the coupon date basis and the accrual date basis, respectively.

Israeli (Annual Compound, 5 decimals)
•

Bond
Bond coupon rate r (in %) is converted to the annual compound rate as follows:
Equation 2-99 Accrued Interest: Israeli (Annual Compound, 5 decimals) Bond

Where:
t = Time in years between the last (inclusive) and next (exclusive) coupon dates, calculated
using the appropriate Actual/365 date basis.
r = nominal interest rate
Then, the AI is computed as follows:
Equation 2-100 Israeli (Annual Compound, 5 decimals) Bond - AI calculation

Where P is the principal.

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•

Index Linked Bond
Coupon rate r (in %) is converted to the annual compound rate as follows:
Equation 2-101 Israeli (Annual Compound, 5 decimals) Index Linked Bond

Then, the Index AI is computed as follows:
Equation 2-102 Israeli (Annual Compound, 5 decimals) Index Linked Bond - AI calculation

Where P is the principal.

Israeli (Linear, 5 decimals)
This is the AI method rounded to 5 decimals using the Actual/365 date basis:
Equation 2-103 Accrued Interest: Israeli (Linear, 5 decimals)

AI = R 7 [ r × d ⁄ D ] × P
where
AI

Accrued interest

r

Nominal interest rate (to be paid at time i) as a real number.

d

Time in years between the last coupon date (inclusive) and the value date
(exclusive) calculated using the accrual date basis.

D

Time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/365 date basis.

P

Principal

The index (inflation-adjusted) Accrued Interest is rounded to 5 decimals using Actual/365 date
basis:

•

Index Ratio
Equation 2-104 Accrued Interest: Israeli (Linear, 5 decimals) - index ratio

Index
IndexRatio = R 9 ⎛ -----------------------------⎞
⎝ IssueIndex⎠
•

Index Accrued Interest %
Equation 2-105 Accrued Interest: Israeli (Linear, 5 decimals) - index accrued interest %

IndexAI = IndexRatio × AI

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Italian (5 decimals)
This is the Actual/Actual AI method rounded to 5 decimals:
Equation 2-106 Accrued interest: Italian (5 decimals)

AI = R 7 [ ( r ⁄ 2 ) × d ⁄ D ] × P
where d is the length of the accrual period in actual days and D is the interest period length in actual
days.

Japanese Yield (7 decimals)
This is the Coupon % AI method ( Coupon % methods on page 70) truncated to 7 decimals:
Equation 2-107 Accrued Interest: Japanese Yield

AI = min [ ( R 9 ( 1 + r t ) × P – P ), C ]
where t is the length of the accrual period in years.

Norwegian
The Norwegian accrued interest method is calculated during ex-coupon and based directly on the
number of remaining days next to the coupon using the following equation:
Equation 2-108 Accrued Interest: Norwegian

t
AI = C × --------365
Where
C

The coupon interest percent per annum.

t-------365

The actual number of calendar days from the settlement date (transaction value
date) to the next coupon payment date divided by 365.

Singaporean (8 decimals)
This is the Actual/Actual AI method rounded to 8 decimals:
Equation 2-109 Accrued interest: Singaporean (8 decimals)

AI = R 10 [ ( r ⁄ 2 ) × d ⁄ D ] × P
where

–

d is the time in years between the last coupon date (inclusive) and the value date
(exclusive), calculated using the accrual date basis.

–

D is the time in years between the last (inclusive) and next (exclusive) coupon dates,
calculated using the appropriate Actual/Actual date basis.

South African (5 decimals)
This is the Coupon % AI method truncated to 5 decimals:
Equation 2-110 Accrued interest: South African (5 decimals)

AI = min [ ( R 7 ( 1 + r t ) – 1 )P ,C ]

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where t is the length of the accrual period in years.

US Agency
Equation 2-111 Accrued interest: US Agency

AI = r × ( T – t r ) × P
where T is the length of the coupon period calculated using the accrual date basis (or coupon’s date
basis if the former is missing), and tr is the length of the remaining accrual period (that is, the time
between the accrual date and the end date of the coupon).

2.1.6.2 Annuity calculations
Annuity calculations are based on all interest cashflows having Kind = Annuity Component and a
matching value date, with the amortization cashflows also having Kind = Annuity Component.
This allows cashflows from several interest schedules to be included in the calculation.
Grace periods can be handled by setting up a forward starting amortization schedule: the coupon
dates before will not match the amortization dates and will therefore behave outside any annuity
calculation. The later ones will be part of the annuity calculation.
In practical terms, this means one of the following:

•

Instrument setup can start from a normal fixed rate loan and be defined so that interest and
amortization share the value dates, or create a reference interest schedule from the
amortization schedule

•

Select the calculation methods (either Annuity or Fixed Annuity), on both schedules (P stands for
Principal, Ri for the repayment as i-th value date, Ci for the coupon amount, n the number of
dates).
See the following sections for more information.

2.1.6.2.1 General annuity calculation
This works for any date basis, irregular dates, varying interest rate, and so on, when Interest and
Amortization Calculation Method = Annuity.
Ri + Ci = Ri-1 + Ci-1 whenever i and sum(Ri) = -P
Ci is calculated as usual from the outstanding nominal (that is, P+sum(Ri) where i from 1 to i-1)
Ri and Ci are rounded according to the Leg Amount Precision
Rn is adjusted so that Rn = P + sum(rounded(Ri)) where i from 1 to n-1

–

If the 1st coupon period is short, then you get a "big" amortization and a small coupon
amount

–

Rounded(Ri) + rounded(Ci) are not always equal because of the rounding effect (couple of
rounding units difference maximum)

Note that the cashflow part of the calculation is given the attribute Kind = Annuity Component.
For an irregular annuity, if a rate is specified in the principal schedule, the annuity is computed
equally across all flows, except for the last one. The last payment is adjusted according to the
outstanding principal amount (100 - r).

2.1.6.2.2 Fixed annuity calculation
This works only when the same discount factor is used for all periods, that is, the same interest rate
and date bases, so all periods are worth the same (for example, 30/360 for semi-annual or
quarterly, Actual/Actual for yearly, and so on), when Interest and Amortization Calculation Method =
Fixed Annuity.

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The calculation always uses the last interest period to calculate the annuity amount. It calculates the
repayment amount from a direct formula that assumes that you have the same discount factor for
all periods. The calculation will not work if there are different periods or uneven date bases.
The simplified formula is:
Ri = P * (D-1) * D^(i-1) / (1 – D^n)
D being the discount factor for 1 period, that is (1+rate*180/360), for a semi-annual 30/360
interest.
Therefore, the annuity amount is calculated from:
Cn+Rn = Rn*(D-1) + Rn = Rn * D = P * (D-1) * D^(n-1) / (1 – D^n) * D = P * (D-1) * D^n /
(1 – D^n)
This accumulated annuity is used as the reference annuity amount for all value dates in the rest of
the calculation.
Once amortizations are calculated (using the direct formula), for each date, the remaining amount
from the reference annuity is distributed between interest flows that have Kind = Fixed Annuity, in
relation to their Amount % value (in the case where there are many interest amounts for the same
date).
To handle the short 1st coupon, the attribute 1st Coupon Excluded must be set on the interest
schedule: this removes the Fixed Annuity kind so that the interest amount is calculated as usual,
based on the principal.
Note that the cashflows part of the calculation is given the Fixed Annuity kind as well as the Annuity
Component kind.

2.1.6.2.3 Annuity calculation with rounded repayment factors
This works when Interest Calculation Method = Annuity, and Amortization Calculation Method = Fixed
Annuity.
The calculation precision is set to the number of decimals for the repayment/principal ratio %.
The amortization calculation is similar to the fixed annuity calculation, except that the Ri/P
calculation is rounded to the specified precision.
The interest amounts have to be calculated from the outstanding nominal (requires the Annuity
calculation method) and the sum of repayment and interest varies significantly because of the
repayment ratio% rounding effect.
The same attribute is used to handle the short 1st coupon.

2.1.6.3 FX rate calculation
The following three methods are available for the calculation of valuation date's FX rate (Sv) from FX
Spot rate (S):

•

Spot Rate: This method uses the FX Spot Rate to convert the cashflow currency to the valuation
currency, i.e. the rate is unchanged from the default method.
Equation 2-112 FX method: Spot Rate calculation

Sv = S
•

Today's Rate (Forward Points): This method modifies the FX Spot rate with forward points
between the valuation date and the spot date.
Equation 2-113 FX method: Today’s Rate (Forward Points) calculation

S v = S – p × 0.0001

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where p is the forward points. Typically there are O/N and T/N quotes between the valuation
date and the spot date, in which case:
Equation 2-114 FX method: Today’s Rate (Forward Points) calculation

a

b

a

b

p = ( p1 + p1 ) ⁄ 2 + ( p2 + p2 ) ⁄ 2

where the superscripts
refer to O/N and T/N.

•

a

and b refer to Ask and Bid quotes respectively, and subscripts 1 and 2

Today's Rate (IR Differential): This method modifies the FX Spot rate with the ratio of the
two currencies' discount factors.
Equation 2-115 Today's Rate (IR Differential) calculation

v

S v = SD ⁄ D

c

where

–

Dv is the valuation currency discount factor between the valuation date and the spot date

–

Dc is the cashflow currency discount factor between the valuation date and the spot date.

2.1.6.3.1 Example of FX rate calculation
The following example shows the calculations using the following market date (Rate Monitor):

•

•

FX Rate
Spot

S = 1.5

O/N points

•

p 1 = 0.02

T/N points

•

p 2 = – 0.03

b

b

a

Bid

•

p 1 = 0.06

Bid

•

p 2 = – 0.01

a

Ask

Discount Factors
O/N

•

Ask

T/N

c

•

D 2 = 0.999985555764

v

•

D 2 = 0.999948197128

Cashflow Currency

•

D 1 = 0.999992955609

Valuation Currency

•

D 1 = 0.999964445709

c

v

Forward Points
Equation 2-116 Example - FX method: Today’s Rate (Forward Points) calculation

a

b

a

b

p = ( p 1 + p 1 ) ⁄ 2 + ( p 2 + p 2 ) ⁄ 2 = 0.02

S v = S – p × 0.0001 = 1.499998

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•

IR Differential
Equation 2-117 Example - FX method: Today's Rate (IR Differential) calculation

c

c

c

v

v

v

D = D 1 D 2 = 0.999977500389355

D = D 1 D 2 = 0.999912644678814

v

c

S v = SD ⁄ D = 1.49990271424530

2.2 Yield curves
TRM boot straps zero coupon yield curves in order to carry out valuations that are based on
discounting future cashflows and/or estimating the amounts of unfixed future cashflows. Three
types of bootstrapped zero coupon yield curves exist in TRM:

•

Yield Curves, i.e. zero coupon yield curves calculated from IR quotes (e.g. deposit, swap and
FRA quotes) MM futures and/or bonds. These curves are generally used for discounting (and
estimating) any arbitrary set of cashflow.

•

Tenor Basis Swap Curve, i.e. zero coupon yield curves calculated from tenor basis swap quotes
and a base yield curve. These curves are used as estimation curves in tenor basis swap valuation
(of the leg for which the spread is quoted) in order to capture the affect of the tenor basis spread
quotes.

•

Cross Currency Basis Swap Curve, i.e. zero coupon yield curves calculated from cross currency
basis swap quotes and a base yield curve. These curves are used as valuation curves in cross
currency basis swap valuation (of the leg for which the spread is quoted) in order to capture the
affect of the cross currency basis spread quotes.

The bootstrapping logic for all these yield curves is explained below.

Note: See the TRM User Guide for general information about setting up yield curves.

2.2.1 Yield curve
A yield curve is a curve that gives the prices of discount bonds maturing in the future as a function
of time. Since any cashflow maturing in the future can be regarded as a discount bond, a yield curve
can be used to value any instrument that can be represented as a collection of cashflows.
In principle, it is also possible to price linear derivatives which have a price that only depends on
forward interest rates (for example, short futures, ignoring convexity adjustment) using forward
rates derived from the zero curve. In practice, however, this should be treated with caution since
the derived forward rate will depend on the method used in the construction of the zero curve much
more than the spot rates depend on it.
The information on interest rates that can be observed in the market comes in various forms. There
are deposit rates that give the discount bond prices directly, but these are mainly available only for

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maturities shorter than one year. Longer interest rates are embedded in the swap rates, FRA and
short future rates, and bond prices.
The objective of yield curve construction is to recover the discount bond price information from the
market information. The guiding principle is that when the quoted instruments are priced against
the zero coupon curve, the original quotes should be reproduced. Since this requirement does not
uniquely define the zero curve, some additional conditions on the functional form and the
smoothness of the curve have to be imposed.
Discount factors are the fundamental elements on which most valuation calculations are based. If
valuation needs for example an interest rate over a period in order to calculate the market value of
a caplet, it is the discount factors for the start and end dates of that period that are given as input to
valuation, and the desired interest rate is derived from these.

2.2.1.1 Input
The starting point of a bootstrap curve is a given set of interest rate related market information.
This information may consist of deposit prices, bond prices, or swap prices, for example.
In general, any instrument for which a liquid quote exists, and the theoretical price can be
calculated using only zero-coupon information, can be used.
Normally, it is assumed that all the instruments have the same risk offset. That is, the bootstrap
calculation produces a zero curve that is the sum of the risk-free rate and the spread.
Each price quote creates a set of cashflows, which are used as input for the bootstrap algorithm (see
2.2.1.3 Bootstrap algorithm on page 83).

2.2.1.1.1 Deposit quotes
A deposit quote generates a negative unit cashflow at spot, and a positive unit plus interest cashflow
at the maturity of the deposit. The interest amount corresponds to the interest type defined for the
deposit quote. The maturity date of the deposit follows the definition of the tenor of the deposit.

2.2.1.1.2 Swap quotes
A swap quote creates a negative unit cashflow at spot, and a positive unit cashflow at the maturity
of the swap. In addition, the fixed coupons (yearly, semi-annual, and so on) of the swap are
created, and their amounts calculated using the date basis and interest type of the quote.

2.2.1.1.3 FRA quotes
Each FRA creates a node point at its maturity. The bootstrap curve will have the property that the
discount factor over the FRA period is equal to the discount factor implied by the FRA quote.
The market quote of an FRA provides an estimate of the interest rate between two dates in the
future: the value date and the maturity date of the FRA. This can be converted into the forward price
on the value date of a zero-coupon bond on the maturity date of the FRA.
Given the market quote of the FRA (r) and the length of the FRA period (t) (calculated using the
appropriate date basis), the price on the value date (dv) of a discount bond that matures on the
maturity date (dm) of the FRA is given by:
Equation 2-118 FRA quotes

1
P ( d v ,d m ) = ------------1 + rt

2.2.1.1.4 Money market future quotes
Each MM future creates a node point at its maturity. The bootstrap curve will have the property that
the discount factor over the future period is equal to the discount factor implied by the future quote.
The market quote of the price of the future provides an estimate of the forward interest rate over
the period of the future. This can be converted into a discount factor between the start and the end
of the future period.

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Given the MM future quote (F), the corresponding interest rate over the period of the future is r
=100 - F, from which the discount price over the period can be calculated, either using the equation
for FRA quotes, or if the quote is of the discount type using:

P ( d v, d m ) = 1 – rt

Equation 2-119 Money market figure quotes

2.2.1.2 Bootstrap date basis and interest type
If a cashflow of a bootstrapping instrument (swap, bond, FRA, or MM future) does not fall on a node
point of the bootstrap curve, interpolation is needed to find the discount factor for the date in
question.

Note: The base date for interpolation is the spot date corresponding to the figure date of the
calculation.

2.2.1.3 Bootstrap algorithm
The bootstrap curve has the following properties:

•

The (zero coupon) market prices derived from the bootstrap curve will be equal to the given
market prices.

•

The bootstrap curve follows a given functional format and satisfies a smoothness condition
(bootstrap curve is continuous).

Within each interval, the chosen bootstrap rate is given by:
y ( t ) = ai + bi ( t – ti )

Equation 2-120 Bootstrap algorithm

where:

–

ai and bi are parameters calculated by the bootstrap process, and ti is the starting point of
the interval in question.

–

The default interest type is Continuous Yield.

2.2.1.3.1 Node points
The maturities of the input instruments are always used as node points.

2.2.1.4 Example: Bootstrapping zero-coupon curve
In this example, the zero-coupon curve is based on deposit quotes for the short end (for maturity
periods of up to one year) and swap quotes for the long end (for maturity periods of two years and
longer).

Note: The number of periods in the curves has been kept to a minimum in order to simplify the
illustration of the method. In reality, the curves would have many more periods defined.

•

Depo Quotes
For the deposit quotes, the following periods have been defined:
Tenor

Date Basis

Interest Type

Interest Structure

O/N

Actual/360

Periodic Rate

At Maturity

T/N

Actual/360

Periodic Rate

At Maturity

6M

Actual/360

Periodic Rate

At Maturity

1Y

Actual/360

Periodic Rate

At Maturity

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•

Swap Quotes
For the swap quotes, the following periods have been defined:

•

Period

Date Basis

Interest Type

Interest Structure

2Y

30/360

Periodic Rate

Annual

3Y

30/360

Periodic Rate

Annual

Parameters
Interpolation method is Linear (with flat rate extrapolation), based on Continuous Yield, date
basis 30/360.
The deposit and swap quotes are as follows:
Period

Deposit

Swap

Bid

Ask

Bid

Ask

O/N

4.8

4.88

T/N

4.78

4.84

6M

5.1

5.1

1Y

5.161

5.161

2Y

5.257

5.257

3Y

5.32

5.32

The yield curve uses the average of the bid and ask quotes as input. The deposit quotes are
already zero-coupon quotes, thus the resulting yield curve is simply the average of the deposit
bid and ask quotes:
Period

Deposit

Swap
Bid

Yield Curve

Bid

Ask

Ask

O/N

4.8

4.88

4.84

T/N

4.78

4.84

4.81

6M

5.1

5.1

5.1

1Y

5.161

5.161

5.161

2Y

5.257

5.257

3Y

5.32

5.32

Average

The remaining rates for the yield curve, for the 2Y and 3Y periods, have to be solved from the
existing rates using bootstrapping.

2.2.1.4.1 Finding the 2-year rate
The object of the zero-coupon curve calculation is to derive a set of rates that, when used to price
the fixed leg of the swap specified in the underlying swap curve, will price all the fixed-leg payments
at par on the spot date.

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To calculate the market value at spot MVspot of the fixed leg of a 2-year swap, the following
equation is used:
Equation 2-121 2-year swap: market value at spot MVspot

A × r 2s × cp 1 A × ( 1 + r 2s × cp 2 )
MV spot = -------------------------------- + ----------------------------------------------D 1Y
D 2Y
where:

–

A = nominal amount

–

r2s = 2-year swap rate

–

cp1 = period from the spot date to the first coupon date

–

cp2 = period from the first coupon date to the second coupon date

–

D1Y = discount factor for the period between the spot date and the 1 year date

–

D2Y = discount factor for the period between the spot date and the 2 year date.

If the swap is priced at par, then the market value at par is equal to the nominal amount:
Equation 2-122 Swap priced at par

A × r 2s × cp 1 A × ( 1 + r 2s ) × cp 2
A = -------------------------------- + ----------------------------------------------D 1Y
D 2Y
r 2s × cp 1 ( 1 + r 2s × cp 2 )
therefore: 1 = --------------------- + -----------------------------------D 1Y
D 2Y
Since the 1 year zero-coupon rate is already known (it is taken directly from the underlying deposit
quotes), the 1 year discount factor can be calculated.
This equation can be rearranged to solve D 2Y as follows:
Equation 2-123
( 1 + r 2s × cp 2 )
D 2Y = -------------------------------------------------------( 1 – ( r 2s × cp 1 ⁄ D 1Y ) )
The coupon periods cp1 and cp2 are calculated from the spot date and the swap coupon dates using
the date basis of the swap quote (30/360).
The date counts for the swap coupons are as follows:
Period

Date

Days from spot (30/360
date basis)

Days from spot
(Actual/360 date basis)

Spot

24-11-2000

0

0

1Y coupon

26-11-2001

362

367

2Y coupon

25-11-2002

721

731

Since the 30/360 date basis is used for the interpolation, the period lengths are:
cp 1 = 362 / 360
cp 2 = (721 - 362) / 360 = 359 / 360
The 2-year swap rate (from the swap quotes) r 2s = 5.257%.

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The discount factor for the 1 year rate, D1Y, can be calculated from the 1 year rate (5.161%), using
the date basis (Actual/360) and interest type (Periodic Rate) defined for that tenor:
5.161 367
D 1Y = ⎛ 1 + ------------- × --------- ⎞ = 1.05261353
⎝
100 360 ⎠
The discount factor D2Y then becomes:
( 1 + 0.05257 × 359 ⁄ 360 )
D 2Y = --------------------------------------------------------------------- = 1.1080711
× 362 ⁄ 360 ⎞ ⎞
⎛ 1 – ⎛ 0.05257
----------------------------------------------⎝
⎝
⎠⎠
1.0526135
From this the 2-year zero-coupon rate r2Y can be calculated, using the date basis (30/360) and
interest type (Compound Yield) defined for that tenor:
( 1 + r 2Y )

( 721 ⁄ 360 )

= D 2Y

therefore: r 2y = 1.1080711

( 360 ⁄ 721 )

– 1 = 0.05257465

2.2.1.4.2 Finding the 3-year rate
The zero-coupon curve must also price the 3-year swap at par, and so the 3 year discount factor D3Y
for the period from the spot date to the 3-year date must satisfy the following condition:
r 3s × cp 1 r 3s × cp 2 ( 1 + r 3s × cp 3 )
1 = --------------------- + --------------------- + -----------------------------------D 1Y
D 2Y
D 3Y
where:

–

r3s = the 3-year swap rate

–

cp1 = the period from the spot date to the first coupon date

–

cp2 = the period from the first coupon date to the second coupon date

–

cp3 = the period from the second coupon date to the third coupon date

–

D1Y = the discount factor for the period between the spot date and the 1 year date:

–

D2Y = the discount factor for the period between the spot date and the 2 year date:

This equation can be rearranged to solve D3Y as follows:
( 1 + r 3s × cp 3 )
D 3Y = -------------------------------------------------------------------------------------------------------( 1 – ( r 3s × cp 1 ⁄ D 1Y ) – ( r 3s × cp 2 ⁄ D 2Y ) )
The coupon periods cp1, cp2, and cp3 are calculated from the spot date and the swap coupon dates
using the date basis defined for the bootstrapping (30/360).
The following date counts for the swap instrument coupons are as follows:
Period

Date

Days from spot
(30/360 date basis)

Days from spot
(Actual/360 date basis)

Spot

24-11-2000

0

0

1Y coupon

26-11-2001

362

367

2Y coupon

25-11-2002

721

731

3Y coupon

24-11-2003

1080

1095

Since the 30/360 date basis is used for the interpolation, the period lengths are:
cp1 = 362 / 360

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cp2 = (721 - 362) / 360 = 359 / 360
cp3 = (1080 -721) / 360 = 359 / 360
The 3-year swap rate (from the swap quotes) r3s = 5.32%.
The discount factors for the 1 year and 2 year rates (D1Y and D2Y) have already been calculated:
D1Y = 1.0526135
D2Y = 1.1080711
So the discount factor D3Y becomes:
( 1 + 0.0532 × 359 ⁄ 360 )
D 3Y = ---------------------------------------------------------------------------------------------------------------------------- = 1.1683699
0.0532
× 362 ⁄ 360 ⎞ ⎛ 0.0532
× 359 ⁄ 360 ⎞ ⎞
⎛ 1 – ⎛ --------------------------------------------------------------------------------------⎝
⎝
⎠ –⎝
⎠⎠
1.0526135
1.1080711
From this the 3-year zero-coupon rate r3Y, can be calculated using the date basis 30/360 and the
interest type Continuous Yield defined for that tenor:
( 1 + r 3Y )

( 1080 ⁄ 360 )

= D 3Y

therefore: r 3Y = 1.1683699

( 360 ⁄ 1080 )

– 1 = 0.05323865

The complete zero-coupon curve is shown in the table below:
Period

Deposit

Swap
Bid

Yield Curve

Bid

Ask

Ask

Average

O/N

4.8

4.88

4.84

T/N

4.78

4.84

4.81

6M

5.1

5.1

5.1

1Y

5.161

5.161

5.161

2Y

5.257

5.257

5.257465

3Y

5.32

5.32

5.323865

2.2.1.4.3 Finding the 3-year rate
The zero-coupon yield curve must also price the 3-year swap at par, and so the 3 year discount
factor D3Y for the period from the spot date to the 3-year date must satisfy the following condition:
r 3s × cp 1 r 3s × cp 2 ( 1 + r 3s × cp 3 )
1 = --------------------- + --------------------- + -----------------------------------D 1Y
D 2Y
D 3Y
where:

–

r3s = the 3-year swap rate

–

cp1 = the period from the spot date to the first coupon date

–

cp2 = the period from the first coupon date to the second coupon date

–

cp3 = the period from the second coupon date to the third coupon date

–

D1Y = the discount factor for the period between the spot date and the 1 year date:

–

D2Y = the discount factor for the period between the spot date and the 2 year date:

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This equation can be rearranged to solve D3Y as follows:
( 1 + r 3s × cp 3 )
D 3Y = -------------------------------------------------------------------------------------------------------( 1 – ( r 3s × cp 1 ⁄ D 1Y ) – ( r 3s × cp 2 ⁄ D 2Y ) )
The coupon periods cp1, cp2, and cp3 are calculated from the spot date and the swap coupon dates
using the date basis defined for the bootstrapping (30/360).
The following date counts for the swap instrument coupons are as follows:
Period

Date

Days from spot
(30/360 date basis)

Days from spot
(Actual/360 date basis)

Spot

24-11-2000

0

0

1Y coupon

26-11-2001

362

367

2Y coupon

25-11-2002

721

731

3Y coupon

24-11-2003

1080

1095

Since the 30/360 date basis is used for the bootstrapping, the period lengths are:
cp1 = 362 / 360
cp2 = (721 - 362) / 360 = 359 / 360
cp3 = (1080 -721) / 360 = 359 / 360
The 3-year swap rate (from the swap quotes) r3s = 5.32%.
The discount factors for the 1 year and 2 year rates (D1Y and D2Y) have already been calculated:
D1Y = 1.0526135
D2Y = 1.1080711
So the discount factor D3Y becomes:
( 1 + 0.0532 × 359 ⁄ 360 )
D 3Y = ---------------------------------------------------------------------------------------------------------------------------- = 1.1683699
× 362 ⁄ 360 ⎞ ⎛ 0.0532
× 359 ⁄ 360
⎛ 1 – ⎛ 0.0532
-------------------------------------------– -------------------------------------------- ⎞ ⎞
⎝
⎝
⎠ ⎝
⎠⎠
1.0526135
1.1080711
From this the 3-year zero-coupon rate r3Y, can be calculated using the date basis 30/360 and the
interest type Continuous Yield defined for that tenor:
( 1 + r 3Y )

( 1080 ⁄ 360 )

= D 3Y

therefore: r 3Y = 1.1683699

( 360 ⁄ 1080 )

– 1 = 0.05323865

The complete zero-coupon curve is shown in the table below:
Period

Deposit

Swap

Bid

Ask

O/N

4.8

4.88

4.84

T/N

4.78

4.84

4.81

6M

5.1

5.1

5.1

1Y

5.161

5.161

5.161

2Y

88

Bid

Yield Curve

5.257

Ask

5.257

Average

5.257465

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Period

Deposit
Bid

Swap
Ask

3Y

Yield Curve

Bid

Ask

Average

5.32

5.32

5.323865

2.2.1.5 Example: Yield Curve calculated using bonds
Consider this example of a bootstrap yield curve calculated using bond prices, with the following
definition:
Data

Value

Spot Days

2

Calculation Date

18-07-2005

Effective Date

20-07-2005

For the deposit, there is the following data:
Periods

Dates

Date Basis

Rate

Discount Factor

0/N

19-07-2005

Actual/360

4

0.9998889012

T/N

20-07-2005

Actual/360

4.1

0.9998861241

1W

27-07-2005

Actual/360

4.12

0.9989747482

1M

22-08-2005

Actual/360

4.14

0.9959952360

2M

20-09-2005

Actual/360

4.15

0.9926801325

3M

20-10-2005

Actual/360

4.16

0.9892581249

6M

20-01-2006

Actual/360

4.17

0.9789111777

9M

20-04-2006

Actual/360

4.18

0.9689484804

1Y

20-07-2006

Actual/360

4.19

0.9590334329

In addition, two bond instruments are used as input for the curve.

•

The cashflow structure of the first bond is:
Amount

Value Date

Time

-99.014305

20-07-2005

0.005479452

5.0694444

08-04-2006

0.723287671

5.069444

08-04-2007

1.723287671

100

08-04-2007

1.723287671

The first cashflow is the dirty price of the bond at the effective date.

•

The cashflow structure of the second bond is:
Amount

Value Date

Time

-98.01367611

20-07-2005

0.005479452

4.84639

08-04-2006

0.723287671

4.84639

08-04-2007

1.723287671

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Amount

Value Date

Time

4.85967

08-04-2008

2.726027397

4.84639

08-04-2009

3.726027397

100

08-04-2009

3.726027397

The first cashflow is the bond dirty price at the effective date.
The assumption is that the zero curve is piecewise linear between two node points. In this specific
case, it is assumed that the zero rate is continuously compounding and the date basis is Actual/365.
The maturity of the instrument is used as node points in the bootstrap algorithm: see 2.2.1.5.1
Scenario 1 - Maturity of bonds as node points on page 90.

2.2.1.5.1 Scenario 1 - Maturity of bonds as node points
For the period [20/07/2006,08/04/2007]
For the first bond, the coupon date 08-04-2006 falls between the 6M and the 9M periods. The
discount factor is converted into continuous compound rate and the rate is interpolated to derive the
discount factor at 08-04-2006:
Date

Discount Factor

Time

Rate

20-01-2006

0.50958904

0.041826583

0.9789111777

08-04-2006

0.72328767

0.041730381

0.9702678903

20-04-2006

0.75616438

0.041715581

0.9689484804

Since the zero rate is piecewise linear between the node points, that is, between one year and bond
maturity [20/07/2006,08/04/2007], the one year discount factor needs to be converted into a
continuous compound rate:
Date

Discount Factor

Time

Rate

20-07-2006

0.959033433

1.005479452

0.041601389586

Let us denote the slope by b, so the Pricing equation for the first bond can be written as:
– 99.0143 × 0.99977504 =
5.069444 × 0.97026789 +
105.069444 × exp ( – ( 0.04160139 + b × ( 1.72328 – 1.0054794 ) ) × 1.72328 )
From this we can deduce that b = 0.031411691
The rate and the discount factor at the first bond maturity are as follows:
0.04160139 + b × ( 1.7232877 – 1.0054794 ) = 0.06414896
exp ( – ( 0.04160139 + b × ( 1.7232877 – 1.0054794 ) ) × 1.7232877 ) = 0.89534415

For the period [08/04/2007,08/04/2009]
At the beginning of the period, we have:
Date

Discount Factor

Time

Rate

08-04-2007

0.895344149

1.723287671

0.064148959214

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Again, since the zero rate is a piecewise linear function, the slope of the line needs to be found so
that the Pricing equation for the second bond is satisfied:
– 98.01368 × 0.99977504 =
4.84639 × 0.97026789 + 4.84639 × 0.89534415 +
4.85967 × exp ( ( – ( 0.06414896 + b × ( 2.7260274 – 1.7232877 ) ) × 2.7260274 ) ) +
104.84639 × exp ( ( – ( 0.06414896 + b × 3.7260274 – 1.7232877 ) ) × 3.7260274 ) )
The slope b is then calculated as -0.00364043.
The time between the effective date 18-07-2005 and the 2Y node point 20-07-2007 is
2.005479452.
The 2Y rate and discount factor at the value date 20-07-2007 can be calculated as:
0.06414896 + b × ( 2.0054795 – 1.7232877 ) = 0.06312166
exp ( – ( 0.06414896 + b × ( 2.0054795 – 1.7232877 ) ) × 2.0054795 ) = 0.88109556
The time between the 18-07-2005 and the maturity of the second bond (08-04-2009) is
3.726027397.
The rate and the discount factor are then:
0.06414896 + b × ( 3.7260274 – 1.7232877 ) = 0.05685813
exp ( – ( 0.06414896 + b × ( 3.7260274 – 1.7232877 ) ) × 3.7260274 ) = 0.80908206

For the period [08/04/2009,

∞ +[

08-04-2009 is the last node point.
The algorithm makes a flat extrapolation based on the continuous compound rate (that is,
0.056858126).
Therefore, the 5Y discount factor corresponding to 20-07-2010 (that is, for time 5.008219178), is:
exp ( – ( 0.05685813 ) × 5.0082192 ) = 0.75219629

2.2.2 Basis swaps
2.2.2.1 Tenor Basis Swap Curve
This section describes the algorithm used in converting tenor basis swap spreads into discount
factors. The input to the algorithm consists of a base yield curve and a series of tenor basis spread
quotes, resulting in a tenor basis swap curve. We search for a series of discount factors such that
the value of the tenor basis swap is at par. The estimation curve method is used in tenor basis
swaps, i.e. the underlying curve is used for discounting, and the derived tenor basis swap curve for
the estimation of the swap coupon amounts (for the leg for which the spread is quoted).

2.2.2.1.1 Input
•

Spot date

•

Basis swap quotes: These are tuples (start date, maturity, spread, coupon frequency), with
some implicit rules for the generation of coupons.
Discount curve: A fixed curve that provides discount factors ( Dd ) for required dates.

•
•

Coupon estimation: This is a function E [ D 1, D 2, s, ϒ ] that returns a coupon estimate, given two
discount factors, coupon period, and a spread.

The bootstrap algorithm input is generated from this data.

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For each swap quote we generate the coupon date data (see Equation 2-124 on page 92),
corresponding to the start, end, and payment dates, and the length of the coupon period of the ith
coupon of the jth quote.
Equation 2-124 Coupon date data

We shall also need the discount factors derived from the discount curve for all payment dates:
Equation 2-125 Discount factors for all payment dates

Given the interpolation date basis, all dates are transformed into times from spot date, so that we
have coupon time triplets (Equation 2-126 on page 92) and swap maturity times (Equation 2-127 on
page 92).
Equation 2-126 Coupon time triplets

Equation 2-127 Swap maturity times

2.2.2.1.2 Algorithm
Initially, set T, the last known node point, to zero (i.e. spot).
1. Choose the smallest maturity greater than the last known node point T, i.e. choose J:
Equation 2-128 Smallest maturity

There could, in principle be more than one, but start by assuming that J is unique.
2. For all i such that t ei ≤ T , calculate the coupon estimate based on the known part of the
J
bootstrap curve:
Equation 2-129 Coupon estimate

Where some interpolation may be needed, use the interpolation method specified for the derived
curve.
3. Calculate the stub price of the swap as the sum of the known coupons of each leg:
Equation 2-130 Stub price of the swap

Note: For discounting, we use the discount curve that was given as input. The term Dd [ TJ ] can be
interpreted as the discounted value of the redemption payment, in which case the other

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leg has value 1. Likewise, we may interpret the term 1 – Dd [ T J ] as the value of the other leg
in case there is no principal exchange.
4. Initialize iteration: Create a new node point for the bootstrap curve at T J , with initial value
Dn = 0.00001
5. For each coupon with t ei J > T , calculate the estimate based on D e [ T ] (known) and Dn , see
Equation 2-129 on page 92.
where the discount factors may have to be interpolated from D e [ T ] and Dn , using the
interpolation method specified for the derived curve.
Calculate the value of the swap:
Equation 2-131 Swap value

If P n is positive, let D p = D n , and P p = P n . If P n is negative, stop.
6. Repeat step 5. on page 93 using Dn = 1 .
If P n is negative let D l = D n and P l = P n . If P n is positive, stop.
7. Generic step: Use a goal seek algorithm and the method described in step 5. on page 93 to find
D n so that the value of the Jth swap is zero.
8. Set T = T J and create new node D e [ T J ] = D n . If T < max j [ T j ] , then go to step 1. on page 92,
otherwise stop.

2.2.2.2 Cross Currency Basis Swap Curve
This section describes the algorithm used in converting cross currency basis swap spreads into
discount factors. The input to the algorithm consists of a base yield curve and a series of cross
currency basis spread quotes, resulting in a cross currency basis swap curve. We search for a series
of discount factors such that the value of the cross currency basis swap is at par. The discount curve
method is used in cross currency basis swaps, i.e. the underlying curve is used for estimating the
swap coupon amounts, and the derived cross currency basis swap curve for discounting (the leg for
which the spread is quoted).

2.2.2.2.1 Input
•

Spot date

•

Cross currency basis swap quotes: These are tuples (start date, maturity, spread, coupon
frequency), with some implicit rules for the generation of coupons.

•

Estimation curve: A fixed curve that provides discount factors ( D e ) for the required dates.
Coupon estimation: This is a function E [ D 1, D 2, s, ϒ ] that returns a coupon estimate, given two
discount factors, coupon period, and a spread.

•

The bootstrap algorithm input is generated from this data.
For each swap quote, we generate the coupon date data (see Equation 2-124 on page 92),
corresponding to the start, end, and payment dates; and the length of the coupon period of the ith
coupon of the jth quote.
Then, using the estimation method, together with the estimation curve discount factors for the start
and end dates of the coupon,

and

, we can create the corresponding coupons using

Equation 2-129 on page 92.

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Given the interpolation date basis, all dates are transformed into times from spot date, so that we
have coupon payment times

and swap maturity times (Equation 2-127 on page 92).

2.2.2.2.2 Algorithm
Initially, set T, the last known node point, to zero (i.e. spot).
1. Choose the smallest maturity greater than the last node point: That is, choose J so that
T J = minj [ T j > T ] .
There could, in principle be more than one, but start by assuming that J is unique.
2. Calculate the stub price of the swap as the sum of the known discounted coupons minus the
known price of the other leg (assumed at par, i.e. principals are exchanged).
Equation 2-132 Discount curve: stub price

3. Initialize iteration: Create a new node point for the bootstrap curve at T J , with initial value
D n = 1.0 .
4. Calculate the value of swap:
Equation 2-133 Discount curve: swap value

where the discount factors may have to be interpolated from D d [ T ] and D n , using the
interpolation method specified for the derived curve. The last term is the principal payment: in
this method, we always assume that principals are exchanged.
If P n is positive, let D p = D n and P p = P n . If P n is negative, stop.
5. Repeat step 4. on page 94 using D n = 0.0000001 .
If P n is negative, let let D l = D n and P l = P n . If P n is positive, stop.
6. Generic step: Use a goal seek algorithm and the method described in step 4. on page 94 to find
D n so that the value of the Jth swap is zero.
7. Set T = T J and create new node D d [ T J ] = D n . If T < maxj [ Tj ] go to step 1. on page 94, otherwise
stop.

2.2.2.3 Basis swap bootstrapping
This section describes the algorithm used in converting basis swap spreads into discount factors.
Two different approaches are presented: estimation curve bootstrapping and discount curve
bootstrapping.
In both approaches, the input to the algorithm consists of an underlying zero curve and a series of
basis spread quotes. In both algorithms, we search for a series of discount factors such that the
value of the calculated spread leg is at par. (Section 2.2.2.3.3 Non-par market value on page 97
addresses the case when the other leg is not at par.)
The estimation curve method is used in tenor basis swaps, while the discount curve method is used
in cross currency basis swaps.

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2.2.2.3.1 Estimation curve bootstrapping
This section describes the bootstrap algorithm for estimation curve bootstrapping. In estimation
curve bootstrapping, we use the underlying curve for discounting, and the bootstrapped curve for
the estimation of the swap coupon amounts. This method is used in tenor basis swaps.

Input data generation
•

Spot date

•

Basis swap quotes: These are tuples (start date, maturity, spread, coupon frequency), with
some implicit rules for the generation of coupons.

•

Discount curve: A fixed curve that provides discount factors (Dd) for the required dates.

•

Coupon estimation: This function
discount factors, coupon period, and a spread.

returns a coupon estimate, given two

The bootstrap algorithm input is generated from this data. For each swap quote, we generate the
coupon date data (

), corresponding to the start, end, and payment dates and the

length of the coupon period of the ith coupon of the Jth quote.
We shall also need the discount factors derived from the discount curve for all payment dates:
.
Given the interpolation date basis, all dates are transformed into times from the spot date, so that
we have coupon time triplets (

), and swap maturity times (

).

The algorithm
Initially, set T, the last known node point, to zero (i.e. spot).
1. Choose the smallest maturity greater than the last known node point T. That is, choose J so that
TJ=minj[Tj > T]. There could, in principle, be more than one, but start by assuming that J is
unique.
2. For all i such that
bootstrapped curve:

, calculate coupon estimate based on the known part of the
Equation 2-134 Estimation curve bootstrapping: coupon estimate

–

If interpolation is needed, use the interpolation method specified for the bootstrapped curve.

3. Calculate the stub price of the swap as the sum of the known coupons of each leg:
Equation 2-135 Estimation curve bootstrapping: calculated stub price of the swap

Note: For discounting, we use the discount curve given as input. The term can be interpreted as
the discounted value of the redemption payment, in which case the other leg has value
Dd[TJ]. Similarly, we may interpret the term as the value of the other leg in case there is
no principal exchange.

4. Initialize iteration: Create a new node point for the bootstrap curve at TJ, with initial value
Dn=0.00001

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5. For each coupon with

, calculate the estimate based on De[T] (known) and Dn:
Equation 2-136 Estimation curve bootstrapping: calculate the estimate

–

Where the discount factors may have to be interpolated from De[T] and Dn, using the
interpolation method specified for the bootstrapped curve, calculate the value of swap:
Equation 2-137 Estimation curve bootstrapping: calculate the value of the swap

–

If the value is negative, stop. Otherwise, let Dp=Dn and Pp=Pn

6. Repeat step 5. on page 96 using Dn=1. If the resulting price is positive, stop. Otherwise, let and
Dl=Dn and Pl=Pn
7. Generic step: Use a goal seeker algorithm and the method described in step 5. on page 96 to
find Dn so that the value of the Jth swap is zero.
8. Set T = TJ and create the new node De[TJ]=Dn. If T < maxj[Tj] go to step 1. on page 95,
otherwise stop.

2.2.2.3.2 Discount curve bootstrapping
This section describes the bootstrap algorithm for discount curve bootstrapping. In discount curve
bootstrapping these roles are exchanged: the underlying curve generates the coupon estimates, and
the bootstrapped curve is used in discounting. The discount curve method is used in cross currency
basis swaps.

Input data generation
•

Spot date

•

Basis swap quotes: These are tuples (start date, maturity, spread, coupon frequency), with
some implicit rules for the generation of coupons.

•

Estimation curve: A fixed curve that provides discount factors (De) for required dates.

•

Coupon estimation: This is a function
two discount factors, coupon period, and a spread.

that returns a coupon estimate, given

The bootstrap algorithm input is generated from this data. For each swap quote, we first generate
the coupon date data (
), corresponding to the start, end, and payment dates, and the
length of the coupon period ith of the coupon jth of the quote (sj). Then, using the estimation
method with the estimation curve discount factors for the start and end dates of the coupon,
and

, we can create the corresponding coupons using the following equation:
Equation 2-138 Discount curve bootstrapping: creating the coupons

Given the interpolation date basis, all dates are transformed into times from spot date, so that we
have coupon payment times (

96

) and swap maturity times (

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The algorithm
Initially, set T, the last known node point, to zero (i.e. spot).
1. Choose the smallest maturity greater than the last node point: That is, choose J so that
TJ=minj[Tj>T]. There could, in principle be more than one, but start by assuming that J is
unique.
2. Calculate the stub price of the swap as the sum of the known discounted coupons minus the
known price of the other leg (assumed at par, i.e. the principals are exchanged).
Equation 2-139 Discount curve bootstrapping: stub price

3. Initialize iteration: Create a new node point for the bootstrap curve at Tj, with initial value
Dn=1.0.
4. Calculate the value of swap:
Equation 2-140 Discount curve bootstrapping: value of the swap

–

Where the discount factors may have to be interpolated from Dd[T] and Dn, using the
interpolation method specified for the bootstrapped curve. The last term is the principal
payment: in this method, we always assume that the principals are exchanged.

–

If the value is negative, stop. Otherwise, let Dp=Dn and Pp=Pn.

5. Repeat step 4. on page 97 using Dn=0.0000001. If the resulting price is positive, stop.
Otherwise, let Dl=Dn and Pl=Pn.
6. Generic step: Use a goal seeker algorithm and the method described in step 4. on page 97 to
find Dn so that the value of the swap is zero.
7. Set T=TJ and create the new node Dd[TJ]=Dn. If T < maxj[Tj]. If go to step 1. on page 97,
otherwise stop.

2.2.2.3.3 Non-par market value
The bootstrapping algorithm described in section 2.2.2.3 Basis swap bootstrapping on page 94
applies to the basic setup, where we want to bootstrap a new curve (estimation or discounting) for
the spread leg, and assume that the other leg (i.e the leg whose value is taken as an input to the
bootstrapping algorithm) of the swap is valued at par.
There are cases when this assumption is no longer valid:

•

Case 1. Instead of spread leg, we calculate the new curve for the flat leg. In this case the other
leg is the spread leg, which is not at par.

•

Case 2. We want to use two different curves for estimation and discounting of the other leg,
which will then have a non-par value.

In these cases the value of the other leg needs to be calculated: We have to generate its cashflows
(using the estimation curve defined for the other leg) and discount them (using the discount curve
defined for the other leg). The coupon structure of the other leg may differ from the structure of the
calculated leg and is given in IR Quote and Yield Curve Editor's Tenor page. The estimation and
calculation curves are given in IR Quote and Yield Curve Editor's Other Leg Yield Curves page once the
optional feature Other Leg Yield Curves is selected. For more information about this editor, see TRM
User Guide.

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Using the same notation as above, but with bars above the symbols to indicate that they refer to the
other leg and are known in advance, the value of the other leg becomes:
Equation 2-141 Non-par market value

This value has to replace the value in Equation 2-135 on page 95, which becomes:
Equation 2-142 Non-par market value

Otherwise, bootstrapping follows the same steps as described previously.

2.2.2.4 Interpolation before first swap quote
The first calculated node of a basis swap curve is usually at one year. Without any additional
information, one would use the interest rate of the bootstrapped curve at the first node for all dates
before it. However, it is reasonable to assume that instead of being flat, the bootstrapped curve
should follow the underlying curve.
To achieve this, the yield creation algorithm creates an additional virtual quote for each gap of the
underlying curve that is no closer than 14 days before the first actual quote. Each virtual quote has
the same value as the first actual quote, but they are treated as deposits instead of swaps.
The virtual quotes are included in the bootstrapping process, and their presence causes the
bootstrapped curve to follow the shape of the underlying curve also before the first spread quote.

2.2.3 Yield Curve interpolation
An interpolation method is a way of estimating the shape of a yield curve between points for which
quotes exist. TRM performs interpolation to calculate these rates from the closest known quotes
according to the variables specified in the interpolation method.
The default interpolation method of yield curves is Linear, Flat Rate Extrapolation with date basis
Actual/365 and interest type Continuous Yield.

2.2.3.1 Interpolation periods
The starting point of yield curve interpolation is a set of known yields for a number of periods (the
node points), all having the same start date (spot date). The objective is to find the discount factor
between the spot date and another date for which there is no direct data.
All input quotes are first converted into discount factors between the spot date and the end date of
the quote period (or start date, if the quote is for a period before the spot).
Quotes that do not start or end at the spot date can be used if there is also a series of quotes
starting from or ending at the spot date (for example, T/N and S/N in markets where the spot date is
today). By combining the discount factors from the spot to the end dates of the forward quotes, a
synthetic quote from the spot can be obtained. This can then be used in the same way as regular
quotes from the spot.
Before the first input period and after the last, extrapolation is required. The methods required are
specified in the interpolation method definition.

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2.2.3.2 Interpolation date basis
The interpolation algorithm uses the period lengths, between the common starting point of all
periods and the end point of each period, as input data.
When the interpolation result is requested for a target date, the period length between the common
start date and the target date is needed. To calculate these period lengths, a date basis is required.
The same date basis is used for all periods, regardless of the date basis used for the discount factor.
The date basis specified in the interpolation method definition is used both for the calculation of the
interpolation period lengths and to convert discount factors into the interpolation rate (except, of
course, if the interpolation rate is a discount factor, in which case, conversion is not needed).

2.2.3.3 Interpolation over spot date
When we seek a discount factor for a date after spot and before the first forward quote (most often
the one week quote), the nearest known discount factor before the target date is for spot (D=1).
However, that discount factor cannot be converted into rate, since the period length is zero.
Therefore, the previous existing quote (usually, O/N) is used as if it were the quote for the
zero-length period from spot to spot.

2.2.3.4 Type of interpolation
2.2.3.4.1 Linear
To calculate the interest rate for a date for which no direct quote exists, linear interpolation is used
to calculate the interest rate rm for the period tm (to spot date) between the closest quoted periods
t1 and t2 such that t1 < tm < t2.
Interest
%

r2
rm
r1

Period

t1

tm

t2

1. The rates r1 and r2 need to be converted to the correct interest type before they can be used in
the linear interpolation.
To do this, two calculations need to be done:
a. Calculate the discount factors D1 and D2 for the periods t1 and t2.
For example, if the interest type is Annually Compounded Rate and the date basis is Actual/365,
then the discount factors D1 and D2 are calculated as follows:
Equation 2-143 Linear interpolation: Discount factor D1
–d
--------1-

r 1 365
D 1 = ⎛ 1 + ---------⎞
⎝
100⎠

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and
Equation 2-144 Linear interpolation: Discount factor D2
–d
--------2-

r 2 365
D 2 = ⎛⎝ 1 + ---------⎞⎠
100
where d1 and d2 are the actual number of days between the spot date and the period end
dates for the periods t1 and t2.
b. From these discount factors D1 and D2, the rates can be calculated with the correct interest
type (r1C and r2C). The interest type and date basis that you selected for the interpolation of
the yield curve will be used.
Here, we use the interest type Continuous Yield date basis Actual/365:
Equation 2-145 Linear interpolation: interest type r1C

– 100
r 1C = ------------ 1nD 1
t1
and
Equation 2-146 Linear interpolation: interest type r1C

– 100
r 2C = ------------ 1nD 2
t2
2. Linear interpolation is then used to calculate the rate rmc.
The date basis used is the one selected in the interpolation setup. The interpolation setup is
described in the TRM User Guide.
This rate will have the same interest type as r1C and r2C:
Equation 2-147 Linear interpolation: calculated rate rmc

( t 2 – t m )r 1C + ( t m – t 1 )r 2C
r mc = ---------------------------------------------------------------t2 – t1
3. The discount factor Dm, from the cashflow value date to the spot date, is calculated from the
linearly interpolated rate rmc.
The form of the equation is based on the date basis and interest type of the linear interpolation
method.
For continuous yield:
Equation 2-148 Linear interpolation: Continuous Yield

Dm = e

– r mc
-----------t m
100

4. The discount factor Dm derived from the linearly interpolated rate rmc is multiplied by the
discount factors for the period from the spot date to the valuation date, using market quotes.
For example, if the number of spot days is 2, we would use DO/N and DT/N:
D = DO/NDT/NDm

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Example: Interest rate interpolation
In this example, the interest rate for a cashflow at 1.5 years is calculated using two IR quotes at 1
and 2 years.

Note: In this example, all calculated amounts are rounded.
Data

Symbol

Value

Value Date

22-11-2000

Spot Days

2

Spot Date

24-11-2000

IR quote (1Y)

r1

5.161%

Date basis of 1Y quote

d/B

Actual/360

Number of days from spot date to 1Y cashflow on 26-11-2001

367

Interest type of 1Y quote

Periodic

IR quote (2Y)

r2

5.2575%

Date basis of 2Y quote

d/B

30/360

Number of days from spot date to 2Y cashflow on 25-11-2002

721

Interest type of 2Y quote

Annually Compounded Rate

O/N quote

rO/N

4.84%

T/N quote

rT/N

4.81%

Date basis of O/N and T/N quotes

d/B

Actual/360

Instrument date basis

d/B

Actual/360

Number of days from spot date to 1.5Y on 24-05-2002 using
instrument date basis

546

For this example, it is assumed that a linear interpolation method has been defined with the date
basis Actual/365 and interest type of Continuous Yield.

•

Step 1 - Convert the reference rates to continuous yield rates
To convert the reference rates r1 and r2 to continuous yield rates, first the discount factors for
these rates is calculated, using the date bases and interest types defined for these two quotes.

–

The 1Y quote has an Actual/360 date basis and Periodic Rate interest type.
This gives the following formula:
Equation 2-149 Example: Interest Rate Interpolation

r1
d1
D 1 = ⎛ 1 + --------- × ---------⎞
⎝
100 360⎠

–

–1

5.161 367 –1
= ⎛ 1 + ------------- × ---------⎞ = 0.950016
⎝
100 360⎠

The 2Y quote has a 30/360 date basis and Annually Compounded Rate interest type.
This gives the following formula:
Equation 2-150 Example: Interest Rate Interpolation
–d
--------2-

r 2 360
5.2575
D 2 = ⎛⎝ 1 + ---------⎞⎠
= ⎛⎝ 1 + ----------------⎞⎠
100
100

–
721----------360

= 0.902469

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–

Next, the continuous yield rates r1C and r2C are calculated from these discount factors, using
the interpolation method date basis Actual/365 and interest type Continuous Yield):
Equation 2-151 Example: Interest Rate Interpolation

– 100
– 100
r 1C = ------------ 1nD 1 = ---------------------- 1n ( 0.950016 ) = 5.0997
t1
367 ⁄ 365
Equation 2-152 Example: Interest Rate Interpolation

– 100
– 100
r 2C = ------------ 1nD 2 = -------------------------- 1n ( 0.902469 ) = 5.124
t2
( 731 ) ⁄ 365

•

Step 2 - Linear interpolation
Linear interpolation with the recalculated reference rates from the first step is used to calculate
the continuous yield rate rmc.

Note: tm is recalculated using the interpolation method date basis Actual/365.
Equation 2-153 Linearly interpolated rate rmc

r mc

•

– 546
546 – 367
⎛ 731
------------------------⎞ 5.0997 + ⎛ ------------------------⎞ 5.124
⎝ 365 ⎠
⎝ 365 ⎠
( t 2 – t m )r 1C + ( t m – t 1 )r 2C
= ---------------------------------------------------------------- = ------------------------------------------------------------------------------------------------ = 5.11165
t2 – t1
– 367-⎞
⎛ 731
----------------------⎝ 365 ⎠

Step 3 - Discount factor to spot date (Dm)
The discount factor Dm, from the cashflow value date to the spot date, is calculated from the
linearly interpolated rate rmc from the previous step (Equation 2-153 on page 102). The
equation in this example is based on the interpolation interest type Continuous Yield and date
basis Actual/365:
Equation 2-154 Discount factor to spot date

Dm = e

•

r mc ⎞
- t
– ⎛ -------⎝ 100⎠ m

= e

5.11165
– ⎛⎝ -------------------⎞⎠ ( 546 ⁄ 365 )
100

= 0.926386

Step 4 - Discount factor to valuation date (D)
To get the discount factor to the valuation date, the discount factor Dm to the spot date is
multiplied by the discount factors for the period from the spot date to the valuation date, DO/N
and DT/N. The number of spot days is 2.
This gives the following equation:
D = DO/NDT/NDm
The discount factors DO/N and DT/N are calculated from the O/N and T/N rates, using the date
basis and interest type defined for the quotes.
In this case, they have both been defined with date basis Actual/360 and interest type Periodic

Rate.

Equation 2-155 Discount factors DO/N

4.84
1 –1
D O ⁄ N = ⎛ 1 + ---------- × ---------⎞ = 0.9998656
⎝
100 360⎠

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and
Equation 2-156 Discount factors DT/N

4.81
1 –1
D T ⁄ N = ⎛⎝ 1 + ---------- × ---------⎞⎠ = 0.9998664
100 360
D = DO/NDT/NDm = 0.926386 * 0.9998656 * 0.9998664 = 0.926137
If a discount factor between two dates is needed, neither of which is the spot, the two discount
factors between the spot and the two days in question are calculated, and divided one by the
other.

2.2.3.4.2 Cubic splines interpolation
The interpolation method is defined by choosing the optional feature Yield Curve Interpolation Setup,
and then, in the Interpolation page, by selecting one of the interpolation methods. Choices for cubic
spline are: Hermite Spline (Two Points), Hermite Spline (Three Points) or Cubic Spline. The first two refer to
Hermite Spline ( Hermite spline on page 105) with slopes at node points (mi) defined by either a
two-point difference or a three-point difference, as explained in section Setting the slopes at node
points on page 106. The third option (Cubic Spline) corresponds to classic spline described in section
Classic spline on page 104. For more information about setting up yield curves, see TRM User Guide.
The input to the interpolation module is a set of points, usually giving the value of interest rate at a
set of times. The task of the interpolator is to provide the value of the dependent variable (e.g.
interest rate) at an arbitrary point, i.e. to extend a function defined at a restricted number of points
to a function defined everywhere (or more typically, for non-negative numbers when we are dealing
with time as an independent variable). The interpolation function will go through the points given as
input.
In the quasi-cubic spline interpolation, we also require that the interpolation function be continuous
and differentiable at all points. Furthermore, a classic spline will have a continuous second derivative
at all points.
The yield curve interpolation is used in two different settings: where the input points are known in
advance and when the shorter end of the curve is needed to construct new points in the longer end.
The latter situation takes place in bootstrapping when there are coupons falling on dates, which are
not maturity dates of the input quotes. (That is, we need to interpolate from the existing curve to
discount such coupons.)
The classic spline has the property that when any input point is changed, the whole curve moves. On
the other hand, Hermite splines depend only on two or four points around the interval to be
interpolated, and are therefore easier to use in bootstrapping.

Technical definition
Given a set of points
(with
and
,
a cubic spline is a continuous function that goes through the points in I, and is a cubic polynomial
within each interval
intervals altogether), and is either continuously
differentiable (quasi-cubic spline) or has a continuous second derivative (classic cubic spline).

Boundary conditions
Let us call Pi the cubic polynomial forming the spline within interval Ii. Then, a quasi-cubic spline
satisfies the following conditions:
Equation 2-157 Cubic spline: conditions

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This gives us 3N - 4 conditions. For classic splines, the continuity of the second derivative provides
another N - 2 conditions:
Equation 2-158 Cubic spline: classic splines

To determine all N - 1 cubic polynomials, 4N - 4 parameters need to be set. This means that for
classic spline, two additional conditions are needed, while for quasi-cubic splines N additional
conditions are necessary.
With classic spline, the additional two conditions are usually set at either boundary, for example:
Equation 2-159 Cubic spline: natural condition and clamped spline

where λ 1 and λ N are the slope of the curve at either end.
For the bootstrapping algorithm, it is convenient to be able to set the two additional conditions at
the short end of the curve:
Equation 2-160 Cubic spline: bootstrapping algorithm conditions

Classic spline
The value of the spline at a point
is given in terms of the second derivatives at node
points (zi) as shown in Equation 2-161 on page 104:
Equation 2-161 Classic spline: value of spline

where

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The parameters zi can be solved by requiring that the derivatives at interior nodes
(

) be continuous:
Equation 2-162 Classic spline: continuous derivatives at interior nodes

and that the boundary conditions are satisfied, which in case of clamped boundary conditions
means:
Equation 2-163 Classic spline: clamped boundary conditions

In matrix form, Equation 2-162 on page 105 and Equation 2-163 on page 105 can be written as
follows:
Equation 2-164 Classic spline: matrix

Hermite spline
In each sub interval Ii, we can normalize the argument t by mapping it to the interval [0, 1]
Equation 2-165 Classic spline: normalize t

where

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Then, we may represent the cubic polynomial as a linear combination of the third order Hermite
polynomials over the normalized interval [0, 1]:
Equation 2-166 Classic spline: third order Hermite polynomials

where mi is the derivative at point ti.
It is the setting of these N derivatives at the node points that uniquely determines the quasi-cubic
spline.
From Equation 2-166 on page 106 we can find the value of the second derivative of the curve at
each node. The left hand-side derivative is:
Equation 2-167 Classic spline: Left hand side derivative

•

Setting the slopes at node points
There are various methods for determining mi, and we shall consider the following four:

–

Three-point difference
Equation 2-168 Cubic spline: three-point difference method

If we use clamped initial and final conditions, then:
Equation 2-169 Cubic spline: three-point difference method, clamped

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–

Two-point difference
Equation 2-170 Two-point difference

If we use clamped initial and final conditions, then:
Equation 2-171 Two-point difference: clamped initial and final conditions

For the classic (continuous second derivative) case, we have the additional N - 2 conditions
that the second derivative at each interior node point is continuous:
Equation 2-172 Two-point difference: Classic

–

With clamped boundary conditions
following set of equations:

, mi can be solved from the
Equation 2-173 Clamped boundary conditions: equations

Note: Equation 2-173 on page 107 is equivalent to Equation 2-162 on page 105 and Equation

2-163 on page 105, except that here we use the slopes as parameters, while in the classic
formulation second derivatives are used.

–

Replacing the long end boundary condition (mN = 2) with an initial condition on the second
derivative () we have the following set of equations, which can be solved sequentially:
Equation 2-174 Clamped boundary conditions: initial condition on the second derivative

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Extrapolation
For values t < t1 and t > tN we have to use extrapolation. For yield curve interpolation it makes
sense to use linear interpolation, typically with zero slope. In this case, to maintain continuity of the
first derivative, clamped boundary conditions are appropriate for the spline itself. If we apply two
initial conditions for a classic spline, we have no control over the slope at the long end of the curve,
and the first derivative will be discontinuous.

2.2.3.4.3 Spline building algorithm
The structure of the spline building algorithm depends on whether the node points (ti, fi) are all
known in advance, or whether we have to solve the values if as we go along (as in bootstrapping).
There are three cases:

•

All node points are known: In case the values at the node points are known, we can use the
methods described in Setting the slopes at node points on page 106 directly.

•

Bootstrapping is required to construct the curve, but interpolation is not necessary during curve
construction.

•

Bootstrapping uses interpolation. If interpolation is needed during bootstrapping, there are two
possibilities:

–

If the information up to a given point fully defines the interpolation curve up to that point,
then we can use sequential bootstrapping ( Sequential bootstrapping on page 108).

–

If the information beyond the current node is necessary for the interpolator, we need an
iterative algorithm ( Iterative algorithm on page 109).

Sequential bootstrapping
If we have to boot strap the values at node points, or if we use classic spline, a sequential algorithm
is needed. We only consider classic case with initial conditions (
) and quasi-cubic case with
the two-point difference, since these are the cases amenable to the bootstrapping type of algorithm.
Classic spline with boundary conditions and quasi-cubic spline with three-point difference are
described in section Iterative algorithm on page 109.
Set
Equation 2-175 Spline building algorithm: sequential bootstrapping

Equation 2-176 Spline building algorithm: sequential bootstrapping - Classic case only

For the ith interval, given the value fi+1 at the right-hand end of the interval, we set for the classic
case:
Equation 2-177 Spline building algorithm: sequential bootstrapping - ith interval

where for i > 1:
Equation 2-178 Spline building algorithm: sequential bootstrapping (i > 1)

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And for the quasi-cubic case:
Equation 2-179 Spline building algorithm: sequential bootstrapping (quasi-cubic case)

In either case, the ith spline is now given in terms fi+1.
If fi+1 is known, then the sequential bootstrapping is finished. Otherwise, this function can now be
used iteratively to solve the bootstrapping step, yielding a value fi+1 that provides the market price
for the ith bootstrapping instrument.

Iterative algorithm
The sequential algorithm for classic spline, while well adapted to the solving of the bootstrap
problem, cannot be made to satisfy the boundary condition at the long end of the curve. On the
other hand, for quasi-cubic spline with three-point differences the sequential algorithm cannot be
applied at all. For these cases we need an iterative approach.

•

Quasi-cubic spline
In this algorithm, we solve the problem of missing node values by using the values from the
previous iteration round. To initialize the values, we use sequential bootstrapping with two-point
differences.

–

Bootstrap using the sequential algorithm with two-point differences.

–

Bootstrap using the sequential algorithm with three-point differences. Takes the values for
nodes beyond the current one from the previous iteration round. Repeat until slopes no
longer change.

In practice, only one iteration is needed.

•

Classic spline
The objective here is to use the sequential algorithm iteratively to find a classic spline with the
proper slope at the long end of the curve. The idea is to apply sequential bootstrapping with the
given initial slope and to adjust the initial second derivative so that the final slope, which is
determined by the initial conditions and the sequential bootstrapping process, will be equal to
the requested value.
To ensure a good initial guess, we first carry out bootstrapping using linear interpolation and
create a cubic spline through its node points. We then use the second derivative at the first node
point as the initial value ( η ) for the iteration algorithm.
Iteration algorithm

1. Initialize: Set the initial slope and second derivative:
Equation 2-180 Cubic spline interpolation: Iteration algorithm

2. Sequential bootstrapping: Using the initial conditions and sequential bootstrapping (see
Sequential bootstrapping on page 108), find the interpolation curve.
3. Iteration k: Find the error in the end condition slope:
Equation 2-181 Cubic spline interpolation: Iteration algorithm

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k
where λ 1 is the target value, and m N is the slope at the kth iteration. If |ek| is small enough,
stop, otherwise adjust the free initial variable:

Equation 2-182 Cubic spline interpolation: Iteration algorithm

Slope to a change in the initial second derivative. Go to 2. on page 109.

2.2.3.4.4 Reference time
In interpolating a yield curve, the value to be interpolated is either the discount factor between two
dates or the corresponding interest rate. One of these dates has to be common to all interpolated
values, and the interpolation results depend on the choice of the common date. Since usually most
of the market quotes used in the construction of the curve are from the spot, TRM uses the spot
date as the common reference point for all interpolated values.
This leads to a two-phased bootstrapping process:

•

Before spot: In the first phase, we use the valuation date as reference and apply bootstrapping
only to the input quotes with maturity on or before the spot date, thus creating a stub yield
curve between the valuation date and spot date.

•

After spot: In the second phase, we move the reference date to spot, and apply bootstrapping
to all input quotes with maturity after the spot date. To these quotes, we add the discount
factors between the spot date and each date from the valuation date to the spot date (including
the former and excluding the latter) derived from the stub curve constructed in the first phase.

Whenever a discount factor between two dates (d1 and d2) is needed, the following steps are taken:
1. Find the discount factor (D1) between the spot date (ds) and d1. To do this, calculate the length
of period between ds and d1 in year using the interpolation date basis defined for the curve, and
find the value of the interpolation variable at that point of time. If the interpolation variable is
not a discount factor but a rate, convert the rate into discount factor by using the rate type and
date basis defined for the curve.
2. Similarly, find the discount factor (D2) between ds and d2.
3. Finally, the discount factor between dates d1 and d2 is D12 = D2/D1.

2.2.3.4.5 Exponential splines
If scaling is set to Logarithmic (interpolation setup), then the interpolation is carried out on the
logarithms of the original values.
The interpolation curve then has the form:
Equation 2-183 Exponential splines: interpolation curve

y(x) = e

2

a + bx + cx + dx

3

where:

•

The parameters a, b, c, d vary from interval to interval.

2.2.4 FX rate interpolation
Forward FX rates are the result of interest rate differences.
When a market FX exchange rate is needed on a date for which no direct quote is available, the
exchange rate needs to be interpolated from other quotes. In FX markets, all market rates except S
(spot) are quoted in terms of

110

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To find out, on valuation date dr, a market rate F on a future date d, one of the following methods is
used:

•

If d is before the next banking day, then:
Equation 2-184 FX rate interpolation: market rate

( d – dr )
F = S – ΔF T/N – ΔF O/N -----------------d O/N
where:

–

dO/N is the number of days from the valuation date to the next business day.

Note: For FX rates before the spot date, the forward points are taken from the opposite side of

the spread. That is, the bid rate is calculated from the bid spot rate and ask points and the
ask rate is calculated from the ask spot rate and bid points.

•

If d is before the spot date but after the next business day, then:
Equation 2-185 FX rate interpolation: before spot date. after business day

( d – dT )
F = S – Δ F T/N --------------------d T/N
where:

–
•

dT is the next business day and dT/N is the number of days from the next business day to the
spot.

If d is the spot date, then:
F=S

•

If there is an exact quote

Δ Fd (number of forward points) for date d, then:
Equation 2-186 FX rate interpolation: exact number of forward points

F = S + Δ Fd

•

If there are two market quotes

Δ Fd1 and Δ Fd2 such that d1 < d < d2 then:
Equation 2-187 FX rate interpolation: two market quotes

Δ F d2 – Δ F d1
- ( d – d1 )
F = S + Δ F d 1 + -------------------------d2 – d1

This is illustrated in the following figure.
Forward
points
%
ΔFd2
ΔFd
ΔFd1

Period

•

d1

d

d2

If the quote for d1 is S, then ΔF d1 = 0

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If the date d is after the last quoted rate, then we extrapolate linearly using the slope between
the two last quotes:

•

Equation 2-188 FX rate interpolation: after last quoted rate

where dN is the last quote date and d N– 1 is the penultimate quote date.

2.2.4.1 Example: FX rate interpolation
In this example, the USD/JPY exchange rate is calculated at a date 121 days after spot, with spot
date 11-01-1999.
We have the following data:
Data

Symbol

Value

Maturity

d

121 days

USD/JPY spot rate

S

137.9

Quote for 3 months in forward points

ΔF d1

-190

Quote for 6 months in forward points

ΔF d2

-380

Date basis for currency

Actual/360

d1 = 31 + 28 + 31 = 90
d2 = 31 + 28 + 31 + 30 + 31 + 30 = 181
Therefore, using the following equation:
Equation 2-189 FX rate interpolation: interpolated forward rate

Δ Fd2 – Δ Fd1
- ( d – d1 )
F = S + Δ F d 1 + -------------------------d2 – d1

The interpolated forward rate for 121 days = 137.65:
Equation 2-190 FX rate interpolation: example interpolated forward rate

– 0.380 – ( – 0.190 )
F = 137.9 + ( – 0.190 ) + ----------------------------------------- ( 121 – 90 ) = 137.9 – 0.254 = 137.65
181 – 90

2.3 Key-figures
The following section describes the available key-figures for basic fixed cashflows. For key figures
for dual currency cashflows, see 2.3.5 Dual currency on page 147.

2.3.1 Valuation
Detailed calculations are available in the instrument-specific sections.

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2.3.1.1 Interest Rate
The interest rate is the rate that is used in the calculation of IR exposure for the period between the
cashflow's risk date and spot date. The interest rate is based on the Present Value Discount Factor
(Dv) and Present Value Spot Discount Factor (Ds):

where R[] is the rate type defined in the Instrument Editor's IR Exposure page (Base IR Exposure Setup
feature), and t is the time between the spot date and risk date, calculated using the Date Basis
defined in the Instrument Editor's IR Exposure page.

Note: If the risk calculation is based on the risk yield, the yield type and date basis are derived
from the setup in the Risk Yield page (Risk Yield feature) of the Instrument Editor.

Depending on the setup, the Interest Rate key figure displays:

•

The zero coupon rates of the valuation curve (by default)

•

The same rate (yield-to-maturity), when the instrument's risk yield is set with Method =
Yield-to-Maturity in the Risk Setup page (the Risk Setup page is available when the Feature Risk Setup
(Bond) is selected).

2.3.1.2 Market Value
The market value of the transaction (cashflow) calculated using the valuation method specified for
the instrument, given in the figure currency.

2.3.1.3 Market Value Local
The market value of the transaction (cashflow) calculated using the valuation method specified for
the instrument, given in the currency of the transaction (cashflow).

2.3.2 Profit and Loss
2.3.2.1 Accrued Interest
Accrued interest of the coupon converted into figure currency.

2.3.2.2 Accrued Interest Local
Accrued interest in the coupon/cashflow currency.

2.3.2.3 Accrued Profit
Non-interest accrued profit, for example, accrued discount premium for bonds, or amortized fees
and option premiums, converted into figure currency.

2.3.2.3.1 Accrued Profit (BVC)
The Accrued Profit (BVC) component of accrued profit is a Closing the Books figure which is
calculated separately for each BVC adjustment, as follows:
Accrued Profit (BVC) = BVC Amount (D_left - D_total) / (1 - D_total)
Where:

–

D_total = discount factor for the period from adjustment to maturity using all-in yield as of
the adjustment date.

–

D_left = discount factor for the period from valuation to maturity using all-in yield as of the
adjustment date.

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2.3.2.3.2 Accrued Profit (Costs)
This is a Closing the Books figure and is the part of Accrued Profit directly related to costs (for
example, fees), which is calculated separately for each fee, as follows:
Accrued Fee Profit = Fee Amount (D_left - D_total) / (1 - D_total)
Where:

–

D_total = discount factor for the period from adjustment to maturity using all-in yield as of
the adjustment date.

–

D_left = discount factor for the period from valuation to maturity using all-in yield as of the
adjustment date.

2.3.2.3.3 Accrued Profit (Discount)
This is a Closing the Books figure and is the part of Accrued Profit directly related to Discount
Premium (for example, fees), which is calculated for the Discount (Premium) of a Bond, as follows:
Accrued Discount Profit = Discount/Premium Amount (D_left - D_total) / (1 - D_total)
Where:

–

D_total = discount factor for the period from adjustment to maturity using all-in yield as of
the adjustment date.

–

D_left = discount factor for the period from valuation to maturity using all-in yield as of the
adjustment date.

2.3.2.3.4 Accrued Profit (Residual)
The Accrued Profit (Residual) figure (that is, the discount/premium component) is then the
difference between the total Accrued Profit figure and the Accrued Profit (Costs) and Accrued Profit
(BVC) figures.

2.3.2.4 Accrued Profit Local
Non-interest accrued profit, for example, accrued discount premium for bonds, or amortized fees
and option premiums, in the currency of the transaction (cashflow).

2.3.2.5 FX Profit
The part of the difference between the market value and the book value of the transaction
(cashflow) due to changes in FX Spot rates.

2.3.2.6 Accrued Margin Profit
Accrued Margin Profit Local converted to figure currency.

2.3.2.7 Accrued Margin Profit Local
Accrued part of the margin amount. The margin profit is calculated by accruing the margin amount
calculated linearly throughout the life of the transaction.

2.3.2.8 Margin Profit
Margin Profit Local converted to figure currency.

2.3.2.9 Margin Profit Local
The residual margin profit, i.e. Total Margin Profit Local - Accrued Margin Profit Local.

2.3.2.10 Total Margin Profit
Margin Profit Local converted to figure currency.

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2.3.2.11 Total Margin Profit Local
Profit resulting from transaction margins, i.e. the discounted margin amount, expressed in the
currency of the transaction/margin. Margins are currently supported for short-term loans (3.8 Short
term loan on page 305) and FX spots and FX forwards (6.1 FX spot and FX forward on page 383 and
FX swaps (6.4 FX swap on page 416.)

2.3.2.12 MtoM Profit
The part of the Profit due to changes in market variables other than FX rates, converted into figure
currency.

2.3.2.13 MtoM Profit Local
The part of the Local Profit due to changes in market variables other than FX rates, expressed in the
currency of the transaction (cashflow).

2.3.2.14 Other Profit
The part of the Profit not attributable to the other profit types (MtoM, FX, or Accrued), converted
into the figure currency.

2.3.2.15 Other Profit Local
The part of the Local Profit not attributable to the other profit types (MtoM, FX, or Accrued),
expressed in the currency of the transaction (cashflow).

2.3.2.16 Total Profit
The difference between the market value and the book value of the transaction (cashflow),
converted into figure currency.

2.3.2.17 Total Profit Local
The difference between the market value and the book value of the transaction (cashflow),
expressed in the currency of the transaction (cashflow).

2.3.3 Option figures
FX option key figures are calculated using the valuation model set up by the user:

Note: For more information about option valuation models, see section 10.8.6.2.2 on page 611.
Equation 2-191

where

–

S is the FX Spot Rate

–

X is the FX Strike Rate

–

Γa is the Asset currency continuous rate

–

Γc is the Cash currency continuous rate

–

τe is the time to expiry date

–

dρ is the time delay between expiry and payment date

–

σ is the volatility

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The valuation formula may use other transaction parameters, such as gap, barrier, or exercise
schedule, or model parameters, such as Quality, but these will be considered implied and not shown
in the formulas.

2.3.3.1 Asset and cash currencies
The values of some key figures will depend on the choice of asset and cash currencies. The asset
currency is by default the currency with the higher priority (as defined in Currency Priority Editor),
or the base currency in case the traded currencies have no priorities defined. For more information
about setting currency priorities, see TRM User Guide, Client Priorities.
You can change the (defaulted) asset currency in Transaction Manager. This impacts the option
figures displayed in Transaction Manager.

2.3.3.2 Greeks
Greeks are sensitivities of option price to changes in the variables determining the price. These are
calculated numerically using:
Equation 2-192 Greeks - sensitivities of option price

where

ε

is a small number.

TRM calculates the Greeks described in the following sections:
Basic sensitivities

Formula

Cross sensitivities

Delta

Asset Rho Speed

Gamma

Cash Rho Speed

Strike Delta

Vega Speed (Vanna, Wega)

Strike Gamma

Theta Speed

Asset Rho

Delta Bleed

Asset Yield Gamma

Gamma Bleed

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Basic sensitivities

Formula

Cross sensitivities

Cash Rho

Asset Rho Bleed

Cash Yield Gamma

Cash Rho Bleed

Vega

Vega Bleed

Formula

Sigma Gamma (Volga)

Theta

Time Gamma

For barrier options, TRM offers some additional key figures, which describe the behavior of the
option’s value near the barrier. These figures replicate the standard sensitivity calculations, except
that the valuation is done at the barrier, without crossing it.
Upper barrier sensitivities

Formula

Lower barrier sensitivities

Upper Barrier Delta Gap

Lower Barrier Delta Gap

Upper Barrier Gamma Gap

Lower Barrier Gamma Gap

Upper Barrier Strike Delta Gap

Lower Barrier Strike Delta Gap

Upper Barrier Strike Gamma Gap

Lower Barrier Strike Gamma Gap

Upper Barrier Asset Rho Gap

Lower Barrier Asset Rho Gap

Upper Barrier Asset Yield Gamma Gap

Lower Barrier Asset Yield Gamma Gap

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Upper barrier sensitivities

Formula

Lower barrier sensitivities

Upper Barrier Cash Rho Gap

Lower Barrier Cash Rho Gap

Upper Barrier Cash Yield Gamma Gap

Lower Barrier Cash Yield Gamma Gap

Upper Barrier Vega Gap

Lower Barrier Vega Gap

Upper Barrier Sigma Gamma Gap

Lower Barrier Sigma Gamma Gap

Upper Barrier Theta Gap

Lower Barrier Theta Gap

Formula

2.3.3.3 Intrinsic and time value
There are three methods for intrinsic value calculation:
Method

Formula

Description

Zero Volatility

Calculate option price assuming volatility
zero.

Forward

Calculate option price assuming volatility
zero, and substituting zero for cash rate
and IR difference for asset rate.

Spot

Calculate option price assuming volatility
zero, and substituting zero for cash and
asset rates.

For barrier options intrinsic value calculated at upper and lower barriers is called Upper Barrier
Digital and Lower Barrier Digital respectively.

2.3.3.4 Risk figures
Sensitivity figures are calculated for one unit of asset currency and expressed in cash currency. To
convert them into risk key figures they are multiplied by cash amount (including the sign of the
transaction) and FX rate between the cash currency and the figure currency. In addition, theta
figures, which are originally calculated for one unit of time (year), are divided by 365 so that they
will correspond to a daily change in option value.
Similarly, volatility figures (vega, vanna, wega) are calculated for one unit change in volatility
(100%). They are divided by 100 so that they will correspond to a change of one percentage unit in
volatility.

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2.3.4 Risk
Note: For Theoretical valuation, present value is equal to market value in all cases except for
bond futures in IR risk figures calculation.

2.3.4.1 Exposures
Exposures in general measure sensitivity of the present value to a change in a market rate.

2.3.4.1.1 FX Exposure
The sensitivity of the present value of the cashflow to a change in the FX Spot rate.
The magnitude of the change is defined for each currency in Currency Editor (as a percentage).
FX exposures are netted within each currency (in Currency Editor), as well as within each class
currency (in Currency Class Editor), see TRM User Guide. Totals that include different currencies or
different currency classes are taken from the absolute values of the currency or the total exposures
of the currency class.

2.3.4.1.2 IR Exposure 1
The sensitivity of the present value of the cashflow to a parallel shift of 1 basis point (1bp) in the
yield curve.
The value of a position can be seen as a function of a number of discount factors for different
maturities:
V = V [ D1, D2, ... , Dn]
where other dependencies, such as FX rates, have been suppressed since they are immaterial to the
issue under consideration.
Alternatively, since each discount factor depends on the interest rate for the period in question, it is
possible to write:
V = Vr [ r1, r2, ... , rn]
However, the interest rates in the second formula depend on the definition of the date basis as well
as on the type of interest rate (periodic, compounded, and so on).
Therefore, the first formula is more fundamental, and IR exposure calculations are based on that
one.
Based on the first equation, the sensitivities on discount factors can be calculated as:

∂V
V i = --------∂D i
For fixed cashflows, Vi is simply the amount of the cashflow, while for floating-rate instruments and
derivatives, the formula will be more complex.
Once the sensitivity with respect to the discount factor is found, the corresponding sensitivity with
respect to an interest rate can be derived, given the type of interest rate and date basis.

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For example, for a yearly compounded rate:

D [ t ,r ] = ( 1 + r )

–t

∂D
------- = – t ( 1 + r ) – t – 1 = – tD ( t + 1 ) ⁄ t
∂r
Di
∂V
∂V- ∂------∂V- ( ti + 1 ) ⁄ ti
------- = ------- = – ------tD
∂r i ∂D i ∂r i
∂D i i i
( t + 1 ) ⁄ ti
∂V
∂V
E 1bp = ------- × 0.0001 = – -------- t i D i i
× 0.0001
∂r i
∂D i
where:

–

ti is the length of period calculated according to the chosen date basis.

For other interest rate types, we get similar formulae.
∂V
However, the term V r = --------- does not change with the choice of risk yield type and date basis.
∂D i
The value of V r is shown in Transaction Manager as the Figure Risk Value.

Note: The date basis and yield type that is used for IR exposure calculations can be defined at

instrument level using the feature Base IR Exposure Setup: see A.2.48 Base IR Exposure
Setup on page 732.
If the instrument uses the feature Risk Yield, the date basis and yield type defined for the
risk yield override the IR exposure setup for the period from spot date to risk date: see
A.2.291 Risk Yield on page 859.

2.3.4.1.3 Discounting via spot date
Often, discounting to the valuation date is done via spot date, with two different yield curves used
for the part between the risk date and spot date (Valuation Curve), and the spot date and the
valuation date (Discount Curve).
In this case, we calculate the discount factor sensitivity separately for each discount factor ( D 2 [ r 2 ]
from the risk date to the spot date, D 1 [ r 1 ] from the spot date to the valuation date where interest
rate r 2 and discount rate r 1 are the rates over the corresponding periods). The total sensitivity to
change in discount factors is then:
Equation 2-193 IR exposure 1: total sensitivity of DF

2.3.4.1.4 To spot
If the switch To Spot in IR Exposure page of the Instrument Editor is set (see A.2.48 Base IR Exposure
Setup on page 732), IR exposure calculation is based on discounting to spot instead of to valuation

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date. That is, D 1 [ r 1 ] ,the discount factor between the spot date and the valuation date is set to 1
(and the corresponding sensitivity to zero):
Equation 2-194 IR exposure 1: with To Spot switch

2.3.4.2 Spot IR Exposure 1
Spot IR Exposure 1 only takes into account the part of IR exposure due to a movement of the
interest rate between the spot date and the risk date:
Equation 2-195 Spot IR Exposure 1

where

•

D 2 is the discount factor between the spot date and the risk date,

•

r 2 is the corresponding interest rate, converted from D 2 using the date basis and rate type
defined in the IR Exposure page of Instrument Editor. r 2 is shown as Figure Interest Rate.

Note: The switch To Spot in IR Exposure page of the Instrument Editor has no effect on Spot IR
Exposure 1bp.

2.3.4.3 Present Value
The market value of the transaction (cashflow) calculated using the risk method specified for the
instrument, given in the figure currency.

2.3.4.4 Present Value Local
The market value of the transaction (cashflow) calculated using the risk method specified for the
instrument, given in the currency of the transaction (cashflow).

2.3.4.5 Basis Point Value
Basis point value is used in the risk calculations of bond instruments and represents the value of 1
basis point.
The figure is scaled so that it corresponds to a unit of the instrument, not to the position size, and is
calculated as follows:
(10,000.0 * (- ir_exp_down + ir_exp_up) / 2.0 / (nominal_amount * fx_convert)
Where:

–

IR Exposure Down and IR Exposure Up are calculated with an offset equal to 0.0001

–

The offset returns a value of 10,000.0 (1 / 0.0001)

–

2.0 reflects the approximation used for the calculation of the numerical derivative.

The individual figures can be found in Transaction Manager (that is, the sum of Figure IR Exposure
Down / Up from cashflows, Nominal Amount of the transaction, and Figure FX Convert from the
cashflows).

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2.3.4.6 Yield
Yield is shown at transaction and position levels. It is defined as:
Equation 2-196 Yield key figure

i

y =

ri Vp
∑
----------------i
∑ Vp

where

•

r i is the interest rate used for discounting the i th cashflow in the position

•

V p is the present value of the cashflow.

i

If an instrument is set up with the Risk Yield feature (A.2.291 Risk Yield on page 859), the same
interest rate (yield to maturity) is used for the discounting of all cashflows and key figure Yield
shows the yield to maturity:
Equation 2-197 Yield key figure: Yield to Maturity

i

y =

r Vp
∑
---------------i
∑ Vp

i

=

∑ Vp
r -------------i
∑ Vp

= r

2.3.4.7 Spread
2.3.4.7.1 Z-DM (Discount Margin)
Z-DM is the (constant) spread that has to be added to the risk-free rate used to discount the future
(fixed or estimated) cashflows of a bond in order to have the total of the discounted cashflows equal
to the market value of the bond (at spot date). The date basis and interest type used in the Z-DM
calculation can be set up by adding feature Z-DM/Spread Setup to the instrument: see A.2.343
Z-DM/Spread Setup on page 882. If there is no setup, then the default values are used: Date Basis:
Actual/Actual ISDA, Interest Type: Continuous.
Z-DM ( μ ) is calculated by solving:
Equation 2-198 Key figures: Spread = Z-DM calculation

P =

∑ ci D [ R [ Di ,ti ] + μ ,ti ] + D [ R [ Dmat ,tmat ] + μ ,tmat ]

where P is the (dirty) price of the instrument at spot, Di and Dmat are discount factors from the risk
free curve between spot and payment dates of cashflows, ti and tmat are the times between spot
date and payment dates, and ci are the coupon amounts (fixed or estimated) per unit nominal
amount. Functions D[] and R[] convert the interest rate into the discount factor, and vice versa,
according to the interest type setup.

2.3.4.7.2 Z-Spread
Z-spread is the ratio between the Present Value Discount Factor and the Risk Free Discount Factor,
converted into the rate using the date basis and interest type defined for risk free curve's
interpolation. The risk free curve can be defined in the Currency Editor: see TRM User Guide. If it is
not defined, the default curve of the currency is used.

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The calculation for Z-Spread ( μ z ) is:
Equation 2-199 Key figures: Spread: Z-Spread calculation

μ z = R [ D p ⁄ D rf ,t ]
Where Dp and Drf are Present Value Discount Factor and Risk Free Discount Factor, respectively, and
t is time between risk base date and cashflow risk date, and is the function that converts discount
factor into rate.

Risk method Z-Spread
In the risk method Z-Spread, the Present Value Discount Factor is calculated by adding Z-DM to the
risk free rate (for the period from the spot to the risk date). Discounting from the spot to the
valuation date uses the discount curve defined for the instrument as usual.
When Z-DM is added to the risk free rate (rrf), it will be used according to the date basis and
interest type defined for the risk free rate. For consistency, the Z-DM/Spread Setup has to use the
same date basis and interest type as the risk free rate.
The key figures Z-DM and Z-Spread are very similar, but not necessarily the same. Even if Z-DM
and risk free curve setups match, there is the difference that Z-DM is calculated for the period
between the spot and the payment date, while Z-Spread is calculated for the period between the
risk base date and the payment date. If IR Exposure Setup (A.2.48 Base IR Exposure Setup on page
732) uses the To Spot switch, Z-DM and Z-spread will be calculated using the same time period.
There is still another difference: While Z-DM is added to the risk free rate, Z-Spread is based on the
ratio of discount factors. If the time period used (To Spot), the date basis, and the interest type
setups match, we have:
Equation 2-200 Key figures: Spread discount factors

μ z = R [ D [ r rf + μ ,t ] ⁄ D [ r rf + t ] , t ]
If we use Continuous Yield, i.e. D [ r, t ] = exp [ – r × t ] and D [ D, t ] = – log [ D ] ⁄ t
then we get:

μ z = – log [ exp [ – ( r rf + μ ) × t ] ⁄ exp [ – r rf × t ] ] ⁄ t

μ z = – log [ exp [ – μ × t ] ] ⁄ t = μ
So, in this case, Z-DM is equal to Z-Spread. If the other interest types are used, there may be some
minor differences.

2.3.4.7.3 Spread IR Exposure 1 bp
The Spread IR Exposure 1 bp is the sensitivity of the present value of the cashflow to a shift in the
yield used for discounting from risk date to risk base date. It is defined for fixed cashflows as:
Equation 2-201 Key figures: Spread IR Exposure 1 bp

∂D 2
∂D 1
E μ = V r ⎛ D 1 --------- + D 2 ---------⎞ × 0.0001
⎝ ∂r 2
∂r 1 ⎠

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∂D 2
∂D 1
E μ = V r ⎛ D 1 --------- + D 2 ---------⎞ × 0.0001
⎝ ∂r 2
∂r 1 ⎠
That is, the formula is the same as for IR Exposure 1 bp: see 2.3.4.1.2 IR Exposure 1 on page 119.
For floating cashflows, there is a new (not displayed) key figure, Spread Risk Value, which is equal
to Figure Payment Amount for the interest cash flow, and zero for the pseudo risk cash flows. In
terms of spread risk value, spread IR exposure 1bp is:
Equation 2-202 Key figures: Spread IR Exposure 1 bp

∂D 2
∂D 1
E μ = V μ ⎛ D 1 --------- + D 2 ---------⎞ × 0.0001
⎝ ∂r 2
∂r 1 ⎠
Where is V μ the spread risk value.
That is, the exposure formula is the same for both floating and fixed cashflows, the only difference
being how the risk value is obtained.
The date basis and interest type used in these calculations are determined either by the IR exposure
setup (feature Base IR Exposure Setup), if given, or by the interpolation method specified in the curve
in the discounting (the valuation curve specified in the risk method Zero-Coupon, and the risk-free
curve in the risk method Z-Spread). See A.2.289 Risk Setup (FRN) on page 858 or A.2.288 Risk Setup
(BOND) on page 858. For fixed bonds, if the risk method Yield to Maturity is used, then the date basis
and interest rate defined for the risk yield are applied, even if there is an IR exposure setup (feature
Base IR Exposure Setup). See A.2.48 Base IR Exposure Setup on page 732.

2.3.4.7.4 Beta exposure
The beta exposure is simply the Spread IR Exposure 1bp scaled with risk method Z-Spread:
Equation 2-203 Key figure: beta exposure

Eβ = Eμ × μz
Where μ z is the Z-Spread.

2.3.4.8 Risk profiles
This section describes each risk profile by explaining which risk dates are created, what market and
cashflow data are used, and how calculations are carried out. A risk profile is a method to carry out
interest rate risk calculations that are specific to a certain type of instrument.
Risk profiles are set up at the instrument level by attaching the feature Floating Valuation Setup
(A.2.338 Valuation Setup (Floating) on page 879). Each risk profile generates risk cashflows for the
cashflows of the transaction, calculating risk values and convexity matrix in the prescribed manner.
Risk values can be viewed in the Cashflow / Event Figure view of Transaction Manager. For more
information on how IR exposure is calculated from risk values, see 2.3.4 Risk on page 119.

Input
A risk profile calculation uses two types of input data: market data and cashflow data. Market data
includes estimation curve, valuation curve and discount curve. These are set up in the Instrument
Editor, Yield Curves page. Additionally, certain risk profiles use volatility and past quotes for the fixing
rate.

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All risk profile calculations are carried out at the cashflow level. Different risk profiles use different
properties of the cashflow in the calculations. The following sections provide detailed information
about these profiles.

Output
Each risk profile creates a list of risk dates and a corresponding list of risk values, which together
characterize the interest rate exposure of the specific cashflow. In addition, for each cashflow the
risk profile estimates the fixing rate and the amount of the coupon.

2.3.4.8.1 Plain Vanilla
Plain vanilla risk profile corresponds to the standard floating cashflow, where the coupon period is
the same as the fixing period. Risk dates are: payment date, coupon start date (since when), and
coupon end date (until when).
Input data used in calculations:

tc
s
Dp
D1
Dn

Coupon period length
Spread
Discount factor for the payment date (from valuation and discount curves)
Discount factor for the start of the coupon period (from estimation curve)
Discount factor for the end of the coupon period (from estimation curve)

Coupon estimate
Equation 2-204 Risk profile: Plain vanilla: Estimated amount

A e = D 1 ⁄ D n – 1 + st c
Valuation
Risk values:
Equation 2-205 Plain vanilla: Risk values

D1
V p = ------ – 1 + st c
Dn
Dp
V 1 = -----Dn
Dp D1
V n = ------------2
Dn

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Convexity matrix:
Equation 2-206 Plain vanilla: Convexity matrix

V pp = 0
1
V p1 = -----Dn
D1
V pn = – ------2
Dn
V 11 = 0
Dp
V 1n = ------2
Dn
Dp D1
V nn = 2 ------------3
Dn
2.3.4.8.2 Generic
Risk dates are: payment date, fixing period start date, and fixing period end date.
Input data used in calculations:

t
tf
tc
σ
σc
s
Xc
Xf

Time to fixing date

f
D p , D1 , Dn

Factor (=-1 for inverse floater)

Fixing period length
Coupon period length
Volatility
Convexity adjustment volatility
Spread
Cap rate
Floor rate

Discount factors

Calculated variables:

F
R
aa
ac
af

Forward rate

d1 , d2

Black76 factors

Adjusted rate
Convexity adjustment
Cap adjustment
Floor adjustment

Normal distribution

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where
Equation 2-207 Generic

V = t c ( R f + s + a c + a f )D p

2

⎛ e tσc – 1⎞ t F 2
⎝
⎠ f
a a = --------------------------------tf F + 1
R = F + aa

⎛ D1
⎞
– 1⎟
⎜ -----Dn
F = ⎜ ---------------⎟
⎜ t ⎟
⎝ f ⎠

ac = N ( d1 ) R – N ( d2 ) X
af = N ( –d2 ) X – N ( –d1 ) R
2

R
σ t
log ⎛ ------------⎞ + -------⎝ X – s⎠
2
d 1 = ----------------------------------------σ t
2

R
σ t
log ⎛ ------------⎞ – -------⎝ X – s⎠
2
d 2 = ----------------------------------------σ t
The risk values are calculated numerically.

2.3.4.8.3 Constant Maturity
Risk dates are: Payment date, start dates, and coupon dates of the underlying swap. We shall
consider an individual constant maturity swap (CMS) coupon, since all unfixed coupons are handled
in the same way. A fixed coupon becomes a fixed cashflow and is handled likewise.
Input data:

tp
t1
t2
ts

Time to payment date
Start date of the coupon period
End date of the coupon period
Start date of the underlying swap

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si
ei
σ
s
D p, D 1, D i ,

Start dates of the underlying swap coupons
End dates of the underlying swap coupons
Volatility
e
Di

Discount factors corresponding to the previously mentioned dates

Calculated variables:

y
yc
ac

Forward rate
Convexity-adjusted rate
Convexity adjustment

The fair value of CMS coupon is:
Equation 2-208 fair value of CMS coupon

V = yc ( t2 – t1 )
where yc, the convexity adjusted forward swap rate, is calculated as shown below.
For risk values and convexity matrix, we regard the adjusted swap rate as a function of discount
factors, and calculate numerically the following derivatives:
Equation 2-209 Constant maturity: derivative calculations

∂y c
∂V
V x = ---------- = ( t 2 – t 1 ) ---------∂D x
∂D x
2

V xy

2
∂ yc
∂ V
= -------------------- = ( t 2 – t 1 ) -------------------∂D x ∂D y
∂D x ∂D y

Convexity adjusted swap rate
First, we calculate the forward swap yield from the underlying discount factors:
Equation 2-210 Constant maturity: Forward swap yield

D1 – D1
y = ------------------∑ τi Di

where D1 and D2 are discount factors at the start and end of the swap, respectively, and τi = ti – t i–1
are the swap coupons’ period lengths (where we set t0 = ts).
The convexity adjustment applied to the forward yield y for a swap, starting at time T is given by:
Equation 2-211 Constant maturity: convexity adjustment

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where σ is the yield volatility and p[yd;y] is the price of the fixed leg of the swap as function of the
yield yd.
The price function is given by:
Equation 2-212 Constant maturity: price function

p [ y d ;y ] = D [ y d, t n ] + y c

∑ τi D [ yd, ti ]
i

where t i are the payment dates of the fixed leg , τi are the length of the coupon periods and the
discount factor D[yd;ti] are calculated using compounding with the swap frequency.
The adjusted swap yield is then:
Equation 2-213 Constant maturity: adjusted swap yield

2.3.4.8.4 Compound (O/N)
The Compound (O/N) risk profile corresponds to a coupon determined by compounding overnight
rates over the coupon period. Within the compounding period, the result of the compounding up to
the valuation date is known, and the rate compounded over the remaining period is estimated from
discount factors at the beginning and end of the remaining period. Therefore, the risk dates are:
payment date, valuation date, and the coupon end date (until when).
Before the start of the coupon period, valuation date is replaced by coupon start date (since when).
Input data used in calculations:

Dp
D1

Discount factor for the payment date (from valuation and discount curves)

Dn

Discount factor for the end of the coupon period (from estimation curve)

During the coupon period = 1, before coupon period discount factor for the start of
the coupon period (from estimation curve)

The coupon amount is compounded over the period from d s to d e , typically including only business
days:
Equation 2-214 Compound (O/N) coupon amount

where r d is the overnight rate for day d and l d is the length of the period between two consecutive
days using the appropriate day count method. The coupon amount can be estimated by:
Equation 2-215 Compound (O/N) estimated coupon amount

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where A f is the known part of the compound factor:
Equation 2-216 Compound (O/N) compound factor

and we use

as the estimate for the compounding factor for the rest of the period.

Risk values:
Equation 2-217 Compound (O/N) risk values

Convexity matrix is:
Equation 2-218 Compound (O/N) convexity matrix

2.3.4.8.5 Generic Compound (O/N)
The Generic Compound risk profile is a generalization of Compound (O/N) risk profile, allowing
multiplicative spread as well as an additive one. In addition, the daily rate may be capped.
Input data:
s

Spread

h

Multiplicative spread

c

Cap for the daily rate (spread-adjusted).

Dp

Discount factor for the payment date (from valuation and discount curves)

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D1

During the coupon period = 1, before coupon period discount factor for the start of
the coupon period (from estimation curve)

Dn

Discount factor for the end of the coupon period (from estimation curve)

The payment amount of a compound floater with additive and multiplicative spreads and a cap is:
Equation 2-219 Generic Compound (O/N)

where the product is taken over the compounding period, A is the nominal amount of the transaction
(from now on we use A = 1.0, and leave it out from subsequent formulas), s (additive spread), h
(multiplicative spread), and c (cap) are constants, d is the length of a day (e.g 1/360 or 1/252,
depending on the date basis, and r i is the compounding rate for day i (expressed as annually
compounded rate).

Valuation
On a given valuation day k, we know the historical part of the compounding:
Equation 2-220 Generic Compound (O/N) valuation day

and in terms of the known part the estimated payment amount becomes:
Equation 2-221 Generic Compound (O/N) estimated payment amount

Writing A f = A k + 1 , and D p for the discount factor between valuation day k and the payment date,
the fair value of the payment becomes:
Equation 2-222 Generic Compound (O/N) fair value of payment

where E[] is the expectation operator. The fair value (Equation 2-222 on page 131) can be
calculated numerically given an interest rate model. However, for practical purposes the
non-linearity of this instrument is negligible, and it will be more efficient to ignore the optional
features embedded in the min operator, and carry out the valuation in a deterministic world. Also,
we shall not consider the effect of rounding, since rounding renders the fair value function
non-differentiable, and its effect on valuation is small anyway.
Furthermore, in order to get rid of the dependence on the O/N discount factors, we shall apply the
following approximation:
Assume that either r i ≤ c for all i > k or r i > c for all i > k

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That is, if

, we shall use the estimate
Equation 2-223 Generic Compound (O/N) estimate A 1

Otherwise,
Equation 2-224 Generic Compound (O/N) estimate A

•

Fixed estimate
In the first case, the cashflow can be treated as fixed, for which standard cashflow valuation and
risk analysis will suffice. That is, let n be the number of days left in the fixing period.
Then the estimated amount is:
Equation 2-225 Generic Compound (O/N) fixed estimate

As we now consider this cashflow fixed, risk values are:
Generic Compound (O/N) fixed estimate risk values

and the convexity matrix is empty.

•

Variable estimate
In the second case, we shall use the following approximation:
Let n be the number of days left in the fixing period and let D 1 and D n be the discount factors
for the start and end of the (remaining) fixing period respectively.

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Then we make the approximation:
Equation 2-226 Generic Compound (O/N) variable estimate

where we have set
. That is, we assume that the overnight rates during
the remaining fixing period are equal. Finally, let us write:
Equation 2-227

Then, the estimated fixing amount becomes:
Equation 2-228

The risk profile calculates the following key figures:

–

Estimated Amount
Equation 2-229 Generic Compound (O/N) variable estimate: estimated amount

–

Present Value
Equation 2-230 Generic Compound (O/N) variable estimate: present value

Risk Values (Discount Factor Sensitivities):
For risk values, it is useful to define the following differentials:
Equation 2-231 Generic Compound (O/N) variable estimate: risk value differentials

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Then, risk factors become:
Equation 2-232 Generic Compound (O/N) variable estimate: risk factors

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–

Fixing Period Start
Equation 2-233 Generic Compound (O/N) variable estimate: fixing period start

–

Fixing Period End
Equation 2-234 Generic Compound (O/N) variable estimate: fixing period end

–

Convexity Matrix
Equation 2-235 Generic Compound (O/N) variable estimate: convexity matrix

Notice that if the multiplicative spread h is zero, we get:
Equation 2-236 Generic Compound (O/N) variable estimate: multiplicative spread is zero

and if the additive spread s is zero, we get:
Equation 2-237 Generic Compound (O/N) variable estimate: additive spread is zero

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2.3.4.8.6 Compound (Simple)
The Compound (Simple) risk profile is applicable to coupons based on compounded average interest
rate. The actual compounding expression is only used for the estimation of the current coupon
amount. Future coupons and risk are calculated using a simple generic approximation.
Input data used in calculations:
tc

Coupon period length

tf

Fixing period length

s

Spread

r

Compounded rate up to the valuation day

Dp
D1

Discount factor for the payment date (from valuation and discount curves)

Dn

Discount factor for the end of the coupon period (from estimation curve)

136

During the coupon period = 1, before coupon period discount factor for the start of
the coupon period (from estimation curve)

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Coupon estimation
Before the start of the coupon period, the estimated coupon is:
Equation 2-238 Compound (Simple) estimated coupon

During the coupon period, we use an estimate that combines the currently known compounded rate
up to the valuation day (r) with a simple estimate of the discount factor for the rest of the period:
Equation 2-239 Compound (Simple) during coupon period: estimate

where D[] and R[] are rate to discount and discount to rate conversion functions, respectively, and
t r is the length of the remaining fixing period.

Valuation
Risk values per unit nominal amount are calculated as:
Equation 2-240 Compound (Simple) risk values

Convexity matrix is:
Equation 2-241 Compound (Simple) convexity matrix

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2.3.4.8.7 Average (Simple)
The Average (Simple) risk profile is applicable to coupons based on interest rate averaged over a
period. The actual averaging expression is only used for the estimation of the current coupon
amount. Future coupons and risk are calculated using a simple generic approximation.
Input data used in calculations:
tc

Coupon period length

tf

Fixing period length

s

Spread

r

Compounded rate up to the valuation day

Dp
D1

Discount factor for the payment date (from valuation and discount curves)

Dn

Discount factor for the end of the coupon period (from estimation curve)

During the coupon period = 1, before coupon period discount factor for the start of
the coupon period (from estimation curve)

Coupon estimate
First, we calculate the estimated forward rate (f) for the remaining fixing period:
Equation 2-242 Average (Simple) estimated forward rate

where t r is the length of the remaining fixing period, and R[] is the function that converts the
discount factor into interest rate according to fixing type. Next, we calculate the expected fixing
rate, based on the rate known up to the valuation date (r) and the estimated forward rate f:
Equation 2-243 Average (Simple) fixing rate

Finally, the estimated amount is:
Equation 2-244 Average (Simple) estimated amount

where D[] is the function that converts interest rate into discount factor according to fixing type.

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Valuation
Risk values per unit nominal amount are calculated as:
Equation 2-245 Average (Simple) risk values

Convexity matrix is:
Equation 2-246 Average (Simple) convexity matrix

2.3.4.8.8 Fed Fund
The Fed Fund risk profile corresponds to the coupon calculated from the average overnight rate over
the coupon period. This average is estimated by assuming that the overnight discount factor stays
constant over the coupon period, in which case, this rate can be calculated as follows:
Equation 2-247 Fed funds: Average overnight rate

where D 1 and D n are the discount factors for the start and end of the coupon period, and d is the
number of days in the period.
For the coupon with start date after the valuation date, the risk dates are payment date, coupon
start date (Since When), and coupon end date (Until When).

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Risk values:
Equation 2-248 Fed funds: Risk values

Convexity matrix
Equation 2-249 Fed funds: Convexity matrix

Estimated amount:
Equation 2-250 Fed Funds: estimated amount

where
tc

Coupon period length

Dp
D1
Dn

Discount factor for the coupon payment (from valuation and discount curves)

140

Discount factor for the start of the coupon period (from estimation curve)
Discount factor for the end of the coupon period (from estimation curve)

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s

Spread

d

Number of days in the coupon period.

Running coupon
For the running coupon, we already know the average rate up to the valuation date. Let r be that
rate, and t0 the length of the known period, te the length of the remaining period, and de the
number of days in the remaining coupon period.
Risk values:
Equation 2-251 Fed Funds - running coupons: risk values

Convexity matrix:
Equation 2-252 Fed funds - running coupon: Convexity matrix

Estimated amount:
Equation 2-253 Fed Funds - running coupons: estimated amount

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2.3.4.9 Duration figures
2.3.4.9.1 Duration
Duration is the mean maturity of money in a transaction. For a simple cashflow, the duration is
simply the maturity t of the cashflow. For transactions containing several cashflows, the duration is
considered as the weighted average maturity of each cashflow, with the weights, the present values
of the cashflows.
Equation 2-254 Key figures: Duration

Σt i V i
U = ------------ΣV i
Where
Vi

Present value of the cashflow i with t i > 0 .

ti

Time to maturity of the cashflow i with t i > 0 .

2.3.4.9.2 Duration (Days)
Duration (Days) is the Duration expressed in days. The Duration (Days) key figure is calculated as
follows:
Equation 2-255 Key figures: Duration (Days) calculation

U ( Days ) = U × B
Where
U

Duration

B

The date basis defined at the instrument level, for example, 365, 360, and so on,

2.3.4.9.3 Effective Duration
Effective duration is the relative change of the present value of a position with respect to a change
to the interest rate. Thus, it can be represented as a relative figure of IR Exposure, based on the IR
exposure calculated with 1 bp (basis point):
Equation 2-256 Key figures: Effective Duration

10000 × E { i1 }
U eff = – ----------------------------------Vp
Note: For a single bond evaluated with the par method and continuously compounded yield, the

effective duration is the same as the Macauley duration; for yearly compounded yield, the
effective duration is the same as the modified duration (see 2.3.4.9.5 Modified Duration on
page 145).

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For a position with present value close to zero, the effective duration, as well as Duration and
Duration (Days), may be unstable (present value in the denominator). For example, if the present
value of the position changes from a small positive number to a small negative number, the
effective duration will change from a large positive number to a large negative number. (This
happens particularly when a bond has been bought but is still in the pending state: the settlement
amount belongs to the position and has a present value very close to the bond's present value.)
In fact, when present value is zero, effective duration would be infinite, and will therefore not be
shown.

2.3.4.9.4 Effective Convexity
Convexity is related to the second order term in the Taylor expansion of the value of an asset as a
function of yield:
Equation 2-257 Convexity

In this case, convexity is defined as

C = V''/V

If instead of yield, we consider zero coupon valuation, there are several variables, and the second
order derivative becomes a matrix:
Equation 2-258

where ri are the zero rates taken into account in the valuation of the asset.
We want to use derivatives with respect to the discount factors D i [ r i ] , in which case
Equation 2-259

for off diagonal elements, and
Equation 2-260

Here we have written:
Equation 2-261

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for the part that is independent of the type of the interest rate and can therefore be calculated just
by knowing the discount factors.
Once we know the risk values and convexity matrix, we can estimate the change in the market
value due to a small change Δ r in the valuation curve by:
Equation 2-262 Duration figures - Effective Convexity: change in market value

Usually, we are interested only in the parallel shift, in which case
Equation 2-263 Duration figures - Effective Convexity: parallel shift

where
Equation 2-264 Duration figures - Effective Convexity: parallel shift

and
Equation 2-265 Duration figures - Effective Convexity: parallel shift

Effective convexity can now be defined as:
Equation 2-266 Duration figures - Effective Convexity

and the convexity term corresponding to an individual risk date is:
Equation 2-267 Duration figures - Effective Convexity: risk date

where Vi is the present value of the ith cashflow.
Note that for an asset with fixed cashflows, the cross-derivatives H ij are equal to zero when i ≠ j .

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In this case we get:
Equation 2-268 Duration figures - Effective Convexity: asset with fixed cashflows

In particular, if the present value is calculated using yield-to-maturity method, i.e. if every cashflow
is discounted with the same yield y m , we obtain:
Equation 2-269 Duration figures - Effective Convexity: YTM method

2.3.4.9.5 Modified Duration
For on-balance instruments modified duration is a relative figure of the IR exposure (1 bp) of the
transaction based on the present value of the transaction. For off-balance instruments (as well as
for on-balance instruments during the settlement period), where the present value is close to zero
and not a good measure of risk taken, we substitute an estimate of the size of the underlying
position.
This estimate depends on the instrument type:

•

FRA and MM future: Average of the absolute value of the present values of the risk values at
each end of the underlying contract period.

•

Bond future: Average of the absolute values of the present value of the position cashflows and
the settlement cashflows of the underlying CTD bond.

•

IR Swap: Average of the present values of the legs.

Example: Bond - Transaction/instrument grouping
If you group by transaction or by instrument in Treasury Monitor, modified duration is calculated as follows:
Equation 2-270 Grouping by transaction: modified duration calculation

10000 × E { i1 }
U mod = -----------------------------------------------sett
pos
φ × ( Vp + Vp )
Where

E { il }
sett

The present value of the settlement cashflows after the figure Spot Date. The value date of the
settlement cashflows is the same as the transaction’s value date.

pos

The present value of the position cashflows after the figure Spot Date. Position cashflows
correspond to all other cashflows, i.e. not settlement.

Vp
Vp
φ

The IR exposure to 1 bp change in the interest rate for the cashflows after the figure Spot Date
(i.e. excluding cashflows before or on the figure Spot Date).

The average of the present value components. φ = 0.5 or 1 depending on the number of
present value components.

Note: For example, if you have a spot position, the only component is the present value of the
position cashflows and in this case φ = 1.

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Note: Settlement cashflows are cashflows with the same date as the value; position cashflows
are all other cashflows.

The IR Exposure 1bp and the Present Value figures are calculated to Valuation Date.

Note: In the case of a partial forward sell or purchase of a position, you should group Instrument

and Liquidity Type (extended), and monitor the 'Committed' part. This excludes the
pending settlement that causes a jump in the present value weight at the instrument level.

Example: Bond - Total grouping
if you group by total in Treasury Monitor, modified duration is calculated as follows:
Equation 2-271 Grouping by total: modified duration calculation

– E { i1 }
U mod = U eff = ⎛ ---------------⎞ × 10000
⎝ Vp ⎠
where

Vp

The present value.

E { i1 }

The IR exposure to 1 basis point (bp) change in the interest rate.

Example: IR Swap - Transaction/instrument grouping
If you group by transaction or by instrument in Treasury Monitor, modified duration is calculated as
follows:
Equation 2-272 Modified Duration: IR Swap

10000 × E { i1 }
U mod = --------------------------------------------------leg1
leg2
φ × ( Vp
+ Vp )
Where

E { il }

The IR exposure to 1 bp change in the interest rate for the cashflows after the figure Spot Date
(i.e. excluding cashflows before or on the figure Spot Date).

leg1

The present value of the cashflows of the first leg after the figure Spot Date.

Vp

leg2

The present value of the cashflows of the second leg after the figure Spot Date.

φ

The average of the present value components.

Vp

Note: φ = 0.5, in the case of IR Swap as we have two present value components (one per leg).

2.3.4.9.6 Effective Spread Duration
Equation 2-273 Key figures: Effective Spread Duration

Eμ
U μ = ----------------------------V p × 0.0001
where E μ is the total spread IR exposure of the position and Vp is the total present value of the
position.

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2.3.4.9.7 Effective Beta Duration
Effective beta duration (duration times spread or DTS) is effective spread duration scaled by
Z-spread. It gives the sensitivity to a relative change in spread, where spread duration is the
sensitivity to an absolute change in spread:
Equation 2-274 Key figures: Effective Beta Duration

Uβ = Uμ × μz
See Risk method Z-Spread on page 123.

2.3.5 Dual currency
A dual currency cashflow is a cashflow where the actual payment is in a different currency to the
cashflow currency. The FX rate used in calculating the settlement amount may be fixed or floating.
The cashflow currency amount may also be fixed or floating. TRM supports the following three
cases:

•

Fixed amount, fixed FX rate, see 2.3.5.1 Fixed amount, fixed FX rate on page 147.

•

Fixed amount, floating FX rate, see 2.3.5.2 Fixed amount, floating FX rate on page 148.

•

Floating amount, fixed FX rate, see 2.3.5.3 Floating amount, fixed FX rate on page 148.

The following sections describe how dual currency cashflows are valuated.

2.3.5.1 Fixed amount, fixed FX rate
In this case the payment amount is known, so that it can be treated the same way as any fixed
cashflow. The essential figures are:

•

Settlement Amount As
As = ASs
where A is Amount, and Ss is Settlement FX Rate

•

Figure Market Value
V = AsD/(SxS)
where Sx is the FX rate between cashflow currency and the settlement currency, S is Figure FX
Convert (between the cashflow currency and the figure currency) and D is the Figure Market
Value Discount Factor.

2.3.5.1.1 Example: Fixed amount, fixed FX rate
Let us consider the following cashflow and market data:
Name

Symbol

Value

Amount

A

7500.0

Settlement FX Rate

Ss

10.0

FX Rate

Sx

9.799

Figure FX Convert

S

1.2

Figure Market Value Discount Factor

D

0.9948283718493263

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Key figures are:
Name

Symbol

Value

Settlement Amount Market Value

As

7500.0 × 10.0 = 75000.0

Market Value

V

75000.0 x 0.9948 / (9.799 x 1.2) = 6345:22

2.3.5.2 Fixed amount, floating FX rate
This case is a risk-wise equivalent to an ordinary single currency cashflow, except that Figure
Payment Amount has to be estimated:
Payment Amount Apay

•

Apay = ASx
where A is Amount, and Sx is FX Rate between cashflow and settlement currencies (not shown in
Transaction Admin).
Figure Market Value

•

Since the FX rate is floating, the market value (and risks) are the same as for a fixed cashflow in
the cashflow currency.
V = AD/S
where D is Figure Market Value Discount Factor (in the cashflow currency).

2.3.5.2.1 Example: Fixed amount, floating FX rate
Market data:
Name

Symbol

Value

Amount

A

1000000.0

FX Rate

Sx

9.799

Figure FX Convert

S

1.2

Figure Market Value Discount Factor

D

0.993433829648000

Name

Symbol

Value

Payment Amount

Apay

1000000.0 × 9.799 = 9799000.0

Market Value

V

1000000.0 x 0.9934 / 1.2 = 827861.52

Key figures are:

2.3.5.3 Floating amount, fixed FX rate
In this case IR exposure is divided between the settlement and cashflow currencies, while FX
exxposure is in the cashflow currency.

•

Payment Amount Ap is estimated using the risk profile defined for the instrument:
Ap = A[D1,D2,s]Ss
where D1 and D2 are the discount factors (in cashflow currency) for the start and end dates of the
interest period, s is the spread, and Ss is the Settlement FX Rate. Function A[] is the payment
amount estimation method provided by the risk profile.

•

148

Figure Market Value is the estimated payment amount discounted and converted to the figure
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V = ApayDpay/(SxS)
where Dp is the discount factor for payment date (in settlement currency).

2.3.5.3.1 Example: Floating amount, fixed FX rate
This example shows calculations with plain vanilla risk profile without spread.
Name

Symbol

Value

Amount

A

1000000.0

FX Rate

Sx

9.799

Settlement FX Rate

Ss

10.0

Figure FX Convert

S

1.2

Figure Market Value Discount Factor

D

0.996858127940000

Figure Present Value Discount Factor (1)

D1

0.999053805572000

Figure Present Value Discount Factor (2)

D2

0.996858127940000

Figure Present Value Discount Factor (p)

Dp

0.996858127940000

Name

Symbol

Value

Payment Amount

Apay

1000000.0 x (0.9991 / 0.9969 - 1) x 10.0 = 22025.98

Market Value

V

22025.98 x 0.9969 / (9.799 x 1.2) = 1867.26

Key figures are:

2.4 Performance calculations
Performance measurement is an area that has become increasingly important as clients of asset
managers have become more sophisticated and demanding. Portfolio managers are expected to
meet or beat a specified benchmark on a regular basis. In order to facilitate calculations and
comparisons of traded and benchmark portfolios, common standards have evolved, such as the
Performance Presentation Standards set up by the Association of Investment Management and
Research (AIMR-PPS). The performance measurement implemented in TRM in Performance Monitor is
based on these standards.
One objective of the performance measurement process is to calculate the performance of traded
portfolios and then compare it to the performance of selected benchmarks. In principle it is possible
to outperform the benchmark by (i) stock (bond) picking, in other words being over or under
exposed in a specific security relative to the benchmark and (ii) using leveraged instruments that
have different payoff profiles than the underlying cash (spot) instruments. Examples of leveraged
instruments include forwards, futures, and options.
The benchmark portfolios used for comparison against the traded portfolios consist of transactions
created from index compositions which represent the target performance for a portfolio. Risk, for
performance measurement, is the amount of deviation from the benchmark rather than absolute
changes in the portfolio market value. Treasury Monitor can be used to produce a key-figure level
analysis of the traded portfolio versus the benchmark.
Performance is measured by the time-weighted rate of return (TWR). TWR measures the change in
the value of a portfolio as a percentage of the capital that has actually been invested.

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2.4.1 Actual basis and all cash basis
The AIMR-PPS standards require that performance is measured on both an actual basis and an all
cash basis. Actual basis and all cash basis can be defined as follows:

•

Actual basis measures the growth of the actual invested capital, in other words it is a
combination of both stock picking and leverage.

•

All cash basis attempts to eliminate the effects of leverage by restating the position into an
equivalent cash position having the same market exposure (the spot equivalent position, SEP).
The all cash basis performance is then the performance measured on the restated cash
equivalent position.

If a fund is using leverage, the AIMR-PPS standards require the presentation of both actual and all
cash basis performance. Since the benchmark is normally non-levered, the comparison between the
benchmark and all cash basis show the stock picking ability of the fund manager whereas the
difference between the actual and the all cash basis performance indicate timely and efficient use of
leverage in managing the fund.

2.4.2 Trade date and value date based performance
Typically a cash (spot) transaction is committed on the trade date but physically delivered and paid
some days later on the value date. Clearly, a bought position is exposed to the market from trade
date but the market value during the period until value date depends on whether the trade or value
date approach is adopted. The two methods are defined as follows:

•

With the trade date method, the market value on the trade date is equal to the value of the
position side of the transaction, and consequently, the cashflow term on the trade date is equal
to the settlement payment. Thus, the trade date method can be seen as trading with
immediately delivery and payment.

•

With the value date method, the market value during the period between trade and value date is
the net value of the position and the settlement payment. On the value day the cashflow term is
equal to the settlement payment and the market value is equal to the value of the position side.

Traditional investment management has adopted the trade date approach, whereas the value date
approach is more prevalent among corporate treasuries. TRM supports both approaches. The default
is the trade date method. The AIMR-PPS standards stated that trade date valuation was required
after 1/1/2005.

2.4.2.1 Bank accounts
If the position includes bank accounts then buying a cash (spot) instrument is just a reallocation of
the needed cash from the bank account into the bought instrument. This should of course not cause
any jumps in the total market value of the position, neither should there be any cashflows in or out
of the aggregated position.
In value date based performance, the total market value does not show any jumps since the money
is physically drawn on the bank account the same day as the bought instrument takes on the full
un-netted market value. The cashflow into the instrument is balanced by the negative cashflow at
the bank account and thus on the aggregated level there are no cashflows in or out of the position.
Using trade date based performance the cashflows do not cancel each other out since the flow into
the instrument happens on the trade date whereas the physical out flow on the bank account is at
value date. Also the total market value jumps as an effect of the trade; at trade date the total value
increases due to the mismatch between the un-netted market value of the bought instrument and
the fact that the money is still in the bank account balance (and will earn interest) until the value
date.
The observed problem can be solved by including a fictitious bank account in the position. On the
calculated fictive account the settlements of bought (sold) instruments are drawn (deposited) at
trade date and subsequently reversed at value date. In this way, when buying (selling) an
instrument we get a negative (positive) cashflow at trade date in the fictitious bank account
balancing the cashflow into (out of) the instrument, and one positive (negative) cashflow at value
date in the fictitious account balancing the flow out of (into) the real bank account. The increase
(decrease) in the market value at instrument level is balanced by the negative (positive) balance in

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the fictitious account. On the aggregated position level, there are no cashflows and no jumps in the
market value, either at the trade date or the value date.

2.4.3 Time-weighted rate of return (TWR)
The ideal TWR index for the period 0 to T, with valuation whenever cashflows occur, is given by:
Equation 2-275

MV 1
MV l + 1
MV L
MV T
P TWRT, 0 = ------------------------- × .... × ----------------------- × .... × --------------------------------------- × -------------------------MV 0 + C 0
MV l + C l
MV L – 1 + C L – 1 MV L + C L
where

–

l = {0, ..., L} is the time, in the period 0 to T, at which the cashflows occur

–

MVl is the market value including accrued income but before any deposits/withdrawals
to/from the portfolio at time l

–

Cl represents the cashflows (deposits, positive flow / withdrawals, negative flow) to/from the
portfolio at time l.

The definitions of the market values and the cashflow terms will depend on: (i) whether
performance is measured on the actual basis or the all cash basis, (ii) whether the trade date or
value date approach is used and (iii) the transaction type, for example whether it is a spot,
forward/future, option or composite instruments such as a swap.
The major drawback with the ideal TWR index is that it requires re-valuing the portfolio each time
there is a cash inflow or outflow. If the portfolio does not include the cash position then every
buy/sell creates a cashflow in/out of the portfolio. Thus, the portfolio has to be re-valued every time
a transaction takes place. This is neither feasible nor practical and thus the ideal TWR index is
normally approximated with the TWR daily sampled index:
Equation 2-276

MV 1
MV t + 1
MV T
P DailyT, 0 = ------------------------- × .... × ----------------------- × .... × --------------------------------------MV 0 + C 0
MV t + C t
MV T – 1 + C T – 1
where

–

MVt is the market value including accrued income but before any deposits/withdrawals
to/from the portfolio on day t,

–

Ct represents the sum of all cashflows (deposits, positive flow / withdrawals, negative flow)
to/from the portfolio during day t:

Ct =

∑

C l̃

l̃ ∈ {t – 1, t }
The Dietz method overcomes the need to know the valuation of the portfolio on the date of each
cashflow by assuming a constant rate of return on the portfolio during the period. The original Dietz
method assumed that all cashflows occurred at the midpoint of the period. The modified Dietz

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method weights each cashflow by the amount of time it is held in the portfolio. The modified Dietz
method for the period from 0 to T is given by:
Equation 2-277

L

MV T +

∑ ( Wl – 1 )Cl

l=0
P Dietz T, 0 = ------------------------------------------------------L

MV 0 +

∑ Wl Cl
l=0

where the weight factor Wl is the proportion of the period (from 0 to T) that the cashflow Cl has been
in/out of the portfolio:

T–l
W l = ----------T
The original Dietz method is obtained by setting the weight Wl = 1/2, for all l.
The AIMR-PPS standards currently require that portfolio performance is evaluated using TWR
calculations at least quarterly and these interim returns are geometrically linked. From 1/1/2001
(periods from that date), monthly valuations are required. The AIMR accept approximation methods
such as the modified Dietz method.

2.4.3.1 Percentage growth from the TWR index
Assuming positive market values, the percentage growth (return) during day t is given by:
Equation 2-278

%

P TWRt, t – 1 = ( P TWRt, t – 1 – 1 ) × 100
Similarly for the whole period from 0 to T the percentage growth is:
Equation 2-279

%

P TWR T, 0 = ( P TWRT, 0 – 1 ) × 100
2.4.3.2 TWR calculations in TRM
In order to calculate daily return in TRM, the intraday Dietz returns are first calculated. Then, the
intraday Dietz returns are geometrically linked as a Time-Weighted Return Index: the product of the
Dietz returns allows for transitions from a short/long position to a long/short position in period 0 to
T. Finally, the daily return in TRM is derived as the growth from the TWR Index between time t and
t-1.

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2.4.3.2.1 Intraday Dietz returns
Due to the problems of determining the exact time of each intra-day cashflow to calculate the
intra-day performance, we assume a constant cashflow weighted by factor W. The intraday Dietz
return is then given by:
Equation 2-280

∑

MV t ( u ) +

∑

( W – 1 )C t ( u )

u∈U
u∈U
P Dietzt, t – 1 = ---------------------------------------------------------------------------------∑ MVt – 1 ( u ) + ∑ WCt ( u )
u∈U

u∈U

where

–

U is the position and u an instrument in that position,

–

MVt(u) is the market value of the instrument u at time t including cashflows during the
period t-1 to t (one day),

–

Ct(u) is the sum of all cashflows in (positive flow) / out (negative flow) to/from the
instrument u during the period t-1 to t:
Ct ( u ) =

∑

C (u)
l̃

l̃ ∈ {t-1, t }

–

W is the constant weight factor applied to the sum of the cashflows (not the individual
cashflows) giving the proportion of the day the intra-day cashflows are assumed to have
been in or out of the position. With w = 1, 1/2, or 0, all cashflows are assumed to take place
at the beginning, middle or end of the day, respectively.

2.4.3.2.2 Geometric linking of intraday Dietz returns
These intraday returns can then be geometrically linked as a Time-Weighted Return Index to
provide PDietzT,0 for the period from 0 to T. This method allows for transitions from a short/long
position to a long/short position in the period 0 to T. With this method, each transition is assumed to
occur at the end of a day.
The M (end day) transition points are collected in the set A:
Equation 2-281

⎛
⎞
⎛
⎞
A = {t: sign ⎜ ∑ MV t ( u ) + ∑ ( W – 1 )C t – 1 ( u )⎟ ≠ sign ⎜ ∑ MV t ( u ) + ∑ WC t ( u )⎟, t=1,..,T}
⎝u ∈ U
⎠
⎝u ∈ U
⎠
u∈U
u∈U
where the variables are as described for Equation 2-280 on page 153 and A(m) is the mth transition
from long/short to short/long (m=1,...,M).
The return for a long sub-period [A(m), A(m+1)] is given by:
Equation 2-282

A ( m+1 )

P FK_TWR [A ( m ),A ( m + 1 )] ( U ) =

∏

P Dietzt, t – 1 ( U )

t = A ( m )+1
and for a short sub-period:
Equation 2-283

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A ( m+1 )

P shortFK_TWR [A ( m ),A ( m + 1 )] ( U ) = 2 –

∏

P Dietz t, t – 1 ( U )

t = A ( m )+1
The combined return index for the whole period from 0 to T, assuming A(0)=0 and A(M+1)=T, is
given by the following:
Equation 2-284

M

P FK_TWR [T,0] ( U ) =

∏ P̃FK_TWR [A( m ),A( m + 1 )] ( U )
m=0

where

P̃ FK_TWR [A ( m ),A ( m + 1 )] ( U )
is given by either

P FK_TWR [A ( m ),A ( m + 1 )] ( U )
if

⎛
⎞
sign ( P FK_TWR [A ( m ),0] ( U ) ) = sign ⎜ ∑ MV A ( m ) ( u ) + ∑ WC A ( m ) ( u )⎟
⎝u ∈ U
⎠
u∈U
or

P shortFK_TWR [A ( m ),A ( m + 1 )] ( U )
if

⎛
⎞
sign ( P FK_TWR [A ( m ),0] ( U ) ) ≠ sign ⎜ ∑ MV A ( m ) ( u ) + ∑ WC A ( m ) ( u )⎟
⎝u ∈ U
⎠
u∈U
2.4.3.2.3 TRM Return as the percentage growth of the TWR Index
Finally, the return during day t is given by:
Equation 2-285 TRM Return as the percentage growth of the TWR Index

%

P TWRt, t – 1 = ( P TWRt, t – 1 – 1 ) × 100

2.4.4 Money-weighted return
Given a portfolio with initial market value V0, cashflows ci on dates ti, and final market value VT at
time T, money weighted return, or internal rate of return (y), is defined as the constant interest rate

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such that the total of the initial value and all cashflows prolonged to time T with y is equal to the
final value:
Equation 2-286

ci
V0
----------------- + ∑ ------------------------- – VT = 0
D ( y ,T )
D (y,T – t i)
i

If the type of the interest rate is compounded (at any frequency), it is possible to choose to discount
all cashflows to the start date, or any other date for that matter, and obtain the same result.
Periodic rate and discount rate will usually provide different results depending on the valuation date.

2.4.4.1 Periodic Rate
If we use interest type Periodic Rate and prolong to the end date of the observation period, the
above equation can be solved without iteration:
Equation 2-287

V 0 ( 1 + yT ) + ∑ c i ( 1 + y ( T – t i ) ) – V T = 0
i

⎛
⎞
V T – V 0 – Σc i = y ⎜ V 0 T + ∑ c i ( T – t i ) ⎟
⎝
⎠
i
V T – V 0 – Σc i
y = --------------------------------------------V0 T + Σi ci ( T – ti )

2.4.5 Instrument market values for third currency
The saved Performance Data (Market Value) of a Portfolio is based on Treasury Monitor's market
value calculation. This performance data is saved by running the Performance Data Calculation
activity.
The Performance Data Calculation activity saves the home currency market value and the local
market value as they are calculated by Treasury Monitor.
Equation 2-288 Home currency market value and local currency market value

V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY }
where
V HomeCCY

The saved performance data (market value)

Sv

The FX conversion from the transaction's Trading Currency (for example GBP) into
the chosen Figure Currency (for example, EUR or USD) depends on the FX method
that is defined at the instrument level (Instrument Editor - Base Valuation page).
See A.2.50 Base Valuation Setup on page 734.
FX method calculations are described in section 2.1.6.3 FX rate calculation on
page 79.

LocalCCY

The transaction currency

HomeCCY

The currency in which the Performance Data Calculation activity was run.

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2.4.5.1 Converting the portfolio home currency into figure currency
By default, the Performance Monitor's market value is calculated and stored in the portfolio trading
currency. Therefore, in order to display the market value in a third currency (i.e. in a figure currency
other than the portfolio trading currency) the Performance Monitor converts the home currency
market value into the third currency using the FX spot rate.

Note: If you want to avoid the FX spot conversion and use the figure currency data that is

calculated in the same way as in the Treasury Monitor, see 2.4.5.2 Figure currency based
on Treasury Monitor's market value calculation on page 156.

To convert the portfolio home currency into the figure currency you use the Performance Data

Calculation activity as follows:
Field

Description

Top Portfolio To Process

Name of the top portfolio. The activity saves the home currency market value in
the portfolio base currency. This is the default behavior if nothing is set in the
Figure Currency field.

Figure Currency

Leave this field empty to save the home currency market value in the portfolio
base currency.

To display the market value in a third currency in the FX Spot Rate figure, the Performance Monitor
converts the home currency market value to the third currency.
Equation 2-289 Home currency market value and local currency market value

V ThirdCCY = V HomeCCY × S { HomeCCY ⁄ ThirdCCY }
where
S

The FX Spot.

Note: Only one home currency market value is saved at a time. When you run the activity again,
the previous market value is replaced with the new one.

2.4.5.2 Figure currency based on Treasury Monitor's market value calculation
The Performance Monitor's market value can also be directly expressed (i.e. without an FX spot
conversion as detailed in 2.4.5.1 Converting the portfolio home currency into figure currency on
page 156) in a third currency i.e. in a figure currency other than the portfolio trading currency.
In this case, like in the Treasury Monitor, the FX conversion of the transaction's cashflow currency
(for example GBP) into the chosen figure currency (for example, EUR or USD) depends on the FX
Method set up in the Instrument Editor in the Base Valuation page (Base Valuation Setup feature). The FX
methods can be:

•

Spot Rate

•

Today's Rate (Forward points)

•

Today's Rate (IR Differential)

See A.2.50 Base Valuation Setup on page 734 for more information.

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To convert the portfolio home currency directly into the figure currency you use the Performance Data
Calculation activity as follows:
Field

Description

Top Portfolio To Process

Name of the top portfolio. The activity saves the home currency market value in
the portfolio base currency. This is the default behavior if nothing is set in the
Figure Currency field.

Figure Currency

The activity saves the home currency market value in the selected figure currency.

For example, if you run the Performance Data Calculation activity with a top portfolio base currency of
USD and nothing in the Figure Currency field, and then you run the activity again with Figure Currency
= EUR, the activity will store both the USD home currency market value and the EUR home currency
market value in the database.

2.4.5.3 Examples
The following the examples illustrate the different FX method calculations for a transaction of
100000000 GBP using the following data:
Data

Example

Top Portfolio base currency

USD

Trading Portfolio base currency

EUR

Transaction currency

GBP

2.4.5.3.1 FX Method = Spot Rate (Default)
This example illustrates two scenarios, one with the Top Portfolio and one with the Portfolio using
the Spot Rate method. The Today' s Rate (Forward Points) method is very similar to the Spot Rate
method and is not described separately.

Note: For the trading of futures, you need to specify a cost of carry instrument at the portfolio
level.

Scenario 1: The activity is run for the Top Portfolio in USD
When the Performance Data Calculation activity is run on the Top Portfolio with a different base
currency to the Trading Portfolio's, the Market Value is saved in the Top Portfolio currency and over
the previously saved market value for the trading currency is overridden.
Equation 2-290 Example - Spot Rate equation

1
V HomeCCY = V LocalCCY × -----------------------------------------------------S { LocalCCY ⁄ HomeCCY }
Equation 2-291 Example - Spot Rate

S { GBP ⁄ USD } = 1.50

Equation 2-292 Example - Spot Rate: Top Currency calculation

V TopHomeCCY = 100000000 × 1.50 = USD150000000

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Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios,
the stored Market Value in the Top Portfolio currency (USD) is converted to the Trading Portfolio
currency (EUR) using the FX Spot Rate. The third currency is calculated as follows:
Equation 2-293 Example - Spot Rate: Third Currency equation

1
V ThirdCCY = V HomeCCY × -----------------------------------------------------S { ThirdCCY ⁄ HomeCCY }

Equation 2-294 Example - Spot Rate

S { EUR ⁄ USD } = 1.20
Equation 2-295 Example - Spot Rate: Third Currency conversion

1
V ThirdCCY = 150000000 × ---------- = EUR125000000
1.20
Scenario 2 The activity is run for the trading portfolio in EUR
When the activity is run for the Trading Portfolio the following calculations are done:
Equation 2-296 Example - Spot Rate: Trading Portfolio equation

V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY }
Equation 2-297 Example - Spot Rate: Trading Portfolio FX Spot

S { GBP ⁄ EUR } = 1.25
Equation 2-298 Example - Spot Rate: Trading Portfolio Currency conversion

V TopHomeCCY = 100000000 × 1.25 = EUR125000000
Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios,
the stored Market Value in the Trading Portfolio currency (EUR) is converted to the Top Portfolio
currency (USD) using the FX Spot Rate. The third currency is calculated as follows:
Equation 2-299 Example - Spot Rate: Trading Portfolio Third Currency equation

V ThirdCCY = V HomeCCY × S { HomeCCY ⁄ ThirdCCY }
Equation 2-300 Example - Spot Rate: Trading Portfolio

S { EUR ⁄ USD } = 1.20
Equation 2-301 Example - Spot Rate: Trading Portfolio Third Currency conversion

V ThirdCCY = 125000000 × 1.20 = USD150000000

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2.4.5.3.2 FX Method = Today' s Rate (IR Differential)
Scenario 1: The activity is run for the Top Portfolio in USD
Equation 2-302 Example - Today' s Rate (IR Differential) Top Portfolio equation

V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY }
Equation 2-303 Example - Today' s Rate (IR Differential) Top Portfolio currency conversion

S v { GBP ⁄ USD } = 1.49983775759643
Equation 2-304 Example - Today' s Rate (IR Differential) Top Portfolio

V TopHomeCCY = 100000000 × 1.49983775759 = USD149983775.76
Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios,
the stored Market Value in the Top Portfolio currency (USD) is converted to the Trading Portfolio
currency (EUR) using the FX Spot Rate. The third currency is calculated as follows:
Equation 2-305 Example - Today' s Rate (IR Differential) Top Portfolio: Third Currency equation

1
V ThirdCCY = V HomeCCY × -----------------------------------------------------S { ThirdCCY ⁄ HomeCCY }

Equation 2-306 Example - Today' s Rate (IR Differential) Top Portfolio: FX Spot

S { EUR ⁄ USD } = 1.20
Equation 2-307 Example - Today' s Rate (IR Differential) Top Portfolio: Third Currency conversion

1
V ThirdCCY = 149983775.76 × ------- = EUR124986479.80
1.2
Scenario 2: The activity is run for the Trading Portfolio in EUR
Equation 2-308 Example - Today' s Rate (IR Differential): Trading Portfolio equation

V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY }
Equation 2-309 Example - Today' s Rate (IR Differential): Trading Portfolio FX Spot

S v { GBP ⁄ EUR } = 1.24988909927463
Equation 2-310 Example - Today' s Rate (IR Differential): Trading Portfolio Currency conversion

V TradingCCY = 100000000 × 1.24988909927 = EUR124988909.93

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Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios,
the stored Market Value in the Trading Portfolio currency (EUR) is converted to the Top Portfolio
currency (USD) using the FX Spot Rate. The third currency is calculated as follows:
Equation 2-311 Example - Spot Rate: Trading Portfolio Third Currency equation

V ThirdCCY = V HomeCCY × S { HomeCCY ⁄ ThirdCCY }
Equation 2-312 Example - Spot Rate: Trading Portfolio

S { EUR ⁄ USD } = 1.20
Equation 2-313 Example - Spot Rate: Trading Portfolio Third Currency conversion

V ThirdCCY = 124988909.93 × 1.20 = USD149986691.91

2.4.6 Instrument market values and cashflows
2.4.6.1 Spot instruments
Spot instruments are un-leveraged instruments and therefore performance measurement based on
actual basis and all cash basis will be identical for those instruments. For the actual basis approach,
the selected trade or value date method defined for the instrument will determine the market values
and cashflows terms. For the all cash basis approach, the trade date values are used.

2.4.6.2 Forward/future instruments
For forward and future instruments the delivery price is typically set such that the contract cost
nothing to enter. The payoff function is linear since a 1 unit increase (decrease) in the unit forward
price implies a 1 unit increase (decrease) in the market value of the (long) forward/future contract.
However, since no initial investment is required the instrument has a leveraged percentage payoff
compared with an equivalent spot position.
As an example, consider a forward contract with delivery price 90, forward price 100 and thus a
market value of 10. If the forward price increases by 1 unit to 101 then the market value of the
forward also increases by 1 unit to 11 leading to a percentages return of (11/10 -1) 10%. The
percentages return on the spot position is around (101/100 - 1) 1% and thus the forward position
can be regarded as geared 10 times compared to the spot position.
The market value at time t of a forward contract is given by:
Equation 2-314

MV t = F t × #unit – K × #unit
where
Ft is the forward price at time t, K is the delivery price and #unit is the contract size. The
sensitivity with respect to the spot rate St is given by:
Equation 2-315

∂MV t
∂( F t × # unit ) ∂( S t × D (t,T) × #unit )
-------------- = ------------------------------- = ------------------------------------------------------ = D (t,T) × #unit
∂S t
∂S t
∂S t
where we have used the arbitrage free relation between the spot and forward rates expressed by
the discount factor D(t,T) for the period between t and the maturity of the contract T.

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The spot equivalent position, SEP (used for the all cash basis approach to performance
measurement) should have the same market exposure as the forward.
Therefore:
Equation 2-316

∂MV SEPt
----------------------- = D (t,T) × #unit → MV SEPt = S t × D (t,T) × #unit = F t × ( #unit )
∂S t
The market value of the spot equivalent position MVSEPt is given by the value of the position side of
the forward/future transaction.
The market values and cashflow terms for the two performance methods are:

•

Actual basis: The performance should measure the growth of the actual invested capital, in
other words the market value is MVt given by Equation 2-314 on page 161. If the transaction
has a cash settlement then the cashflow term at value date is equal to the settled cash amount.
If the transaction results in delivery of the underlying, then this is handled as a spot transaction
committed at the notification date.

•

All cash basis: The effect of the used leveraged should be eliminated by restating the position
into a spot equivalent one, in other words the market value is given by MVSEPt in Equation 2-316
on page 161. The cashflow term at trade date should be equal to the cash needed to buy the
spot equivalent position:
Equation 2-317

C 0 = MV SEP0 = F 0 × # unit = K × # unit
The periodical fixing of futures will cause the period market value change to be realized. From a
performance perspective this is equivalent to selling/buying market value and thus the cashflow
term will balance the change in market value such that the performance is unaffected by the
mark-to-market process.

2.4.6.3 Option instruments
There is a large variety of different option contracts in the market which have a non-linear payoff
function with respect to the price of some underlying instrument. One option position and one spot
position requiring the same initial investment will certainly have very different percentages returns.
Typically, the return of the option position will have larger volatility than the return of the spot
position. In this sense the option position is a leveraged position.
First we assume an option valuation model, in TRM it is the Black-Scholes model, linking the
theoretical unit value of the option f and the spot rate of the underlying instrument St:
Equation 2-318

MV t = f ( S t, t, .... )
The sensitivity of the option position is then given by:
Equation 2-319

∂MV t
∂( f ( S t, t, .... ) )
-------------- = -------------------------------- × #unit = Δ ( S t, t, .... ) × #unit
∂S t
∂S t
where the partial derivative using the Black-Scholes model is delta, a risk key-figure. The spot
equivalent position (SEP) should have the same instantaneous market exposure as the option
position.
Therefore:
Equation 2-320

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2.4 Performance calculations

∂MV SEPt
----------------------- = Δ ( S t, t, .... ) × #unit → MV SEPt = S t × Δ ( S t, t, .... ) × #unit
∂S t
Thus, the SEP position is equal to:

Δ ( S t, t, .... ) × #unit
units of the underlying instrument. The delta typically varies over the life of the option and thus the
unit size of the SEP position is not constant over time.
From the above analysis the following definitions follow:

•

Actual basis: The performance should measure the growth of the actual invested capital, in
other words the market value is MVt given by Equation 2-318 on page 162. If the transaction
has a cash settlement then the cashflow term at value date is equal to the settled cash amount.
If the transaction results in delivery of the underlying, then this is handled as a spot transaction
committed at the exercise date.

•

All cash basis: The effect of the used leveraged should be eliminated by restating the position
into a spot equivalent one, in other words the market value is given by MVSEPt in Equation 2-320
on page 162. The cashflow term at trade date should be equal to the cash needed to buy the
spot equivalent position:
Equation 2-321

C 0 = MV SEP0 = S 0 × Δ ( S 0, 0, .... ) × #unit
where
S0 and

Δ ( S 0, 0, .... )

are the spot rate and delta, respectively, at the time the position was committed. The unit size
of the SEP position may vary with time: increases can be regarded as more units being bought
and decreases as some units being sold. Thus, from a performance perspective the result is a
re-balancing cashflow of:
Equation 2-322

C t = S t × ( Δ ( S t, t, .... ) – Δ ( S t – 1, t – 1, .... ) ) × #unit
2.4.6.4 Swaps and other composite instruments
Swaps and composite instruments such as buy/sell back repos are essentially a combination of other
instruments. In general the actual basis approach treats the composite as a separate instrument
whereas the all cash basis approach handles the components of the composite as separate
transactions. For example, when using the actual basis the market value of a regular interest rate
swap is the net value of the receiving and the paying leg. For the all cash basis however the swap is
regarded as one long spot position in the receiving leg and one short spot position in the paying leg.

2.4.7 Example portfolio
As an example portfolio we will use a cash position together with a spot and forward position in the
same instrument. The initial cash position is 100. On day 1 we first commit one spot transaction of 1
unit at the price 50 for delivery at day 3. Secondly we commit a one month forward transaction of 1
unit at the delivery price 50.5. The market rates used are given in the table below. The overnight
balance on the bank account will earn the constant O/N interest rate of 0.1%.
Day

Spot Rate

Forward Rate

O/N Interest Rate

0

50

50.5

0.1%

1

51

51.5

0.1%

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Day

Spot Rate

Forward Rate

O/N Interest Rate

2

52

52.5

0.1%

3

53

53.5

0.1%

4

54

54.5

0.1%

5

55

55.5

0.1%

6

56

56.5

0.1%

7

57

57.5

0.1%

8

58

58.5

0.1%

9

59

59.5

0.1%

2.4.7.1 Actual basis performance with value date method
The market values and the cashflow terms have been calculated according to the value date version
of the actual basis performance method (see table below). Day 3 is the value date of the spot
transaction and it can be seen that the instrument level cashflow of 50 is balanced by the bank
account cashflow of -50 such that no cashflows occur at the aggregated (portfolio) level.
Day

Spot

Forward

Bank Account

Portfolio

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

0

0

0

0

0

100

0

100

0

1

1

0

1

0

100.10

0

102.1

0

2

2

0

2

0

100.20

0

104.2

0

3

53

50

3

0

50.30

-50

106.3

0

4

54

0

4

0

50.35

0

108.35

0

5

55

0

5

0

50.40

0

110.40

0

6

56

0

6

0

50.45

0

112.45

0

7

57

0

7

0

50.50

0

114.50

0

8

58

0

8

0

50.55

0

116.55

0

9

59

0

9

0

50.60

0

118.60

0

On the portfolio level the performance (see Equation 2-280 on page 153 and Equation 2-279 on
page 152) is given by:

102.1 104.2 106.3 108.35 110.40 112.45 114.50 116.55 118.60
P Dietz 9, 0 = ------------- × ------------- × ------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------100 102.1 104.2 106.3 108.35 110.40 112.45 114.50 116.55
118.60
%
= ---------------- = 1.1860 → P Dietz 9, 0 = ( P Dietz9, 0 – 1 ) × 100 = 18.60%
100
Thus the growth of the invested capital has been 18.60% over the period.
The spot instrument level performance with the weight factor W set to 1 is given by:
The high period performance is more or less due only to the 100% return of day 2 (the infinite
performance of the first day is skipped by setting 1/0 = 1). The high return on day 2 is a
consequence of using the value date method - the market value of the position side and the

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1 2
53
54 55 56 57 58 59
P Dietz9, 0 = --- × --- × --------------- × ------ × ------ × ------ × ------ × ------ × ------ = 2.2692
0 1 2 + 50 53 54 55 56 57 58
%

→ P Dietz 9, 0 = ( P Dietz9, 0 – 1 ) × 100 = 126.92%
payment side of the transaction is netted between trade date and value date. This gives a distorted
instrument level performance that is not easily interpreted.

2.4.7.2 Actual Basis Performance with Trade Date Method
The market values and the cashflow terms have been calculated according to the trade date version
of the actual basis performance method (see table below). On day 1 the spot transaction is
committed and thus we have a cashflow of 50 at the instrument level. In the table we can see that
this cashflow is balanced by the negative cashflow of -50 in the calculated fictive bank account called
Settlement. We also notice that the market value at spot instrument level from trade to value date
is matched by the negative balance in the fictive bank account, such that the market value at
portfolio level is the same as for the value date version of actual basis shown above.
Day

Spot

Forward

Bank Account

Settlement

Portfolio

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

0

0

0

0

0

100

0

0

0

100

0

1

51

50

1

0

100.10

0

-50

-50

102.1

0

2

52

0

2

0

100.20

0

-50

0

104.2

0

3

53

0

3

0

50.30

-50

0

50

106.3

0

4

54

0

4

0

50.35

0

0

0

108.35

0

5

55

0

5

0

50.40

0

0

0

110.40

0

6

56

0

6

0

50.45

0

0

0

112.45

0

7

57

0

7

0

50.50

0

0

0

114.50

0

8

58

0

8

0

50.55

0

0

0

116.55

0

9

59

0

9

0

50.60

0

0

0

118.60

0

On the portfolio level the performance is the same as calculated for the value date method, 18.60%.
The performance at the spot instrument level with the weight factor W set to 1 is now given by:

51
52 53 54 55 56 57 58 59
%
P Dietz 9, 0 = --------------- × ------ × ------ × ------ × ------ × ------ × ------ × ------ × ------ = 1.18 → P Dietz9, 0 = 18%
0 + 50 51 52 53 54 55 56 57 58
showing that the instrument level performance is both stable and connected to the underlying rate
change. In this example the spot rate percentages return is also 18% and thus the match is exact.
With more buys and sells creating more cashflows in and out the match will not be 100%, still the
connection is very strong. The performance attribution analysis of the selection effect have to be
based on the trade date version and not on the value date version since the latter one is distorted by
the trading in the instrument.
The performance of the forward instrument is given by:

1 2 3 4 5 6 7 8 9
%
P Dietz 9, 0 = --- × --- × --- × --- × --- × --- × --- × --- × --- = 9.00 → P Dietz9, 0 = 800%
0 1 2 3 4 5 6 7 8

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Skipping day 0 (setting 1/0 = 1), the return of the forward was 800%. In comparison to the return
on the spot position of 18%, the forward is clearly a leveraged instrument.

2.4.7.3 All cash basis performance (trade date only)
The market values and the cashflow terms have been calculated according to the all cash basis
performance method (see table below). With this method, all spot transactions are handled
according to the trade date version. The figures for the spot transaction in the table below are
therefore the same as for the actual basis performance with trade date method (previous page). The
differences in the rest of the table are due to the fact that the forward position has been restated
into the spot equivalent position (SEP) using the definition in 2.4.6.2 Forward/future instruments on
page 160 (Equation 2-316 on page 161).
Day

Spot

Forward

Bank Account

Settlement

Portfolio

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

Market
Value

Cash
flow

0

0

0

0

0

100

0

0

0

100

0

1

51

50

51.50

50.5

100.10

0

-50

-50

152.60

50.5

2

52

0

52.50

0

100.20

0

-50

0

154.70

0

3

53

0

53.50

0

50.30

-50

0

50

156.80

0

4

54

0

54.50

0

50.35

0

0

0

158.85

0

5

55

0

55.50

0

50.40

0

0

0

160.90

0

6

56

0

56.50

0

50.45

0

0

0

162.95

0

7

57

0

57.50

0

50.50

0

0

0

165.00

0

8

58

0

58.50

0

50.55

0

0

0

167.05

0

9

59

0

59.50

0

50.60

0

0

0

169.10

0

On the forward instrument level the performance (W = 1) is now given by:

·
51
52.5 53.5 54.5 55.5 56.5 57.5 58.5 59.5
P Dietz 9, 0 = ------------------- × ---------- × ---------- × ---------- × ---------- × ---------- × ---------- × ---------- × ---------- = 1.1782
0 + 50.5 51.5 52.5 53.5 54.5 55.5 56.5 57.5 58.5
%

→ P Dietz9, 0 = 17.82%
It can be seen that the all cash basis performance for the forward instrument is very similar to the
18% return on the spot position.
The use of forwards and futures gives the fund manager the possibility to gear the portfolio. In other
words, they can take on more market exposure than there is cash in the portfolio to buy. In this
sense the fund manager borrows money from the market. This implicit borrowing of the fund is
represented at the aggregated portfolio level by a cashflow into the fund at the trade date of the
forward / future. In the table above this can be seen as a cashflow of 50.5 on day 1 at the portfolio
level.
The all cash basis performance on the total portfolio level is given by:
Note that the capital base of the fund was not fully invested; there was about 50 money that could
have been invested in the spot instrument for example. If so, the all cash basis performance at the
portfolio level would have been around 18%.

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P Dietz9, 0 =
152.6
154.7 156.8 158.85 160.9 162.95
165
167.05 169.1
------------------------× ------------- × ------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------165
167.05
100 + 50.5 152.6 154.7 156.8 158.85 160.9 162.95
%

= 1.1236 → P Dietz9, 0 = 12.36%

2.4.8 Risk-adjusted returns
TRM produces risk-adjusted return figures in Performance Monitor. This allows you to measure the
performance of your portfolio in relation to the amount of risk taken.
Throughout this section a simplified notation for the time weighted rate of return (TWR) is used. The
linked intraday Dietz returns used as TWR figures in TRM, defined in Equation 2-284 on page 154
as:

P FK_TWR [T,0] ( U )
will here be denoted simply as:

TWR T, 0 ( P )
2.4.8.1 Sampling frequency
As described in 2.4.3.2 TWR calculations in TRM on page 152, the time-weighted rate of return
(TWR) in TRM is calculated from the intraday Dietz returns, based on daily market values and
cashflows. These returns are then geometrically linked to calculate the TWR for longer periods. Due
to the method of linking, it is generally not possible to calculate the TWR of a sub-period directly
from the sub-period market values and cashflows. The sub-period (from b to a, b ≥ a) TWR of a
portfolio P is instead given by the following equation:
Equation 2-323

TWR b, 0 ( P )
TWR b, a ( P ) = ----------------------------TWR a, 0 ( P )
where
TWRx,0(P) is the cumulative performance, from time 0 to x (a or b) of the portfolio P based on
intraday Dietz returns.

2.4.8.1.1 Sub-period return
The periodic return (%) of the sub-period is:
Equation 2-324

R periodic ( b, a ) ( P ) = 100 × ( TWR b, a ( P ) – 1 )
The continuously compounded return (%) for the sub-period is:
Equation 2-325

R cont ( b, a ) ( P ) = 100 × ln ( TWR b, a ( P ) )

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where
ln() is the natural logarithm. Research has shown that the periodic return data tend to be
skewed whereas the continuously compounded return data are more normally distributed. This
is a tendency which becomes more pronounced with longer sub-periods. The measures of
risk-adjusted return implemented in TRM assume normally distributed returns.
The following sampling frequencies T, or sub-periods, expressed in calendar days are supported in
TRM:
T (sampling frequency)

Calendar Days

1

1 day

1W

7 days

1M

30 days

3M

90 days

During non-business days, the portfolio is assumed to have zero return and will therefore only
accrue interest. For business days, the return for the sub-period, expressed in calendar days from
d-T to d is therefore:
Equation 2-326

TWR d, 0 ( P )
R d, d – T ( P ) = 100 × ln ⎛⎝ ------------------------------------⎞⎠
TWR d – T, 0 ( P )
(continuous yield)
Equation 2-327

TWR d, 0 ( P )
R d, d – T ( P ) = 100 × ⎛ ------------------------------------ – 1⎞
⎝ TWR d – T, 0 ( P ) ⎠
(periodic)

2.4.8.2 Aggregation periods
Statistical measures (mean, variance and standard deviation) of the return given by Equation 2-326
on page 167 or Equation 2-327 on page 167 above can be calculated for either fixed or moving
aggregation periods. Each measure will be associated with (and displayed at) the end date of the
aggregation period. The aggregation period is expressed in terms of the sampling frequency, or
T-periods (1 day, 1 week etc.). The total aggregation period length is given as N T-periods, where N
is an integer.
The return calculations, and hence the statistical measures, are based on the daily linked TWR
series. If the length of the TWR series (which is in days) is not an integer multiple of N*T for fixed
periods, or simply T for the moving periods, then the first period will be a short period.
For example, assume that we have daily returns for one and a half years from 31/12/96 to 30/6/98,
monthly sampling (T =1M) and a 12-month fixed aggregation period (N=12). The set of end dates
would then be given by:
Datesfixed = {30/6/98, 30/6/97}
where the first period, to 30/6/97, would be a short period (only 6 months data available, from
31/12/96). For a 12-month moving aggregation period the set of end dates would be given by:
Datesmoving = {30/6/98, 31/5/98, 30/4/98, 31/3/98, 28/2/98, 31/1/98, 31/12/97}
and the first period, to 31/12/97, would be a full 12-month period.

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2.4.8.3 Portfolio returns
The cumulative return of portfolio P for the aggregation period consisting of N T-periods and with
an end date d is denoted by Rd,d-NT(P) and is calculated in the same way as for the sub-period
return (Equation 2-326 on page 167 or Equation 2-327 on page 167):
Equation 2-328

TWR d, 0 ( P )
R d, d – NT ( P ) = 100 × ln ⎛ ----------------------------------------⎞
⎝ TWR d – NT, 0 ( P )⎠
(continuous yield)
Equation 2-329

TWR d, 0 ( P )
R d, d – NT ( P ) = 100 × ⎛ ---------------------------------------- – 1⎞
⎝ TWR d – NT, 0 ( P ) ⎠
(periodic)
The annualized return is then given by:
Equation 2-330

K(T)
R annual, d, d – NT ( P ) = ⎛ -------------⎞ R
(P)
⎝ N ⎠ d, d – NT
(continuous yield)
Equation 2-331

K(T)

------------⎛
⎞
R d, d – NT ( P )⎞ N
⎛
⎜
– 1⎟
R annual, d, d – NT ( P ) = 100 × 1 + -----------------------------⎜⎝
⎠
⎟
100
⎝
⎠
(periodic)
where
K(T) is the number of T-periods making up a business year. The number of days, weeks and so
on of a business year will differ from year to year. In order to simplify the calculations K(T) is
fixed according to the sampling frequency T as follows:
T (Sampling frequency)

K(T) (no. of T-periods in business year)

1 (non-business days included)

365

1 (non-business days excluded)

260

1W

52

1M

12

3M

4

Annualizing the returns in this way makes the returns for different period lengths and sampling
frequencies more comparable. Fund reports typically present return and risk adjusted return figures
on an annualized basis.

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2.4.8.3.1 Statistics of the portfolio return
The mean, variance and standard deviation of the portfolio return for portfolio P over the
aggregation period are given as key-figures in Performance Monitor. Zero returns (from
non-business days) are not included in these calculations and so these are estimates of the
underlying market. A slightly different notation to that used for the return figures is employed for
statistical figures.
Mean
Equation 2-332

T, N
Rd ( P )

1
= ---Ñ

N–1

∑ Rd – nT,d – ( n + 1 )T ( P )
n=0

Variance
Equation 2-333

T, N
Var ( R d ( P ) )

1
= ------------Ñ – 1

N–1
T, N

∑ ( Rd – nT,d – ( n + 1 )T ( P ) – Rd

(P))

2

n=0

Standard Deviation
Equation 2-334

T, N

σ ( Rd

(P)) =

T, N

Var ( R d

(P))

where
d is a period end date (as defined in 2.4.8.2 Aggregation periods on page 168), T is one of the
supported sampling frequencies, N is the length of the period, expressed in T-periods
and Ñ is the number of T-periodic returns that are non-null (business days).
To clarify the notation used here for the statistical figures, we shall calculate the mean and variance
for the last period ending 30/6/98 from the example given above in 2.4.8.2 Aggregation periods on
page 168. (Daily returns for one and a half years from 31/12/96 to 30/6/98, monthly sampling (T
=1M) and a 12-month aggregation period (N=12). The last period is the same for both the fixed and
moving aggregation periods.
Mean
11

1M,12
R 30/6/98 ( P )

1
= ------ ∑ R 30/6/98-n × 1M, 30/6/98- ( n + 1 ) × 1M ( P )
12
n=0

1
= ------ ( R 30/6/98, 31/5/98 ( P ) + ........ + R 31/7/97, 30/6/97 ( P ) )
12

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Variance
11

1M,12
Var ( R 30/6/98 ( P ) )

2
1M,12
1
= ------ ∑ ( R 30/6/98-n × 1M, 30/6/98- ( n + 1 ) × 1M ( P ) – R 30/6/98 ( P ) )
11
n=0

2
2
1M,12
1M,12
1
= ------ ( ( R 30/6/98, 31/5/98 ( P ) – R 30/6/98 ( P ) ) + ( R 31/7/97, 30/6/97 ( P ) – R 30/6/98 ( P ) ) )
11
The volatility is the annualized standard deviation of the cumulative return.
Volatility
Equation 2-335

T, N

σ annual ( R d

(P))=

T, N

K ( T ) × σ ( Rd

(P))

where
K(T) is the number of T-periods making up the business year. This scaling makes the volatility
from one sampling frequency comparable with the volatility calculated from a different sampling
frequency.
The covariance between two portfolios describes the association between them. For example if a
positive (negative) return in the portfolio P is associated with a positive (negative) return in the
benchmark portfolio B, then the covariance between the portfolios will be positive. If a positive
return in one of them is associated with a negative return in the other, then the covariance between
them will be negative. Given that the returns are normally distributed then a covariance of zero
implies that the returns are totally independent; if you observe the return of one portfolio it gives
you no additional information about the likely return of the other portfolio. The covariance
calculations in TRM exclude the null returns (the returns for non-business days) and so the
covariance estimates are based on the underlying market.
Covariance
Equation 2-336

T, N

Cov ( R d
1 -----------Ñ – 1

T, N

( P ), R d

( B ) )=

N–1
T, N

∑ ( Rd – nT,d – ( n + 1)T ( P ) – Rd

T, N

( P ) ) × ( R d – nT,d – ( n + 1 )T ( B ) – R d

(B))

n=0

The standardized covariance is called the correlation coefficient and can have values ranging
from -1 to +1. A correlation coefficient of +1 implies perfect positive correlation and -1 implies
perfect negative correlation. Perfect positive (negative) correlation means that there is a positive
(negative) linear relation between the returns of the two portfolios. For example if you observe a
positive return in the benchmark portfolio B then you also know the positive (negative) return of the
portfolio P.

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Correlation Coefficient
Equation 2-337

T, N
ρ ( R d ( P ),

T, N
Rd ( B ) ) =

T, N

T, N

Cov ( R d ( P ), R d ( B ) )
-------------------------------------------------------------------------------------T, N
T, N
Var ( R d ( P ) ) × Var ( R d ( B ) )

2.4.8.3.2 TRM variables
The following key-figures related to portfolio return are available in Performance Monitor. The statistics
are provided for user analysis. Standard risk adjusted return measures (for example the Sharpe
Ratio and the Treynor Ratio) are also provided, and are described in 2.4.9 Risk-adjusted return
measures on page 175.

•

The return, cumulative return and annualized return figures: Return, Return (Cumulative) and
Return (Annualized) key-figures, respectively.

•

The statistics of the portfolio (cumulative) return: Return Mean, Return Variance, Return
Standard Deviation, Return Volatility, Covariance, Correlation Coefficient.

2.4.8.4 Excess returns
In performance analysis the fund manager is more interested in the return relative to the
benchmark portfolio than the return of the portfolio itself. The cumulative excess return of
portfolio P relative to the benchmark portfolio B is the difference in returns:
Equation 2-338

R d, d – NT ( P – B ) = R d, d – NT ( P ) – R d, d – NT ( B )
The annualized excess return is then calculated in a similar way to the annualized return as
shown above:
Equation 2-339

K(T)
R annual, d, d – NT ( P – B ) = ⎛⎝ -------------⎞⎠ R
(P – B)
N
d, d – NT
(continuous yield)
Equation 2-340

K(T)

------------⎛
⎞
R d, d – NT ( P – B )⎞ N
⎜
⎛
– 1⎟
R annual, d, d – NT ( P – B ) = 100 × 1 + ---------------------------------------⎜⎝
⎠
⎟
100
⎝
⎠
(periodic)

2.4.8.4.1 Statistics of the excess return
The mean, variance, and standard deviation of the excess return of the portfolio P relative to the
benchmark B are given as key-figures in Performance Monitor. Tracking error is the same as
the standard deviation. The annualized tracking error is calculated in the same way as the
volatility figure above. Zero returns (from non-business days) are not included in these calculations.

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Mean
Equation 2-341

T, N
Rd ( P

1
– B ) = ---Ñ

N–1

∑ Rd – nT,d – ( n + 1 )T ( P ) – Rd – nT,d – ( n + 1 )T ( B )
n=0

Variance
Equation 2-342

T, N

Var ( R d
1 -----------Ñ – 1

(P – B)) =

N–1
T, N

∑

( ( R d – nT,d – ( n + 1 )T ( P ) – R d – nT,d – ( n + 1 )T ( B ) ) – R d

(P – B))

2

n=0

Standard Deviation
Equation 2-343

T, N

σ ( Rd

(P – B)) =

T, N

Var ( R d

(P – B))

Tracking Error
Equation 2-344

T, N

TE ( R d

T, N

( P – B ) ) = σ ( Rd

(P – B))

Tracking Error (Annualized)
Equation 2-345

T, N

TE annual ( R d

(P – B)) =

T, N

K ( T ) × TE ( R d

(P – B))

where

–

d is a period end date (as defined in 2.4.8.2 Aggregation periods on page 168)

–

T is one of the supported sampling frequencies

–

N is the length of the period, expressed in T-periods

–

Ñ is the number of T-periodic returns that are non-null (business days) and

–

K(T) is the number of T-periods making up the business year.

2.4.8.4.2 TRM variables
The following key-figures are available in Performance Monitor. The statistics are provided for user
analysis. Standard risk adjusted return measures (for example Alpha, Beta, the Information Ratio)
are also provided, and are described in 2.4.9 Risk-adjusted return measures on page 175.

•

172

The excess return, cumulative excess return and annualized excess return: Excess Return,
Excess Return (Cumulative) and Excess Return (Annualized) key-figures, respectively.

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•

The statistics of the excess return: Excess Return Mean, Excess Return Variance, Excess Return
Standard Deviation, Tracking Error, Tracking Error (Annualized), Excess Return Volatility (same
as Tracking Error (Annualized)).

2.4.8.5 Linear regression
The figure below shows concurrent portfolio and benchmark returns together with the estimated
best-fit linear regression (least squares method).

If we assume that we have the following set of concurrent portfolio returns:

{ R d – nT,d – ( n + 1 )T ( P ), ( R d – nT,d – ( n + 1 )T ( B ) ), n = 0, ..... , N -1 }
where
n represents each ‘pair’ of concurrent portfolio R(P) and benchmark R(B) returns, then the linear
regression function for each pair is then given by the following straight-line equation:
Equation 2-346

R d – nT,d – ( n + 1 )T ( P ) = α + β × R d – nT,d – ( n + 1 )T ( B )
α (alpha) and β (beta) are selected such that the sum of the squared differences between each
pair of concurrent returns (estimation error) is minimized. The estimation error is given by:
Equation 2-347

N–1
T, N
Err d ( α,

β) =

∑ [ Rd – nT,d – ( n + 1 )T ( P ) – (α + β × Rd – nT,d – ( n + 1)T ( B )) ]

2

n=0

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Minimizing the estimation error gives the following relationships:
Equation 2-348

T, N

α* = R d

T, N

( P ) – β* × R d

(B)
Equation 2-349

T, N

T, N

Cov ( R d ( P ), R d ( B ) )
β* = ------------------------------------------------------------T, N
Var ( R d ( B ) )
Equation 2-350

T, N

Err d

T, N

( α*, β* ) = ( N – 1 ) × Var ( R d

2

(P)) × (1 – R )

where
R2 is given by:
Equation 2-351

T, N
T, N
⎛
⎞2
Cov
(
R
(
P
),
R
(
B
)
)
2
T, N
T, N
d
d
R ( R d ( P ), R d ( B ) ) = ⎜⎜ ---------------------------------------------------------------------------------------⎟⎟
T, N
T, N
⎝ Var ( R d ( P ) ) × Var ( R d ( B ) )⎠

α* and β* are the best fit values of the alpha α and beta β. Alpha is the intercept on the y-axis
and beta is the slope of the linear regression function.

Alpha represents the part of the return from portfolio P which is independent of the benchmark
movement and beta is the sensitivity of the return with respect to the benchmark.
The variable R2, a least squares measure (the correlation coefficient given by Equation 2-337 on
page 171 squared), is an indication of the goodness of fit of the linear regression to the data. The
higher the value of R2, the better the fit of the linear function to the data - in other words, the more
the portfolio returns are determined by the benchmark returns.

2.4.9 Risk-adjusted return measures
In all risk-adjusted return measures the return is related to the risk taken. Therefore we need to
quantify the risk. The most common measures are the portfolio return standard deviation, beta and
the tracking error. The standard deviation can be seen as the risk from the perspective of the end
investor in the fund whereas beta and the tracking error represent more the risk taken by the fund
manager. Other risk figures, described below, are also provided for user risk analysis.

2.4.9.1 TRM variables
The following risk adjusted return measures are provided. These are described in more detail below.
General statistics (mean, variance, standard deviation) of the portfolio and excess returns are also
provided (see 2.4.8.3 Portfolio returns on page 168 and 2.4.8.4 Excess returns on page 171).

•

174

Risk adjusted return measures: Return Standard Deviation (standard deviation of the portfolio
return), Return Volatility (annualized standard deviation of the portfolio return), Beta, Tracking
Error, Tracking Error (Annualized), Alpha, Alpha (Annualized), Information Ratio, Sharpe Ratio,
Modigliani-Modigliani, Treynor Ratio, Jensen’s Alpha.

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2.4.9.2 Return standard deviation
The end investor’s main concern is typically the absolute level of the portfolio returns. For the
investor the risk is therefore the uncertainty of the future portfolio returns. The historical risk is
often measured as the N period standard deviation of the T-periodic returns of the portfolio P, as
shown in Equation 2-334 on page 169 (square root of the variance). If we assume that the portfolio
returns are normally distributed then we can calculate confidence intervals for the future returns,
based on the historical standard deviation (SD) and mean. For example, we can say that the future
returns will be in the interval mean +/- 1SD with 68% confidence and in the interval mean +/- 2SD
with 95% confidence.

2.4.9.3 Return volatility
The volatility is the annualized standard deviation of the cumulative portfolio return -standard
deviation scaled by √K(T), where K(T) is, as shown above, the number of T-periods making up the
business year (Equation 2-335 on page 170). This scaling makes the volatility from one sampling
frequency comparable with the volatility calculated from a different sampling frequency.

2.4.9.4 Beta
The risk for the fund manager is more the uncertainty of the future returns relative to the
benchmark portfolio than the return of the portfolio itself; the risk-less portfolio for a fund manager
is a portfolio that is guaranteed the same future returns as the benchmark. The historical risk
relative to the benchmark can be measured by beta which, as shown in the previous section, is a
measure of the sensitivity of the portfolio P with respect to changes in the benchmark portfolio B:
Equation 2-352

T, N
β ( R d ( P ),

T, N
Rd ( B ) ) =

T, N

T, N

Cov ( R d ( P ), R d ( B ) )
------------------------------------------------------------T, N
Var ( R d ( B ) )

where the covariance is given by Equation 2-336 on page 171 and the variance by Equation 2-333
on page 169. A beta of 1 implies that the portfolio will tend to move with the benchmark, and thus
the fund manager has zero risk relative to the benchmark. A beta greater (less) than 1 means that
the portfolio will fluctuates more (less) than the benchmark and therefore the fund manager has
taken a position relative to the benchmark.

2.4.9.5 Tracking error
Tracking error is another benchmark related risk measure defined as the N period standard
deviation of the T-periodic excess return of the portfolio P relative to the benchmark B (Equation
2-344 on page 172). The annualized tracking error for excess returns is calculated in the same way
as the annualized volatility for portfolio returns above; tracking error scaled by √K(T), where K(T) is
the number of T-periods making up the business year. This scaling, as before, means that
annualized tracking errors calculated with different sampling frequencies (T-periods) can be
compared.
If we assume that the excess returns are normally distributed and that the historical tracking error
is a good prediction of the future then, as for the portfolio return itself above, we can predict
confidence intervals for the future excess returns (mean +/- 1SD with 68% confidence and mean
+/- 2SD with 95% confidence).

2.4.9.6 Alpha
This is the alpha term in the linear regression presented in 2.4.8.5 Linear regression on page 173.
This figure can be written in terms of T-period return:
Equation 2-353

where as before, the covariance is given by Equation 2-336 on page 171, the variance by Equation
2-333 on page 169, and the means by Equation 2-332 on page 169.

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T, N
α ( R d ( P ),

T, N
Rd ( B ) ) =

T, N
Rd ( P )

T, N

T, N

Cov ( R d ( P ), R d ( B ) )
T, N
- × Rd ( B )
- ------------------------------------------------------------T, N
Var ( R d ( B ) )

The annualized alpha is then given by:
Equation 2-354

T, N

α annual ( R d

T, N

( P ), R d

T, N

( B ) ) = K ( T ) × α ( Rd

T, N

( P ), R d

(B))

(continuous yield)
Equation 2-355

T, N
α annual ( R d ( P ),

T, N
Rd ( B ) )

T, N

T, N

α ( R d ( P ), R d ( B ) )⎞
⎛⎛
= 100 × ⎜ ⎜ 1 + -------------------------------------------------------⎟
100
⎠
⎝⎝

K(T)

⎞
– 1⎟
⎠

(periodic)
where
K(T) is, as before, the number of T-periods making up a business year.
The alpha is the part of the return from portfolio P that can’t be attributed to the risk taken in terms
of beta. A positive alpha can be obtained by stock picking and/or market timing. With stock picking
the fund manager tries to be overexposed or underexposed in securities having a mean return
above or below the benchmark return, respectively. With market timing the manager tries to
fine-tune the beta of the fund such that it is less or greater than 1 when the benchmark return is
negative or positive, respectively. A fund tracking the benchmark will, by definition, have an alpha
value of zero. The alpha value can therefore be seen as the contribution to the portfolio’s return
coming from active fund management.

2.4.9.7 R squared
The R2 figure is a measure of how much information alpha and beta provide about the portfolio. It is
a least squares variable (see 2.4.8.5 Linear regression on page 173), an indication of the goodness
of fit of the linear regression to the data. The higher the value of R2, the better the fit of the linear
function to the data - in other words, the more the portfolio returns can be described in relation to
the benchmark returns. Figures over 0.75 or under 0.25 are considered to indicate that the
explanatory power is high or low, respectively. In other words, R2 provides an indication of how well
the behavior of the portfolio returns is described by the alpha and beta values.

2.4.9.8 Information ratio
The information ratio is the annualized period excess return of the portfolio P relative to the
benchmark B, divided by the annualized tracking error:
Equation 2-356

T, N

IR d

R annual, d, d – NT ( P – B )
( P, B ) = -------------------------------------------------------T, N
TE annual ( R d ( P – B ) )

where
the annualized excess return is given by Equation 2-339 on page 171 (continuously
compounded returns) or Equation 2-340 on page 172 (periodic returns), and the annualized
tracking error by Equation 2-341 on page 172.

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For example:
1M, 12

IR 30/6/98 ( P, B )
is the information ratio calculated from the monthly excess returns during the 12-month period
starting at 970630 (980630 - 12*1M) and ending at 980630. A positive information ratio indicates
that the investment decision to deviate from the benchmark was a good decision since it resulted in
a higher return. The higher the information ratio the more excess return was obtained by the same
risk taken. An information ratio of +0.5 is considered to be an acceptable result, a ratio of +0.75 a
good result and a figure of +1.0 is typically seen as an excellent result.

2.4.9.9 Sharpe ratio
The figure below shows the risks and returns of some portfolios - the benchmark B, example
portfolios and a risk-free portfolio. The return is measured as the annualized period return, Rannual,
and the risk as the annualized standard deviation of the T-periodic returns (the volatility σannual).

2.4.9.9.1 Risk-return characteristics (risk measured by volatility)
It is clear that the benchmark B is preferable to portfolio P2 since the return is higher and the risk is
less. The comparison against P1 is not so clear cut; the return of P1 is lower but so is the risk. In
portfolio theory the existence of a risk-free portfolio is usually assumed. The return of the risk-free
portfolio is fixed (in other words the volatility is zero) and known in advance. Furthermore the
investor is allowed to buy the portfolio (invest money at the risk-free interest rate), or sell short the
portfolio (borrow money at the risk-free interest rate, and invest the proceeds in the risky portfolio).
All combinations of the risk-free portfolio and a risky portfolio lie along the straight line connecting
them (line 1 for P1 and line 3 for P2) in the risk-return diagram above. By borrowing at the risk-free

interest rate and investing the proceeds in portfolio P1, the investor can construct the portfolio P′1
that has the same risk as the benchmark B but a higher return. Given the existence of the risk-free
portfolio a rational investor will prefer portfolio P1 to B and P2(and B to P2). The preferred portfolio is
the one with the greatest slope, that is to say with the largest Sharpe ratio:

Equation 2-357

T, N

Sharpe d

R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree )
( P, P riskfree ) = ----------------------------------------------------------------------------------------------------------------T, N
σ annual ( R d ( P ) )

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where the annualized returns are given by Equation 2-330 on page 168 (continuously compounded
returns) or Equation 2-331 on page 169 (periodic returns), and the volatility by Equation 2-335 on
page 170. A high Sharpe Ratio is therefore an indication of high returns relative to the risk taken.

2.4.9.10 Modigliani-Modigliani (M2)
This is a version of the Sharpe ratio analysis that ranks portfolios in exactly the same order as the
Sharpe analysis but gives the result in terms of return and not as a ratio. The risk-adjusted return
measure is called Modigliani-Modigliani, or M2 for short. Given a portfolio P, M2 is the return of the
combination of the risk-free portfolio and P that has the same risk (in terms of volatility) as the
benchmark B. Thus, for portfolio P1 in the figure above (Risk-return characteristics (risk

measured by volatility)), M2 is equal to the return of portfolio P′1. A high value of M2 is therefore
an indication of high returns relative to the risk taken. Mathematically, M2 of portfolio P is given by:
Equation 2-358

M

2 T, N
d ( P,

B, P riskfree )
T, N

= R annual, d, d – NT ( P riskfree ) + σ annual ( R d

T, N

( B ) ) × Sharpe d

( P, P riskfree )

= R annual, d, d – NT ( P riskfree ) +
T, N

σ annual ( R d ( B ) )
-------------------------------------------- × R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree )
T, N
σ annual ( R d ( P ) )
The annualized returns are given by Equation 2-330 on page 168 (continuously compounded
returns) or Equation 2-331 on page 169 (periodic returns), and the volatility by Equation 2-335 on
page 170.

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2.4.9.11 Treynor ratio
The Treynor ratio is similar to the Sharpe ratio but with beta as the risk measure. The figure below
shows the risk and return characteristics for some portfolios where the risk measure is beta. Note
that the benchmark B has a beta of 1 and the risk free portfolio is assumed to have a beta of zero.

2.4.9.11.1 Risk-return characteristics (risk measured by beta)
The Treynor ratio measures the slope of the line connecting the risk-free portfolio and the risky
portfolio:
Equation 2-359

T, N

Treynor d

R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree )
( P, B, P riskfree ) = ----------------------------------------------------------------------------------------------------------------T, N
T, N
β ( R d ( P ), R d ( B ) )

where the annualized returns are, as before, given by Equation 2-330 on page 168 (continuously
compounded returns) or Equation 2-331 on page 169 (periodic returns), and the beta by Equation
2-352 on page 175. As for both the Sharpe Ratio and M2, a high value of this ratio is an indication
of high returns relative to the risk taken.
The fund manager has outperformed the benchmark if the fund has a higher Treynor ratio than the
benchmark. In the figure above, portfolio P1 has outperformed the benchmark in terms of Treynor
ratio (but not P2).

2.4.9.12 Jensen’s Alpha
If the benchmark consists of all securities the fund can invest in (for example the issued equities in
all listed companies besides the tobacco related ones), we make the assumption that the line
connecting the risk-free portfolio and the benchmark (line 2) represents the set of risk-return
effective portfolios. So for every risk level the largest expected return is obtained by investing in a
combination of the risk-free portfolio and the benchmark that has the wanted risk level. If the
wanted risk level in beta terms is β̃ then the expected annualized period return of the effective
portfolio is given by:
Equation 2-360

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R annual, d, d – NT ( P ( β̃ ) )
= R annual, d, d – NT ( P riskfree ) + β̃ × R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree )
Jensen’s Alpha is calculated as the actual return of the portfolio P less the return of the effective
portfolio (Equation 2-360 on page 179) with identical beta:
Equation 2-361

T, N

Jensen d

T, N

– β ( Rd

( P, B, P riskfree ) = R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree )
T, N

( P ), R d

( B ) ) × ( R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree ) )

where the annualized returns are, as for the Treynor ratio, given by Equation 2-330 on page 168
(continuously compounded returns) or Equation 2-331 on page 169 (periodic returns), and the beta
by Equation 2-352 on page 175. A positive value of Jensen’s Alpha indicates that the portfolio has a
higher return than the effective portfolio (a benchmark with the same level of risk) and a negative
value implies a lower return.
In the figure above (Risk-return characteristics (risk measured by beta)), we have a positive
value of Jensen’s alpha for portfolio P1 (the return is higher than for B′) and a negative value for

portfolio P2 (the return is less than for B′′). Therefore portfolio P1 is a more risk-return effective
portfolio than the benchmark (but not P2).

2.4.10 Performance attribution
The goal of performance attribution is to quantify the contribution of the various investment
decisions to the final overall portfolio (excess) return.
The investment decision variables supported are the ones expressed via the Performance Monitor
grouping dimensions, for example, Market, Currency, Branch Codes, Issuer, Maturity Period, and so
on.
The attribution models split the excess return into Allocation, Selection and Interaction effects:

•

Allocation is the investment decision between the selected grouping

•

Selection measures the investment decision within the selected grouping

•

Interaction is the interaction between the allocation and selection term

The benchmark is represented as a portfolio with transactions.

2.4.10.1 Performance attribution methods
The following attribution methods are used in TRM:

•

Single currency portfolios
The Brinson framework.

•

Multi currency portfolios
The Karnosky and Singer framework.

•

Combining attribution effects over time
The Cariño method.

The calculations used in each of these methods are described in the next section.

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2.4.10.1.1 Base currency performance attribution
Here are the calculations used for the Brinson attribution of excess return:
Equation 2-362

R – R = Σ wi Ri – Σ wi Ri = A + S + I
i
i
Allocation
Equation 2-363

A = Σ ( wi – wi ) ( Ri – R )
i
Selection
Equation 2-364

S = Σ wi ( Ri – Ri )
i

Interaction
Equation 2-365

I = Σ ( wi – wi ) ( Ri – Ri )
i

where
wi is the fraction of the market value invested in the i-th sector, and Ri is the return.
The corresponding benchmark values are denoted by

wi and Ri .

2.4.10.1.2 Multi- currency performance attribution
The return of the multi-currency portfolio is given by:
Equation 2-366

R base = Σ w i ( R i – C̃ ccy ( i ) ) + Σ ( w i ( ccy ) + h ccy ) ( C̃ ccy + ε base, ccy )
i
ccy
+ Σ h ccy ( C ccy – C̃ ccy )
ccy

where:

–

wi is the fraction of the market value invested in the i-th asset.

–

Ri is the return of the assets in the i-th segment expressed in the local currency.

–

Cccy is the local currency risk free return.

–

hccy is the currency weight of FX overlay hedge transactions.

–

εccy is the change in the spot FX rate (common to all investments in each currency).

–

Cccy is the local currency return of FX overlay hedge transactions.

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2.4.10.1.3 Asset-related performance attribution
Brinson style factors:
Equation 2-367

A asset = Σ ( w i – w i ) ( ( R i – C̃ ccy ( i ) ) – BRP )
i

Equation 2-368

S asset = Σ w i ( R i – R i )
i

Equation 2-369

I asset = Σ ( w i – w i ) ( R i – R i )
i

where BRP is the benchmark local return premium:
Equation 2-370

BRP = Σ w i ( R i – C̃ ccy ( i ) )
i

Asset leverage:
Equation 2-371

L asset = ( – BRP ) ( Σ w i – Σ w i )
i

i

Equation 2-372

( Σ wi + Σ
i

ccy

h ccy = 1 )

2.4.10.1.4 Currency related performance attribution
Brinson style factors:
Equation 2-373

A hedge = Σ

ccy

( ( w i ( ccy ) + h ccy ) – ( w i ( ccy ) + h ccy ) ) ( ( C̃ ccy + ε base, ccy ) – BCR )
Equation 2-374

S hedge = Σ

ccy

h ccy ( C ccy – C̃ ccy )
Equation 2-375

I hedge = Σ

ccy

( h ccy – h ccy ) ( C ccy – C̃ ccy )

where CRP is the benchmark currency return:
Equation 2-376

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BCR = Σ

( w i ( ccy ) + h ccy ) ( C ccy + ε base, ccy )
ccy
Assumed common FX return might imply a small unexplained residual:
Equation 2-377

R base – R base = A asset + S asset + I asset + L asset + A hedge + S hedge + I hedge
2.4.10.1.5 Linking attribution factors over time
Daily attribution is preferable as weight factors wi are time dependent.
Excess return and arithmetical factors are not additive over time:
Equation 2-378

R – R = ( 1 + R1 ) ( 1 + R 2 ) – ( 1 + R 1 ) ( 1 + R2 ) ≠ ( R1 – R1 ) + ( R2 – R2 )
The error can be distributed over time such that:
Equation 2-379

1
R – R = ---- Σ k t ( R t – R t )
Kt
where
Equation 2-380

ln ( 1 + R ) – ln ( 1 + R )
K = ----------------------------------------------------R–R
and
Equation 2-381

ln ( 1 + R t ) – ln ( 1 + R t )
k t = -------------------------------------------------------Rt – Rt
2.4.10.2 Example of single currency performance attribution
This example is based on four equities grouped into two sectors by branch code: Automobiles-sector
(BMW and General Motors) and Telecom-sector (Motorola and Nokia). There are two portfolios: a
managed trading portfolio and a benchmark portfolio. The performance of the managed trading
portfolio is measured against the benchmark, where each stock has an equal 25% weight at the
beginning of the period.
For the sake of simplification, the performance measurement period is only one day, 23rd of April
2003. The market rates used in this example are fictitious and are set to illustrate the mechanism of
performance attribution.
In the managed trading portfolio, the Telecom-sector is over weighted and, respectively, the
Automobiles-sector is under weighted in comparison to the benchmark with equal weights. The
weights, amounts and returns for equities, sectors, managed portfolio and benchmark are presented
in the Performance Monitor view below.

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The benchmark portfolio has a return of 8.57 % and the managed portfolio has a return of 12.86 %.
The investment decisions of the managed portfolio have created a 4.29% excess return, which can
be further analyzed by Performance Attribution Key-Figures in Performance Monitor.

The Key-Figures Allocation, Selection and Interaction for Automobiles and Telecom sector are
calculated as shown in the following sections.

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2.4.10.2.1 Automobiles

2.4.10.2.2 Telecoms sector
Allocation = (66.00% - 50.00%) * (27.21% - 8.57%) = 2.999677 %.
Selection = 50.00% * (26.26% - 27.21%) = -0.471547 %.
Interaction = (66.10% - 50.00%) * (26.26% - 27.21%) = -0.151837 %.
The Allocation Figure expresses how successful the asset manager has been in allocating funds
between sectors. In this example, it is the decision to overweight the Telecom sector and to
underweight the Automobiles sector. The Telecom sector return is considerably higher than the
negative one of the Automobiles sector. The positive Allocation Figure of the Telecom sector is
intuitively straightforward, since the sector performed well and it was over weighted in the managed
portfolio. The positive Allocation Figure of the Automobiles sector is due to the fact that this lower
return sector was under weighted in the managed portfolio in comparison to the benchmark.
The Selection Figure expresses how successful the asset manager has been in stock picking (to
select equities within a certain group) here within a sector. The negative Figure Selection means
that within the sector, higher return equity was underweighted and lower return equity was
overweighted, in comparison to the benchmark portfolio.
The Figure Intersection represents the part of the excess return that cannot be attributed either to
allocation or selection decisions. The sum of the Allocation, Selection and Interaction figures equals
the difference between managed portfolio and benchmark portfolio returns, that is, the excess
return.

2.4.10.3 Example of multi-currency performance attribution
The following example is based on four equities, which are grouped according to currency
denomination; EUR for BMW and NOKIA and USD for GENERAL MOTORS and MOTOROLA.
The benchmark portfolio consists of these four stocks which have an initial weight of 25 % each.
Therefore, the benchmark portfolio has initially equivalent exposures in both currencies.
The managed trading portfolio consists of the investments in these four stocks, but with different
weights than in the benchmark portfolio. In comparison with the benchmark, USD assets are

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over-weighted: USD denominated stocks total 72% and EUR stocks 28% of the initial market value
of the managed portfolio.
In order to bring currency exposure of the managed portfolio in line with the benchmark, USD
dollars are sold against EUR by FX-Forward transaction. As a result of the hedge, the managed
portfolio has 49.60 % exposure in EUR and 50.40 % exposure in USD.
For the sake of simplification, the performance measurement period is only one day, 23rd of April
2003. During the day, USD is set to depreciate 10 % against the EUR. The market rates used in this
example are fictitious and are set to illustrate the mechanism of multi-currency attribution. All
market values are expressed in EUR.
The following image displays asset market values at the beginning and end of the period:

This image illustrates the portfolio structure:

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These are the intermediate results used to calculate attribution figures:

The Key-Figures Asset Allocation, Asset Selection, Asset Interaction and Asset Leverage for EUR
denominated investments is calculated as follows:

2.4.10.3.1 Asset allocation
The value added by the decision to deviate from the benchmark’s asset allocation is indicated by the
asset allocation key figure.
For multicurrency investments, the relevant benchmark to be used to analyze the value added of
local currency allocation decisions is the average local currency return premium, known as BRP.
Equation 2-382 A asset

where
Wi

Asset Weight of the ith group in the Portfolio
Asset Weight of the ith group in the Benchmark
Return of the ith group in the Benchmark

local currency risk free rate of return

BRP is the benchmark local return premium:
Equation 2-383 BRP

Asset Allocation = (27.62%-50.00%) * (12.97%-8.38%) = -1.028916306%
Equation 2-384 S asset

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Asset Selection = 50.00% * (19.06% - 12.98%) = 3.0397352%
Asset Interaction = (27.62% - 50.00%) * (19.06% - 12.98%) = -1.36075776%
Equation 2-385

Asset Leverage = 8.38% * (99.99% - 100.00%) = -0.000836592%
Equation 2-386

The Key-Figures Hedge Allocation, Hedge Selection and Hedge Interaction for EUR denominated
investments are calculated as follows:

2.4.10.3.2 Hedge allocation
The value added by the decision to deviate from the benchmark’s currency allocation is indicated by
the hedge allocation key figure. When determining the amount allocated to a certain currency, both
the underlying investments and currency overlays are taken into account. When determining
currency returns, both the risk-free return of a currency and change in the FX rate against the
portfolio's base currency are taken into account.
Equation 2-387 A hedge

where

CRP is the benchmark currency return. It expresses the currency return (risk free rate + change
in FX rate against the portfolio's base currency) of the benchmark.

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Currency weight of portfolio FX overlay hedge transactions.

Currency weight of Benchmark FX overlay hedge transactions.

Change in the spot FX rate (common to all investments in a particular currency)

Hedge Allocation = (49.60%-50.00%)*(0.01% - (-4.54%)) = -0.018016123%
Hedge Selection
Equation 2-388 Hedge selection

where
Local currency return of FX overlay hedge transactions.

In this example, the hedge selection figure is zero, since there are no hedges in the benchmark
portfolio.
Hedge Interaction = (21.99% - 0.00%) * (0.01% - 0.009722%) = -0.000038688%.
Equation 2-389 Hedge interaction

2.4.11 Performance measurement key-figures
The key-figures available in Performance Monitor are described in the following table.
These figures include the risk adjusted return measures, for example the Information Ratio and
Modigliani-Modigliani (see 2.4.8 Risk-adjusted returns on page 166). More details about these
key-figures and how they are calculated are given in the section 2.4 Performance calculations on
page 149.
Figure

Definition

Allocation

The Brinson performance attribution factor measuring how well money has been
allocated (relative benchmark) between the selected groups (such as Branch Code),
given by:
Allocation_i (T) = (w_it - W_it)*(R_it - R_i)
where
w_it is the Attribution Weight of the ith group in the portfolio
W_it is the Attribution Weight of the ith group in the Benchmark
R_it is the Return of the ith group in the Benchmark
R_t is the Benchmark total return at time T

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Figure

Definition

Allocation
(Cumulative)

The allocation factor (A) that is additive over time:

where

R = cumulative total Portfolio Return

R

= cumulative total Benchmark Return

and

Rt = total Portfolio return on day t

Rt = total Benchmark Return on day t
Allocation (cumulative) T = sum t=1 to T Excess Return Factor (t) *
Allocation (t) / Excess Return Factor (Cumulative)
Alpha

The part of the return on a portfolio that cannot be attributed to the risk taken (the
risk taken in terms of beta). It is the intercept of the y-axis of the linear regression
function between the portfolio and the benchmark portfolio.

Alpha (Annualized)

The alpha of the portfolio, converted into an annualized figure.

Asset Allocation

The multi-currency performance attribution is based on Karnosky and Singer
framework. The Allocation, Selection, and Interaction terms follow Brinson et al.
framework, similar to the single currency performance attribution.
The Asset Allocation is the performance attribution factor measuring how successfully
funds have been allocated relative to the benchmark between the selected groups
(such as Branch Code) given by:

where
Asset Weight of the ith group in the Portfolio
Asset Weight of the ith group in the Benchmark
Return of the ith group in the Benchmark
Local currency risk free rate of return
BRP is the benchmark local return premium:

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Figure

Definition

Asset Allocation
(Cumulative)

Since Excess Return and arithmetical factors are not directly additive over time, the
following methodology ("Combining Attribution Effects over Time" by D.R . Carino) is
applied to link attribution effects over time:

where

R = cumulative total Portfolio Return

R

= cumulative total Benchmark Return

and

R = cumulative total Portfolio Return

Rt

= cumulative total Benchmark Return

AAsset is the portfolio's cumulative Asset Allocation
AAssett is the portfolio's Asset Allocation effect at time point t.
Asset Interaction

Performance attribution factor measuring the interaction between Asset Allocation
and Asset Selection. It is part of the Excess Return that cannot be divided to either
Allocation or Selection.

Asset Interaction
(Cumulative)

See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over
time is described.

Asset Leverage

The return contribution from leveraged market investment in respect to the total
portfolio market value due to unrealized result of FX hedge transactions.

For example, you buy US bonds worth 100 M Euro and hedge the currency exposure
into Euro using FX forwards. If the dollar goes up 10% the bonds are worth around
110M Euro and you have an offsetting unrealized loss of 10M from the FX forwards. In
this case your bond position is leveraged since you have 110M of a portfolio total of
100M invested into it.

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Figure

Definition

Asset Leverage
(Cumulative)

See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over
time is described.

Asset Selection

Performance attribution factor measuring how successful you have been at selecting
securities relative to the benchmark within the selected groups (such as Branch
Code), given by:

where
Asset Weight of the ith group in the Benchmark
Return of the ith group in the Portfolio
Return of the ith group in the Benchmark

Asset Selection
(Cumulative)

See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over
time is described.

Asset
Selection/Interaction

The combined Asset Selection and Asset Interaction factors given by:

Note: As a difference to the pure Asset Selection, Portfolio Weight is used here.
Asset Selection/
Interaction
(Cumulative)

See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects
over time is described.

Asset Weight

Fraction of the market value invested in ith asset.

Attribution Amount

The market value allocated to the selected cell i at beginning of day t, given by:
Attribution Amount (T) = Market Value Start (T) + Weight Factor * Cashflows (T)

Attribution Weight

The percentage of total Attribution Amount allocated into cell i at time t:
Attribution Weight (T) = Attribution Amount (T) / Total Attribution Amount (T)
(The Total level is defined by the user in the X,Y axis selection lists as in Treasury
Monitor.)

Beta

The gradient of the linear regression function between the portfolio and the
benchmark portfolio. This is a measure of the sensitivity of the portfolio with respect
to changes in the benchmark portfolio. A value of beta greater than 1 means that the
portfolio returns will be more than the benchmark returns (less than 1 means the
returns will vary less).

Correlation

The correlation coefficient between the portfolio and the benchmark portfolio
(standardized covariance). A positive (negative) value indicates that if there is a
positive return for the benchmark portfolio, then there will also be a positive
(negative) return for the portfolio.

Covariance

The covariance between the portfolio and the benchmark portfolio. A positive
(negative) value indicates that if there is a positive return for the benchmark portfolio,
then there will also be a positive (negative) return for the portfolio.

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Figure

Definition

Difference Result

The difference of the monetary returns between a trading portfolio and a benchmark
portfolio, expressed as daily Monetary P/L Excess Return and calculated as follows:

RE t = RE P, t – RE B, t
where
REt is the Monetary P/L Excess Return for day t
REP,t is the Monetary Portfolio Return for day t
REB,t is the Monetary Benchmark Return for day t
This key-figure behaves like Excess Return, except that money amounts are used.

Note: In Treasury Monitor, the key-figures Market Value and Market Value Start are
used. Monetary P/L Excess Return is the difference between the trading
portfolio’s Market Value Change and that of the benchmark portfolio.
Difference Result
(Cumulative)

The sum of daily Monetary P/L Excess Returns during a period of n days.

Difference Return
Contribution

Displayed under the benchmark, this figure is the line-by-line difference between the
Return Contribution of the portfolio and the Return Contribution of the benchmark.
Difference Return Contribution (Cumulative) measures the same difference over time.

Excess Return

This is the portfolio return relative to the benchmark return for the specified interval.

Excess Return
(Annualized)

The difference between the Return (Cumulative) of the portfolio and the Return
(Cumulative) of the benchmark portfolio, converted into an annual figure.

Excess Return Asset
Contribution

This is the difference between local portfolio return premium and base currency
benchmark return premium.

Alternatively, this is the sum of the Asset attribution factors at time point t:

Excess Return Asset
Contribution
(Cumulative)

This is the sum of cumulative Asset attribution factors.

Excess Return
Contribution

This is the sum of the attribution factors at time T:

Excess Return
Contribution
(Cumulative)

This is the sum of the cumulative attribution factors:

Excess Return
(Cumulative)

The difference between the Return (Cumulative) of the portfolio and the Return
(Cumulative) of the benchmark portfolio.

Excess Return Factor

Daily factor used for linking attribution effects over time.

Excess Return Factor
(Cumulative)

Total period factor used for linking attribution effects over time.

Excess Return Hedge
Contribution

Excess return contribution from the hedge strategy, which is the sum of the Hedge
attribution factors at time t:

Excess Return Contribution (T) = Allocation (T) + Selection (T) + Interaction (T)

Excess Return Contribution (Cumulative) = Allocation (Cumulative) + Selection
(Cumulative) + Interaction (Cumulative)

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Figure

Definition

Excess Return Hedge
Contribution
(Cumulative)

This is the sum of the cumulative Hedge attribution factors. See Key-Figure Asset
Allocation (Cumulative), where the methodology to link effects over time is described.

Excess Return (N
Samples)

This is the portfolio return relative to the benchmark return over N sub-periods
(T-periods) of sampling frequency T.

Excess Return
(Sample)

This is the portfolio return relative to the benchmark return over one sub-period
(T-period) of sampling frequency T.

Excess Return Mean

The mean value of excess returns over the aggregation period (aggregation period
length expressed as N T-periods).

Excess Return
Semideviation

Key-figures:

σ ep
Excess Return Semideviation (Negative) σ en
Excess Return Semideviation (Positive)

measure the semideviation of excess return over a benchmark.
If the sample returns of the benchmark are ri, then

Excess Return
Standard Deviation

The standard deviation of excess returns over the aggregation period (aggregation
period length expressed as N T-periods).

Excess Return
Variance

The variance of excess returns over the aggregation period (aggregation period length
expressed as N T-periods).

Excess Return
Volatility

The standard deviation of excess returns over the aggregation period (aggregation
period length expressed as N T-periods), converted into an annualized figure.

Hedge Allocation

The performance attribution factor measuring how successful we have been in our
currency strategy in comparison to the benchmark given by:

where CRP is the benchmark currency return

currency weight of portfolio FX overlay hedge transactions
currency weight of Benchmark FX overlay hedge transactions
change in the spot FX rate (common to all investments in each currency)

Hedge Allocation
(Cumulative)

194

See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over
time is described.

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Figure

Definition

Hedge Interaction

The performance attribution factor measuring the interaction between Hedge
Allocation and Hedge Selection is given by:

Hedge Interaction
(Cumulative)

See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects
over time is described.

Hedge Selection

The performance attribution factor measuring how successful you have been in
hedging the selection of optimal maturity of the hedge transactions is given by:

Local currency return of FX overlay hedge transactions.

Hedge Selection
(Cumulative)

See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects
over time is described.

Hedge
Selection/Interaction

The combined Hedge Selection and Hedge Interaction factors are given by:

Hedge
Selection/Interaction
(Cumulative)

See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects
over time is described.

Hedge Weight

The currency weight of FX overlay hedge transaction.

Information Ratio

A measurement of the return of the portfolio in terms of the risk taken (risk adjusted
return measure). The Excess Return (Annualized) divided by the Tracking Error
(Annualized). A positive value indicates that the decision to deviate from the
benchmark was a good one since it resulted in a higher return. The higher the value of
the Information Ratio, the more excess return was obtained by the same risk taken.

Interaction

The Brinson performance attribution factor measuring the interaction between
allocation and selection, given by:
Interaction_i (T) = (w_it – W_it)*(r_it-R_it)
where
W_it is the Attribution Weight of the ith group in the Benchmark
w_it is the Attribution Weight of the ith group in the portfolio
r_it is the Return of the ith group in the Portfolio
R_it is the Return of the ith group in the Benchmark

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Figure

Definition

Interaction
(Cumulative)

Interaction factors (I) that are additive over time.

where

R = cumulative total Portfolio Return

R

= cumulative total Benchmark Return

and

Rt = total Portfolio return on day t

Rt = total Benchmark Return on day t
Interaction (cumulative) T = sum t=1 to T Excess Return Factor (t)
* Interaction (t) / Excess Return Factor (Cumulative)
Jensen's Alpha

A measurement of the return of the portfolio in terms of the risk taken (risk adjusted
return measure). Jensen’s Alpha is defined as the difference between the return on
the portfolio and the return on the ‘effective’ benchmark portfolio with the same beta.
A positive (negative) value implies that the portfolio has a higher (lower) return than
the effective benchmark with the same level of risk.

Market Value
Movements

Movements between buckets/branches are considered to happen between the dates,
that is, at midnight. Thus, for an instrument worth X moving from bucket B to A at
date T, the market value start at date T will be equal to the market value end at day
T-1 plus the amount X. The Market Value Movements key-figure is equal to X.
In general:
Market Value Start (T) = Market Value End (T-1) + Market Value Movements (T)

ModiglianiModigliani

A measurement of the return of the portfolio in terms of the risk taken (risk adjusted
return measure). Defined as the return of a combination of the portfolio and the
risk-free portfolio that has the same risk (volatility) as the benchmark portfolio. A
high Modigliani-Modigliani value indicates high returns relative to the risk taken.

R2

R squared, is the fit of the linear regression function between the portfolio and the
benchmark portfolio. A measure of how well the behavior of the portfolio returns is
described by the Alpha and Beta values. Figures over 0.75 or under 0.25 are
considered to indicate that the explanatory power is high or low, respectively.

Return

The rate of return (percentage growth) of the portfolio over a specified interval.

Return (Annualized)

The return on the portfolio over the aggregation period (length of this period
expressed as N T-periods), converted into an annualized figure.

Return Contribution

The contribution of the selected cell to the total absolute performance, given by:
Return Contribution (T) = Attribution Weight (T) * Return (T) = Result (T) / Total
Attribution Amount (T)

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Figure

Definition

Return Contribution
(Cumulative)

The cumulative value of Return Contribution.
Rt, Cumulative Return Contribution for cell i over period from 1 to T is:

Here,
R is the cumulative total performance,
Rt is the total performance for period t, and
is the performance of cell i for period t.

Return (Cumulative)

The return on the portfolio over the aggregation period (length of this period
expressed as N T-periods).

Return (N Samples)

The portfolio return over N sub-periods (T-periods) of sampling frequency T.

Return (Sample)

The portfolio return over one sub-period (T-period) of sampling frequency T.

Return Mean

The mean of the cumulative returns over the aggregation period (length of this period
expressed as N T-periods).

Return Semideviation

Displays the standard deviations of returns which are below (above) the average
returns, respectively.
Key-figures:
Return Semideviation (Upside) ( σ u )

Return Semideviation (Downside) ( σ d )
Return Semideviation (Positive) ( σ p )

Return Semideviation (Negative) ( σ n )
are based an sample returns Ri.
Let sample count (the number of consecutive samples used in averaging) be n. Then
for the kth sample:

where

Ri

is the sample mean return.

Return Standard
Deviation

The standard deviation of the cumulative returns over the aggregation period (length
of this period expressed as N T-periods).

Return Variance

The variance of the cumulative returns over the aggregation period (length of this
period expressed as N T-periods).

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Figure

Definition

Return Volatility

The standard deviation of the cumulative returns over the aggregation period (length
of this period expressed as N T-periods), converted into an annualized figure.

Selection

The Brinson performance attribution factor measuring how good you have been at
selecting securities (relative benchmark) within the selected groups (such as Branch
code), given by:
Selection_i (T) = W_it*(r_it-R_it)
where
W_it is the Attribution Weight of the ith group in the Benchmark
r_it is the Return of the ith group in the Portfolio
R_it is the Return of the ith group in the Benchmark

Selection (Cumulative)

The selection factors (S) that are additive over time.

where
R = cumulative total Portfolio Return

R

= cumulative total Benchmark Return

and

Rt = total Portfolio return on day t

Rt = total Benchmark Return on day t
Selection (cumulative) T = sum t=1 to T Excess Return Factor (t) * Selection (t) /
Excess Return Factor (Cumulative)
Selection/
Interaction

198

The combined Selection and Interaction factors given by:

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Figure

Definition

Selection/
Interaction
(Cumulative)

Since Excess Return and arithmetical factors are not directly additive over time, the
following methodology is applied in order to link attribution effects over time:

where

R = cumulative total Portfolio Return

R

= cumulative total Benchmark Return

and

Rt = total Portfolio return on day t

Rt = total Benchmark Return on day t
Sharpe Ratio

A measurement of the return of the portfolio in terms of the risk taken (risk adjusted
return measure). Defined as the difference between the annualized return of the
portfolio and the annualized return of a risk-free portfolio, expressed as a ratio of the
annual standard deviation (volatility) of the portfolio. A high Sharpe Ratio indicates
high returns relative to the risk taken.

Tracking Error

The standard deviation of excess returns over the aggregation period (length of this
period expressed as N T-periods).

Tracking Error
(Annualized)

The standard deviation of excess returns over the aggregation period (length of this
period expressed as N T-periods), converted into an annualized figure.

Treynor Ratio

A measurement of the return of the portfolio in terms of the risk taken (risk adjusted
return measure). Defined as the difference between the annualized return of the
portfolio and the annualized return of a risk-free portfolio, expressed as a ratio of the
beta between the portfolio and the benchmark portfolio. A high Treynor Ratio
indicates high returns relative to the risk taken.

2.4.11.1 Performance measurement (debug) key-figures
Debug key-figures in Performance Monitor are intermediate results for multi-currency performance
attribution.
The return for the multi-currency portfolio is given by the following equation:

R base =

∑ wi ( Ri – Cccy( i ) ) + ∑ ( wi( ccy) + hccy ) ( Cccy + εbase, ccy ) + ∑ hccy ( Cccy – Cccy )
i

ccy

ccy

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The following key-figures are found in the Debug key-figure folder:
Figure

Definition

FX Rate

FX rate between the base currency and the currency in question (for example, Instrument
Currency). Multi-currency attribution uses an implied FX rate (from all transactions
except FX) because, under the multi-currency framework, only one common FX rate for
all transaction types is accepted. Combinations of, for example, O/N, T/N, and Spot rates,
as they are applied elsewhere in TRM valuation depending on the cashflow value date, are
not accepted.

FX Return

Return of the currency with respect to the base currency during the period. This is
basically the return that is the result of the changes in the (implied) FX rate. In the return
formula for multi-currency attribution, this term is marked with εbase,ccy.

IR Return

The currency risk-free rate of return for the period (the shortest maturity rate from the
yield curve defined for the currency).
This rate is taken from the risk-free curve defined for the currency. This yield curve
should only have the O/N-period defined; the rate set for that period will define the
risk-free return of the currency.
In the return formula for multi-currency attribution, this term is marked with:

C ccy ( i )
Adjusted Asset
Return

Local rate of return for the assets within the respective group. In the return formula for
multi-currency attribution, this term is marked with Ri (or

Ri
if the key-figure is displayed under the Benchmark).
Adjusted Hedge
Return

The currency return of the legs of the hedge transaction within the respective group. In
the return formula for multi-currency attribution, this term is marked with hi (or

hi
if the key-figure is displayed under the Benchmark).
Return Premium

Local return premium

BRP =

∑ wi ( Ri – Cccy( i ) )
i

Deposit Return

This is the currency exposure return:

( w i ( ccy ) + h ccy ) ( C ccy + ε base, ccy )

Note: The configuration of implicitly matched instruments in TRM should lead to identical FX

valuations. Any differences will cause the sum of the attribution terms to not sum exactly
to the portfolio excess return. Given the extensive instrument coverage and the flexibility
in valuation techniques in TRM, it is likely that the user will have to accept same degree of
mismatch between the attribution figures and the excess return.

2.5 Value-at-Risk calculations
Value-at-risk (VaR) is a measure of the potential change in value of a portfolio or position with a
defined level of confidence over a selected risk horizon (one day, one month, and so on). For
example, you could measure your maximum potential loss with a 95% confidence level on an FX
deal due to an unfavorable change in the FX rate over one day. (A 95% confidence level means that
your maximum potential loss will not exceed the change in value predicted by this method 95% of
the time, i.e. 5% of the time you risk losing more than this value.)

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The value-at-risk (VaR) calculations in TRM are performed in an integrated real-time module that
allows the full functionality of Treasury Monitor to be used with the VaR key-figures produced.
In order to perform these calculations, certain statistical data (volatility and correlation) of the
market variables are required. These data can be imported from RiskMetrics or any other source
with a similar file interface. The data source can be augmented with proprietary data on market
variables which it doesn't cover. Mapping between TRM market variables and the imported statistical
data is carried out in VaR Mapping Editor. The flexibility of this board allows instruments such as
bonds to be mapped to their own volatility and correlation data instead of using a zero-coupon
curve.
VaR Data Board provides the possibility for extensive stress testing by simulating changes in the
market conditions. User-defined scenarios can be created and the correlation and volatility data can
be edited.
The required confidence level and risk horizon can be defined for each portfolio. In order to do so,
the properties VAR-CONFIDENCE-LEVEL and VAR-HORIZON-ID should be added to the Properties
page in Portfolio Editor.
See TRM User Guide for more information about TRM VaR related applications and portfolio
properties.
The rest of this section assumes that RiskMetrics is the source of the statistical data.

2.5.1 TRM approach to VaR calculations
In order to calculate the VaR figures for a position, an estimate of the probability distribution for that
position is required. This is created from the imported statistical data (the volatilities and
correlations of the market variables) and the sensitivity of the position to changes in those market
variables (deltas).
To use the statistical data to assess the value-at-risk of a position, you need to first perform the
following steps:

•

Import the statistical data into the system (see 2.5.3.1 RiskMetrics data on page 203).

•

Calculate any missing data (see 2.5.4 Transforming RiskMetrics data on page 204).

•

Map the cashflows of the position to the RiskMetrics maturity vertices (see 2.5.4.3 Cashflow
mapping on page 205.

•

Calculate the VaR deltas of the position (see 2.5.5.1 Calculating VaR deltas on page 207).

2.5.2 RiskMetrics data
In RiskMetrics, the basic underlying assumption is that the relative change in each market variable
X, from one period to another, is normally distributed with a mean of zero and standard deviation
σ:

Xt – Xt – 1
------------------------ ∼ N ( 0, σ x )
Xt – 1

Equation 2-390 VaR: RiskMetrics data

Furthermore, the joint distribution of the relative changes in all market variables is assumed to
follow a multivariate normal distribution with the correlations between the market variables given in
the correlation matrix C.
RiskMetrics provides the correlation matrix C and the volatilities of the different market variables.
The volatility V of market variable X is defined as 1.65 σ x .
A detailed description of the creation of these data and the format in which they are available is
given in the RiskMetrics Technical Document.

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2.5.2.1 Variance-covariance matrix
It is simple to reconstruct the standard deviations of the market variables, σ x , from the volatility
data supplied by RiskMetrics (volatility is defined as 1.65 times standard deviation). If other data
sets are used (not RiskMetrics) then the measure of volatility may be different, in which case the
multiplier I0, (1.65 in the case of RiskMetrics) will be given in the data file and stored with the
volatility data.
TRM works with the variance-covariance matrix Σ :
Equation 2-391 variance-covariance matrix

Σ = σCσ
where C is the correlation matrix, σ is a diagonal matrix of the standard deviations of the market
variables and the elements are given by
Equation 2-392 VaR: Correlation-diagonal matrix

Σ ij = σ i C ij σ j
This matrix contains both the volatility and correlation information. Note that since the diagonal
elements of the correlation matrix are equal to one (Cii = 1), the diagonal elements of Σ are the
variances (standard deviations squared: Σ ii = σ i2 ). Also (Cji = Cij).

2.5.2.2 Risk horizons
The range of values within which a market variable is likely to move depends on the time horizon
used. RiskMetrics provide data for two horizons: one day and one month. The maximum potential
loss is sometimes referred to as DEaR, Daily Earnings at Risk, for the one day time horizon whereas
the risk measure for the one month horizon is referred to as VaR, Value at Risk. The data in the
RiskMetrics files are given for the period in question, not as yearly rates.
Theoretically, the volatilities for different time horizons should be obtained from the one day
volatility by multiplying by the square root of time. For example, if σ 1 is the one day volatility and σ 5
the five day volatility, the following equation should hold:
Equation 2-393 VaR: Risk horizons

σ5 =

5σ 1

However, there is evidence that long term volatilities differ from the values obtained using this
equation. Therefore the one month horizon is also needed for calculating long term risk measures.
For risk horizons beyond one month we use the formula above, replacing the one day volatility with
the one month volatility. Risk horizons between one day and one month are interpolated from these
two figures as described in 2.5.4.2 Interpolating volatilities and correlations on page 204.

2.5.3 Market variables
A market variable is any variable for which there is a market quote (for example rate, yield or price)
which affects the value of a cashflow.
The market variables recognized by RiskMetrics differ from those used by TRM. The RiskMetrics
market variables are mapped to the correct TRM market variables in VaR Mapping Editor. The
RiskMetrics data may also have to be transformed in one way or another before it can be used for
calculations in TRM.

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This section describes these different types of data. The section 2.5.4 Transforming RiskMetrics data
on page 204 describes how the RiskMetrics data are transformed into data suitable for TRM.

2.5.3.1 RiskMetrics data
The RiskMetrics data provided are the volatilities and correlations for the market variables given
below. The data are provided for certain periods, the RiskMetrics vertices (for example, 1 month, 2
months, and so on) since providing data for all periods would be unfeasible. Data for periods
in-between these vertices are calculated using cashflow mapping (see 2.5.4.3 Cashflow mapping on
page 205).

•

Foreign exchange (FX) spot rates for certain currencies.
The data are always calculated with US dollar (USD) as the quote currency, for example
SEK/USD. The volatility of an FX rate does not depend on the direction in which it is quoted
(SEK/USD or USD/SEK), but the sign of the correlation between the two rates will change if the
direction is changed.
The symbol for spot quotes is XS (for example, the Swedish krona spot quote is SEK.XS).

•

Money market (MM) rates for the same set of currencies. These rates are for the periods
(vertices) O/N, 1 week, and 1, 2, 3, 6, and 12 months.
The symbols for these rates are of the form R001, R007, R030, and so on (for example,
SEK.R001, SEK.R007).

•

Government bond zero rates for different currencies. Periods (vertices) included are 2, 3, 4, 5, 7,
9 10, 15, 20, and 30 years. The symbols for government zero rates are of the form Z02, Z03, Z04
and so on (for example, for Swedish bonds SEK.Z02, SEK.Z03, SEK.Z04).

•

Swap zero rates for different currencies.
Periods (vertices) included are 2, 3, 4, 5, 7, and 10 years. The symbols for these rates are of the
form S02,S03 and so on (for example, SEK.S02,SEK.S03).

•

Equity indexes. The symbol for a stock index is SE (for example Swedish stock index is SEK.SE).

2.5.3.2 TRM market data
The market data for TRM falls into the following categories:

•

Foreign Exchange (FX) spot rates for any currency involved in trading.
Since the present value of a position is expressed in the portfolio base currency or the
monitoring currency selected in Treasury Monitor, the VaR key-figures should also be expressed
in the same currency. The original data from RiskMetrics are always expressed in terms of US
dollars and so they have to be converted into correlations and volatilities in terms of the base
currency (see 2.5.4.1 Reference currency on page 204).

•

Interest rate (IR) reference rates
In TRM, there are several ways to derive an IR reference rate (see 2.2 Yield curves on page 81).
A reference rate is taken from a defined yield curve. The simplest way to define a yield curve is
to use direct market quotes. It is also possible to derive a zero-coupon yield curve from a set of
instruments or other reference rate yield curves, for example, by using a depo curve for the
short end and a swap curve for the long end. Offsets can be added to previously defined rates in
the yield curve to derive new rates.
Due to the possible complexity of this rate derivation, it is not feasible to derive the correlations
for the derived yield curve from the correlations of the underlying yield curve. Therefore, each IR
reference curve has to be mapped separately to its correlation vertices on the Interest Rate
Mapping page of VaR Mapping Editor.

•

IR instruments
An IR instrument, such as a bond and a bond future can be either mapped to volatilities and
correlations of a yield curve, or directly to its individual volatility and correlation data, if such is
available.

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In the former case, the default is to use the VaR mapping specified for the instrument's
currency, but it is also possible to choose a different mapping by bringing in the feature VaR
Mapping Type, see A.2.336 VaR Mapping Type on page 878.
To use instrument-specific volatility and correlation data, the instrument has to be given its own
mapping in VaR Mapping Editor (Instrument Mapping page).

•

Equities
Equities can either be mapped onto their individual volatility and correlation data or onto a
common index. In the latter case, the beta of the equity is used to obtain the equity's volatility
from the volatility of the index. The beta defined in Rate Monitor can be overridden for VaR
calculations.

2.5.4 Transforming RiskMetrics data
This section describes how the RiskMetrics data are transformed into data suitable for TRM.

2.5.4.1 Reference currency
In RiskMetrics all currencies are quoted against the US dollar. This means that when value-at-risk is
calculated in a different currency, typically the portfolio base currency, or the figure currency of
Treasury Monitor, the variance-covariance matrix has to undergo a transformation. To get
covariances for the cross rates X=A/B and Y=C/D we use the following equation:
Equation 2-394 VaR: Covariances cross rates

Cov ( X, Y ) = Σ AC + Σ BD – Σ AD – Σ BC
If X and Y are the same rate, in other words A=C and B=D, then
Equation 2-395 VaR: Covariances same rate

2

2

2

σ x = Cov ( X, X ) = σ A + σ B – 2Σ AB
If one of the rates is not a cross rate, for example if Y=C, then
Equation 2-396 VaR: Covariances one of the rates is not a cross rate

Cov ( X, C ) = Σ AC – Σ BC
2.5.4.2 Interpolating volatilities and correlations
RiskMetrics provide volatility and correlation data for risk horizons of one day and one month.
Whenever risk horizons differing from these are used, the data have to be interpolated.

2.5.4.2.1 Volatility
It is appropriate to use quadratic interpolation to calculate volatilities for risk horizons (maturities)
other than one day and one month.

•

Case 1: Risk horizon t between t1 (one day) and t2 (one month).
If t is the risk horizon for which the standard deviation is needed and t1 < t < t2, let
Equation 2-397 VaR: Case 1 - Volatility

t – t1
τ = -------------t2 – t1

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then the volatility σ is given by:
Equation 2-398 VaR: Case 1 - Volatility calculation

2

σt =

•

2

σ1
σ2
τt ------ + ( 1 – τ )t -----t2
t1

Case 2: For t outside the range [t1, t2], the volatility is scaled by the square root of time.

–

For t < t1:
Equation 2-399 VaR: Case 2 - Volatility

σt =
–

( t ⁄ t 1 )σ 1

For t > t2:
Equation 2-400 VaR: Case 2 - Volatility calculation

σt =

( t ⁄ t 2 )σ 2

2.5.4.2.2 Correlation data
For correlations, linear interpolation is used. That is, if the two known correlations for the risk
horizons t1 (one day) and t2 (one month) are ρ 1 and ρ 2 , then the correlation ρ t for the risk horizon
t can be calculated using one of the following methods:

•

Case 1: Risk horizon t between t1 and t2.
Equation 2-401 VaR: Correlation data

ρ t = τρ 2 + ( 1 – τ )ρ 1
•

Case 2: Risk horizon t outside the range [t1, t2].

–

For t < t1: ρ t = ρ 1

–

For t > t2: ρ t = ρ 2

2.5.4.3 Cashflow mapping
A financial position is made up of one or more cashflows which need to be marked-to-market
(present value) using current market rates for the VaR calculations. The present value of most
cashflows depends on two variables:

•

The spot rate of the cashflow currency

•

The interest rate for the maturity of the cashflow.

This means that the number of market variables is of the same order as the number of cashflow
dates in the portfolio that is under scrutiny. The volatilities and correlations for all these variables
could be derived from the original data set leading to a very large correlation matrix.
An alternative approach is to restrict the set of market variables to consist of only the spot rates and
interest rates for a given set of periods (the RiskMetrics' vertex periods - 2.5.2 RiskMetrics data on
page 201 gives details of the vertices for the different market variables in RiskMetrics). The

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cashflows that fall between the vertex periods have to be mapped (redistributed) onto a standard
grid of maturity vertices. This is illustrated as follows.

In this way, the market variables of the cashflows are mapped onto the market variables of the
RiskMetrics vertices. For example, if the interest rate of the second cashflow in the previous figure
(at 5 months) is rc and r3m and r6m are the interest rates of the 3 month and 6 month RiskMetrics
vertices respectively, then the present value of the cashflow, Vp(rc) will become Vp(r3m, r6m).
The next step in the VaR approach is to calculate the vector δ (see 2.5.5.1 Calculating VaR deltas on
page 207). This vector contains the VaR deltas (sensitivity of the position to a change in a market
variable) for every market variable.
The goal of the cashflow mapping is to transform this vector δ into another one, δ m , which contains
the sensitivities to changes in the market variables at the maturity vertices used in the VaR
calculations.
This transformation takes the form of a matrix M where the elements Mij provide the mapping from
the ith TRM market variable to the jth VaR market variable.
Equation 2-402 VaR: Cashflow mapping

δ m = Mδ
2.5.4.3.1 Risk equivalent method
The mapping of a cashflow that falls between RiskMetrics vertices is based on the idea that the
interest rate for such a cashflow can be considered as a result of an interpolation from the adjacent
vertices. More precisely, consider a cashflow whose present value is a function Vp(rd) of the interest
rate rd with maturity d. We can regard rd as a linear function of the two closest vertex interest rates
r1 and r2.
Equation 2-403 VaR: Risk equivalent method

r d = ar 1 + br 2
where a and b are interpolation coefficients.
Now, we can consider the present value of our cashflow to be a function Vp(ar1+br2) of r1 and r2
instead of rd.
Using the risk equivalent method, we do not need to calculate the mapped cashflows as previously
described to transform the VaR delta vector δ into δ m , but can simply calculate δ m from the IR
exposure (delta) of the original cashflow. This is particularly convenient for derivative instruments
where the IR exposure is not calculated directly from the cashflows.

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To be more specific, we have:
Equation 2-404 VaR: Risk equivalent method

∂V
∂V ∂r d
------= ------- ------∂r 1
∂r d ∂r 1
∂V p
= a ---------∂r d
and
Equation 2-405 VaR: Risk equivalent method

∂V ∂r d
∂V
------= ------- ------∂r d ∂r 2
∂r 2
∂V p
= b ---------∂r d
Also since a+b=1, the total IR sensitivity is
Equation 2-406 VaR: Total IR sensitivity

∂V p
∂V
∂V
---------- = ---------p- + ---------p∂r d
∂r 1 ∂r 2
It can therefore be seen that in this risk equivalent method, the cashflow itself does not get
mapped, but the IR risk (exposure) does.

2.5.5 VaR calculations
The method used in TRM to calculate value-at-risk is the linear (delta) method. The function V() of
the value of the position is approximated with a linear function via a Taylor series expansion:
Equation 2-407 VaR: Linear (delta) method (Taylor series expansion)

V ( x 1, x 2, …, x n ) ≈ V p + δ 1 ( x 1 – X 1 ) + δ 2 ( x 2 – X 2 ) + … + δ n ( x n – X n ) = V p + δ x
where Vp is the current present value, the xi represent the market variables and Xi the current
values of those market variables, the δ i (elements of the VaR delta vector δ ) are the partial
derivatives of the value function V() with respect to each xi (see 2.5.5.1 Calculating VaR deltas on
page 207).
In order to produce an estimate of the value-at-risk, first of all the VaR deltas need to be calculated
(shown in next section). The standard deviation of the position in question can then be calculated
using these VaR deltas and the variance-covariance matrix (see 2.5.2.1 Variance-covariance matrix
on page 202). From the standard deviation we know the probability function of the position and this
is then used to estimate the value-at-risk at a certain confidence level (probability).

2.5.5.1 Calculating VaR deltas
In order to be able to calculate the overall risk for our position, we shall need the vector
δ = ( δ 1, δ 2, …, δ n )′

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defined by
Equation 2-408 VaR: Vector

∂V p
δ i = ---------∂x i
where δ i is the sensitivity of the present value Vp to a change in the market variable xi

2.5.5.1.1 Simple cashflows
The present value of a simple cashflow of amount A is
Equation 2-409 VaR: Present value (simple cashflows)

A
l
V p = ---------------- S = V p × S
D ( r, t )
A
l
V p = ---------------D ( r, t )
where S is the spot rate between the cashflow currency and the portfolio currency and D(r,t) is the
discount factor calculated with interest rate r and period t. There is therefore dependency on two
market variables, S and r, the spot rate and the interest rate for the cashflow date.

Note: Strictly speaking, due to the complicated method of calculating the discount factor, it may

depend on the interest rate on more than one date. The error made in ignoring this fact is,
however, insignificant.

The corresponding VaR deltas are:

•

FX Delta
Equation 2-410 VaR: FX delta

δ FX

•

∂V p
A
=
= ---------------∂S
D ( r, t )

IR Delta
Depending on the value of the configuration parameter called var yield volatility, the IR deltas will
not be calculated in the same way. The var yield volatility parameter is described in more detail in
the TRM System Admin Guide.

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When the value is true, TRM considers the volatilities stored in the VaR scenarios to be yield
volatilities and calculates the IR deltas as follows:
Equation 2-411 VaR: IR delta calculations
l

Vp = Vp × S
l

l

ΔV p = S × Δ V p + V p × ΔS
l

∂V p
l
ΔV p = S × ---------- × Δr + V p × ΔS
∂r
∂V p
l
ΔV p = ---------- × Δr + V p × ΔS
∂r
∂V p Δr
l
ΔV p = r × ---------- × ------ + V p × ΔS
∂r
r
so that
∂V p
δ IR = r × ---------∂r
In TRM terms:
IR Delta = 1000 x IR Exposure (1bp) x Interest Rate
with
IR Exposure (1bp): Sensitivity of your cashflow Present Value to a change of 1 basis point in the
interest rate.
Interest Rate: Zero-coupon rate used in the Present Value and IR Exposure (1bp) calculation.
When the parameter - var yield volatility is set to false, TRM considers that the volatilities stored in
the VaR scenarios are price volatilities and calculates the IR deltas as follows:
Equation 2-412 VaR: IR delta calculations (in TRM)
l

Vp = Vp × S
l

l

ΔV p = S × Δ V p + V p × ΔS
l

∂V p
l
ΔV p = S × ---------- × ΔD + V p × ΔS
∂D
∂V p
l
ΔV p = ---------- × ΔD + V p × ΔS
∂D
∂V p ΔD
l
ΔV p = D × ---------- × -------- + V p × ΔS
∂D
D
so that
∂V p
δ IR = D × ---------∂D
In TRM terms:
IR Delta = Discounted Risk Value

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2.5.5.1.2 Par method
If Quoted method is used for the value-at-risk of an instrument (see 2.5.3.2 TRM market data on
page 203) then delta is the present value of the instrument itself.

2.5.5.1.3 FX options
For FX options, we have option deltas for both the asset and cash currencies, δ a and δ c which are
calculated with the normal FX option formulas. Similarly the VaR deltas with respect to the interest
rates are obtained by multiplying the IR exposures of the corresponding FX forward deal by the delta
of the option.

2.5.5.1.4 IR options
From cashflows associated with IR options the VaR currency delta is obtained by dividing the FX
exposure by the FX risk offset, and the VaR IR delta by dividing the IR exposure by the IR risk offset
(as shown in 2.5.5.1.1 Simple cashflows on page 208).

2.5.5.1.5 Equities
An equity transaction creates FX, IR, and Price (equity) exposures. The FX and IR exposures are
used to calculate the VaR FX and IR deltas in the normal manner: the FX or IR exposure is divided
by the corresponding risk offset (as in 2.5.5.1.1 Simple cashflows on page 208).
For Price exposure there are two alternatives. The first is that each equity is mapped to its own
market variable. This approach requires that there is volatility and correlation data for each equity
dealt with. However, it is more realistic to assume that the volatility and correlation data only exist
for each equity index. Each equity can then be mapped to the index it belongs to. With this
approach, the variation between the volatilities of the various equities can be determined via the
betas. Each equity is assigned its own beta factor β which describes how strong the link between
the movement of the stock and the index is. (The betas for individual stocks are calculated outside
TRM and are fed in through Rate Monitor.) If beta is equal to one, the volatility of the equity is the
same as the index volatility (the price of the stock is directly proportional to the value of the index).
If beta is two, the equity's volatility is double the index's volatility and so on. A negative beta means
that the price of the stock varies inversely to the value of the index; for example a beta of -2 means
that the value of the stock decreases by 20% if there is an increase of 10% in the value of the index.
The VaR equity delta of an equity is calculated by:
Equation 2-413 VaR: Equities

δ EQ = βN
where N is the number of equities in the position.

2.5.5.1.6 Equity options
The equity exposure of an equity option is based on the delta of the option. Therefore, the VaR
equity delta of an equity option is calculated from:
Equation 2-414 VaR: Equity options

δ EQ = βδN
where N is the number of underlying shares in the contract and δ is the option's delta.

2.5.5.2 Mapped deltas
The VaR IR deltas described above may need to be mapped to RiskMetrics vertices as described in
the 2.5.4.3.1 Risk equivalent method on page 206.

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If the VaR IR delta δ is with respect to an interest rate r for a period t which is not VaR vertex, then
if the closest VaR vertices to t are t1 and t2, δ is mapped to corresponding deltas δ 1 and δ 2 so that
Equation 2-415 VaR: Mapped deltas

δ 1 = aδ r
δ 2 = bδ r
where
t2 – t
a = -------------t2 – t1
t – t1
b = -------------t2 – t1

2.5.5.3 Proportional deltas
The correlation and volatility data from RiskMetrics are given as relative values. To get the actual
values, we have to multiply these relative values by the current values of the market variables. In
order to do this, we use the vector Δ , defined below, instead of the VaR delta vector δ in the VaR
calculations (Equation 2-408 on page 208).
Equation 2-416 VaR: Proportional deltas

Δ = ( δ 1 X 1, δ 2 X 2, …, δ n X n )
where δ 1 is the VaR delta corresponding to the present value in question, and Xi is the current value
of the market variable.

2.5.5.4 Value-at-Risk
Once we know the delta vector for the position (which is then converted into the vector Δ as shown
in Equation 2-416 on page 211) and the appropriate covariances (the variance-covariance matrix Σ
as defined in Equation 2-392 on page 202), we can obtain the standard deviation σ of the total
position:
Equation 2-417 VaR: standard deviation of the total position
2

σ p = Δ′ΣΔ
=

∑ Δi ∑ Σij Δj
i

j

From σ , we can construct various risk measures, the most common of which is the (two-sided)
confidence interval I 90 = 1.65σ p . The probability that the value of our position changes under the risk
horizon less than I90 is 90%. Other confidence intervals can be derived, for example, the probability
that the value of the position changes less than I 95 = 1.96σ p is 95%.
Even if the value does not remain within the interval, it is not necessary that the position's value
diminish, since the value could move up instead of down. Since the tails of the distribution are
symmetric, the probability of moving up beyond the confidence interval is 5% for the 1.65σ p interval
and 2.5% for the 1.96σ p interval. Thus, the probability of losing more than 1.65σ p is, in fact, only 5%
and the probability of losing more than 1.96σ p just 2.5%.

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In the following figure, the shaded area represents the probability that the value of the position will
move below the value-at-risk figure 1.65σ . This probability is 5%.

The VaR key-figures which can be selected in Treasury Monitor are described in more detail in the
TRM User Guide.

2.5.6 Incremental VaR
Incremental VaR is a statistic providing information on the sensitivity of VaR to changes in portfolio
holdings. Let wi be the i component of the delta vector of the portfolio and VaR the total value at
risk of the portfolio, with the i component of the incremental VAR defined as:
Equation 2-418 VaR: Incremental VaR definition

∂VAR
IVAR i = w i ---------------∂w i
As a consequence of the definition,
Equation 2-419 VaR: Incremental VaR calculation

∑ I VARi

= VAR

i

2.5.6.1 Calculation of incremental VaR
Let Cij denote the covariance matrix, w the delta vector and wT the transpose of the delta vector.
Since
Equation 2-420 VaR: Incremental VaR calculation

VAR =

T

w Cw

the i component of the incremental VaR (IVAR) is defined as
Equation 2-421 Incremental VaR (IVAR)

Incremental VaR can then be interpreted as the product of the exposures of the position with
respect to each risk factor wi and the sensitivity of the VaR of the portfolio with respect to changes
in each of those risk factors.

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∑ Cij wj

j
IVAR i = w i ------------------VAR

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Chapter 3

Debt instruments

3.1 Bond
Bonds are negotiable issues, which means that their cashflows are known (in terms of structure and
dates) when the bond is issued. They can be traded in the market.
In TRM, there is a clear distinction between loans and bonds. Loan agreements are set up mostly at
deal entry, while bond issues must be completely defined at instrument level (notably in terms of
cashflows).
As is the case for loans, the definition of cashflows relies completely on the schedule concept (or
cashflow structure).
See Appendix B Schedules on page 883.
Several schedules must be attached to a bond and they drive the generation of the cashflow
structure for the deal.
For the simplest bond, two schedules are associated with the deal: one schedule for interest flows;
and one schedule for principal flows. It is possible to have additional interest schedules in the case
of parallel interest flows.
Bond instruments must be based on an instrument type derived from the class BOND.

3.1.1 Fixed-rate bond
This is the simplest type of bond. Fixed-rate bonds are usually managed as described in the
following sections.

3.1.1.1 Instrument setup
•

Bond main characteristics
This information may be relevant to any kind of fixed-rate bond.
Information

Description

Issuer

Issuer of the bond.

Currency

Currency in which the bond is issued.

Amount Rounding

Specify with how many decimals and with which method the amounts will be rounded.

Default Price
Denom.

For fractional prices, defines the default denominator. If a default price denominator is
specified, the Deal Price can be entered as a fraction at deal entry.
For example, if you enter 32 in this field, a Deal Price entered as 100-5 is displayed as
100 5/32. See the TRM User Guide.

Accrued Interest
Method

How the system computes settlement accrued interest. For most bonds, the Linear
method can be used, but some bonds require a specific method.
For bonds traded at dirty price (i.e. price that includes accrued interest), it is also
possible to specify an accrued interest method. In this case, the accrued interest is
calculated for accounting purposes only (as settlement principal based on dirty price
already includes accrued interest). If this field is left blank, no settlement AI is
calculated
See 2.1.6.1 Accrued interest calculations on page 67 for details of accrued interest
methods.

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Information

Description

Settlement
Switches

If the bond is traded in dirty price it has to be specified here.

Coupon Rate

The interest rate of the fixed-rate bond.

It is also possible to define whether rounding of the settlement principal is per trading
unit, that is, the rounding is done for one unit and then the amount is multiplied by
the number of units to obtain the settlement principal and accrued interest.

See A.2.51 Bond on page 734.

–

Dates details
The issue date and the maturity date must be specified for the bond.

–

Trading unit details
It is possible to define a minimum bid size or trading units of a bond. If a minimum
denomination is defined, deal entry is available either in units or amount and TRM ensures
that the amount is a multiple of the denomination size.

•

Schedules
Select the cashflow structure template you want for the instrument. For each set of cashflows
defined in the template, select the generation parameters.
One system template is provided for fixed-rate plain vanilla bonds (see B.2.1.1.21 Fixed, Bullet
Repayment on page 894); you can choose this template or any other template derived from it.
Once the template is applied to the instrument, the schedules are created and it is then possible
to define their characteristics, such as, date basis, payment convention, calendars, and so on.
See Appendix B Schedules on page 883.

•

Cashflows
As the cashflows are an intrinsic characteristic of an issue, they must be defined at instrument
level. Generation of the cashflows is automatically done in the instrument setup and takes into
account all the information specified in the schedule. Some fields can be manually modified at
cashflow level if necessary.
The cashflows are saved in the database along with the instrument, and they will be used
directly to generate the cashflows of the deal when the bond is sold or purchased.

•

Trading yield
Specify how the yield/price conversion will be made when dealing the instrument.
Information

Description

Yield Convention

The convention defines how the yield/price conversion will be made. TRM supports the
standard conventions. See 2.1.4 Yield/price conversions on page 38.

Price and Rate
rounding

Defines how the system should round prices and rates.

See A.2.323 Trading Yield on page 872.

•

Quoted
It is necessary to specify how a bond is quoted on the market.

216

Information

Description

Price Type

Price % or Yield for a bond.

Quote Handling

If the Bond quote handling is used, the system will notify Rate Monitor that it is a
fixed-rate bond.

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Information

Description

Currency

This quoted notion is time dependant (price type and/or currency may change over
the life of a bond).

See A.2.274 Quoted on page 849.
It is also possible to set up:

•

Spot day calculations

•

Cashflow and transaction charge rules

•

Collateral

•

Branch Codes

•

Security Identifiers

•

Delivery.

See Appendix A Features on page 713.

3.1.1.2 Deal capture
3.1.1.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
a fixed-rate bond.
Information

Description

Deal Price or Deal Rate

If there is a yield/price convention set on the instrument, it is possible to enter either
a rate or a price. The conversion will be made automatically.
If there is no convention set, the deal must be entered in price.
If a default price denominator is specified at instrument setup, Deal Price can be
entered as a fraction. For more information about fractional prices, see the TRM User
Guide.
By default, Deal Price is considered as clean (i.e. does not include accrued interest).
Deal Price is considered dirty if so defined at instrument level (in Settlement Switches) or
if you set the Force Dirty Price transaction column value to Yes when entering the
transaction.

Nominal Amount
Face Amount
Value Date

Enter either the nominal amount or face amount, and the system will compute the
other automatically.
Official date when money is transferred. This defaults to the spot date of the
transaction.

In addition, the following optional information can be captured:
Information

Description

Units

If the denomination of a bond instrument is specified at instrument setup, the deal
can be input in units, and the nominal and face amounts are computed by the system.

Trading Unit Size

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3.1.1.2.2 Generated data
•

Transaction
Book Value (BV) = NA * price / 100
where:
NA = nominal amount
price = deal price

•

Cashflows
TRM copies all the future cashflows of the bond and scales them according to the nominal
amount engaged (using rounding).
Additionally, the system generates a settlement cashflow with amount = BV (see above) and an
accrued interest cashflow according to the AI Method.
The following cashflow structure is generated for a fixed-rate bond:

3.1.1.3 Processing
This section describes the actions that can be done throughout the life of a bond.

3.1.1.3.1 Asset swap
You can easily create an asset swap from a bond transaction by executing the Asset Swap action. The
asset swap is an interest rate swap where the cashflow structure of one leg (the asset leg) is similar
but opposite to the cashflow structure of the bond, and the other leg corresponds to what you have
specified (e.g. quarterly floating).

•

Setup
To enable this action, the Allow Swap feature must be associated with the instrument.
See A.2.23 Allow Swap on page 722.

•

Execution
Right-click a bond transaction that uses an instrument with the Allow Swap feature, and select
Asset Swap action in Transaction Manager. When you execute this action, use the following table
to specify the parameters.
Information

Description

Swap Instrument

Select the instrument for the asset swap transaction.
See 11.1.2 Asset swap on page 656 for information about setting up the Swap
Instrument.

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Information

Description

Opening Date

The opening date and value date of the asset swap transaction.

Value Date
Swap Amount

The nominal amount being swapped, which defaults to the nominal amount of the
underlying bond transaction. This can be changed in order to swap a fraction of the
bond.

Asset Amount

Read-only. The nominal amount of the underlying bond.

Swap Units

Read-only. The number of units being swapped (if the underlying bond is traded by
units).

Asset Units

Read-only. The number of units of the underlying bond (if the underlying bond is
traded by units).

Leg

Leg of the swap that will reflect the asset leg, i.e. which reverses the cashflows of the
bond.

Zero-Coupon
Style

Switch on so that the nominal amount of the other leg (i.e. the non-asset leg) of the
asset swap is adjusted with the deal price of the underlying bond.
The system automatically defaults to the zero-coupon style when there are no interest
cashflows found in the bond transaction.

Include Fees after
Value Date

Switch on so that fees that are to be settled after the value date of the bond are also
copied and reversed asset swap.
If this switch is not on, the fees after the value date are ignored.

Price/Fee Method

Method for reflecting the deal price and the fees of the bond in the asset swap
transaction. As for all swaps, a price that is different from par (100) will result in
upfront payments in the swap.
Choose from:
•

All-In Price - All-In Price of the underlying bond is used as the price of the asset leg

•

Deal Price - Deal Price of the underlying bond is used as the price of the asset leg of

of the swap.
the swap.
•

Deal Price with Fees - Deal Price of the underlying bond is used as the price of the
asset leg of the swap. In addition, the fees of the bond transaction can be
reflected (copied and reversed) as upfront payments in the asset swap
transaction. The Copied Fees field is used for determining which fees are to be
reflected in the swap.

•

Par - Price of the asset leg of the swap is Par, i.e. 100.

•

Par with Discount/Premium and Fees - Price of the asset leg of the swap is Par, i.e. 100,
but in addition discount/premium and fees of the bond transaction can be reflected
(copied and reversed) as upfront payments in the asset swap transaction. The
Copied Fees field is used for determining which fees are to be reflected in the swap.

•

Re-Offer Price - Re-Offer Price of the underlying bond is used as the price of the asset
leg of the swap.

Copied Fees

Fees ()

Select which fees are to be copied (as reversed) from the bond transaction to the
swap transaction as upfront payments:
•

None - No fees are copied.

•

All Fees - All fees are copied.

•

All-In Fees - Only All-In fees are copied (i.e. fees with the All-In attribute).

•

Re-Offer Fees - Only Re-Offer fees are copied (i.e. fees with the Re-Offer attribute).

The fee amounts (in the relevant currency) copied/reversed from the underlying bond
transaction and considered as upfront payments in the asset swap transaction. The
values are defaulted from the bond transaction according to the selections in Price/Fee
Method and Copied Fees fields. You can modify the amounts if needed.

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Information

Description

Adjust Leg 2 Price
With Up-Fronts

Switch on so that the Deal Price of the other leg (i.e. the non-asset leg) of the asset
swap is adjusted with the upfront payments on the asset leg.

By Nominal
Amount

If the underlying bond is traded in units, you can 'force' the swap transaction to be
based on the nominal amount rather than units by setting this switch. If the swap is
based on units, the interest amounts are calculated by one unit and multiplied by the
number of units.

The execution of the action generates a swap transaction.

•

Cancellation
Cancellation of the action is done by canceling the swap transaction.

3.1.1.3.2 Pricing
Pricing of bond transactions can be performed at transaction level using a right-click processing
action.

•

Setup
A choice of two types of Pricing action are available on the transaction if the Bond Pricing feature
is associated with the instrument: Swap Spread or Yield/Price to Maturity.
See A.2.79 Bond Pricing on page 746.

•

Execution

–

Swap Spread
This Pricing action calculates the spread to be add to the floating leg of an asset swap
generated from a given bond so that the market value of the asset swap is zero.

–

Information

Description

Swap Instrument

ID of the Asset Swap instrument.

Floating Leg
Currency

Currency of the floating leg.

Floating Leg
Frequency

Frequency of the floating coupon.

Swap Deal Price

Deal price of the swap.

Swap Spread

Calculated spread after pricing.

Yield/Price to Maturity
This Pricing action calculates a yield (Price) using a given price (Yield) and vice versa. The
calculation assumes the Yield Convention (*ISMA-30E360-ANNUAL or other) as defined in the
Trading Yield page of the Instrument.

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Information

Description

Interest Rate

Rate type of the yield.

Date Basis

Date basis used to convert the time.

Pricing Date

Opening date of the bond transaction.

Pricing Variable

Yield (or the price).

Pricing Target
Variable

(Information only)
Price (or the yield).

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Information

Description

Pricing Target (in %)

Target value that you want to achieve.

Pricing Result

(Information only)
Calculated value of the variable after pricing.

3.1.1.3.3 Benchmarking
It is possible to analyze and compare a bond issue against those of another bond (the benchmark)
or a swap curve, in terms of yields, swap spreads, or par swap rates.
See 3.2 Structured bonds on page 244.

3.1.1.3.4 Transaction conversion
It is possible to allow schedule conversion at predefined dates during a bond's life.

•

Setup (at instrument level)
This process is available on the transaction if the Transaction Conversion feature is associated
with the instrument.
See A.2.325 Transaction Conversion on page 873.
Then, the user can attach conversion schedules (at the instrument level) in the Schedule page of
the Instrument Editor.

•

Execution

–

At instrument level:
To execute the conversion at a predefined date, in the Instrument Editor, Cashflow page, the
user selects the conversion flow and performs Convert action. After this conversion, when
capturing a transaction, cashflows are generated according to the converted schedules.

–

At transaction level:
When capturing a transaction before the conversion date, conversion events are also
generated in the transaction. To execute the conversion, the user right-clicks the row of the
corresponding transaction event and selects Transaction Conversion. The conversion inputs are
displayed.
See A.2.325 Transaction Conversion on page 873.
The execution generates a conversion transaction with the following attributes:

–

Kind: Conversion

–

Opening Date: Conversion opening date

–

Value Date: Conversion value date.
The remaining attributes are inherited from the initial transaction.
The conversion transaction generates closing cashflows for the initial transaction; and future
cashflows are reopened according to the conversion schedules defined at instrument level.

3.1.1.4 Position monitoring
3.1.1.4.1 Setup
The cashflow discounting method used in IR risk calculation depends on the instrument set up:

•

Risk setup:
The default risk method is Zero-Coupon or you can select Z-Spread or Yield to Maturity. For more
information about these methods, see A.2.288 Risk Setup (BOND) on page 858.

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IR exposure setup:

•

–

By default, TRM uses the valuation curve interpolation settings (IR Quote and Yield Curve
Editor - Interpolation page). For example, if the interpolation settings are set up with Interest
Type Continuous Yield, then risk calculations use continuously compounding discounting of the
cashflows.

–

If IR Exposure is set up at the instrument level, then TRM uses these settings. For example,
if IR exposure is set up with yield type Periodic Rate, then risk calculations use periodic
discounting of the cashflows. See A.2.48 Base IR Exposure Setup on page 732.

–

If the risk method Yield to Maturity is used, then the date basis and interest rate defined for the
risk yield are applied, even if there is an IR exposure setup.

For more information about these calculations, see 2.3 Key-figures on page 112.

3.1.1.4.2 Calculations
In this section, numerical examples demonstrate how the different figures are calculated for
fixed-rate bonds.
If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.
This example shows a fixed-rate bond with the following deal data:
Setup data
Instrument Date Basis

Act/360

Currency

EUR

Valuation Method

Theoretical

Risk Method

Theoretical

Valuation Date

Figure Date

Risk Date

Figure Date

Risk Yield Type

Continuous

AI Method

Linear

Schedule

Fixed, Bullet Repayment

Result IR: Accrued Interest

Linear

Result IR: Accrual Method

Linear Accrual

Accrual Yield: Interest Type

Periodic Rate

Accrual Yield: Date Basis

Actual/360

Unless otherwise stated, the figure date used in the calculations is 2001-05-15. On this date, the
market data is as follows:
Market data on 2001-05-15
Figure Date

d_f

2001-05-15

Days to Spot

d_fs

2

Discount Rate

r_d

3.048771%

Other figures calculated by the system are as follows:
•

222

Time to Spot
t_s = d_fs / B
0.005555556 = 2 / 360

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•

MV Spot Discount Factor
D_s = EXP (-t_s * r_d) = 0.9998306382

Transaction data specific to the principal cashflow is as follows:
Transaction data
Opening Date

2001-02-16

Nominal Amount

A

1,000,000

Value Date

dt_v.p

2004-01-01

Payment Date

dt_p.p

2004-01-02

Issue Date

dt_i

2001-01-01

Book Value

V_b.p = A

1,000,000

On the figure date, the market data specific to the principal amount is as follows:
Market data on 2001-05-15
Interest Rate

r.p

4.56933049%

Other market data and figures specific to the principal amount are calculated by the system as
follows:
•

Time to Payment
t_p.p = (dt_p.p - d_f) / B
2.67222222 = (2004/01/02 – 2001/05/15) / 360

•

MV Discount Factor
D_V.p = D_s * D_f.p = 0.8851322685

•

PV Discount Factor
D_P.p = D_s * D_f.p = 0.8851322685

•

Discount Factor From Spot
D_f.p = EXP (-(t_p.p - t_s) * r.p) = 0.8852822015

On the figure date, the market data specific to the coupons is as follows:
Market data

Coupon 1

Interest Rate

r.c1

Coupon 2
3.5485079%

r.c2

Coupon 3
4.145317%

r.c3

4.56933049%

Transaction data specific to the coupon cashflows is as follows:
Transaction data

Coupon 1

Coupon 2

Coupon 3

Amount

A.c1

50,000

A.c2

50,000

A.c3

50,000

Value Date

dt_v.c1

2002-01-01

dt_v.c2

2003-01-01

dt_v.c3

2004-01-01

Payment Date

dt_p.c1

2002-01-02

dt_p.c2

2003-01-02

dt_p.c3

2004-01-02

Other market data and figures specific to the coupons are calculated by the system as follows:
•

Coupon 1
Time to Payment
t_p.c1 = (dt_p.c1 - d_f) / B
0.644444444 = (2002/01/02– 2001/05/15) / 360
MV Discount Factor
D_V.c1 = D_s * D_f.c1 = 0.977418468
PV Discount Factor
D_P.c1 = D_s * D_f.c1 = 0.977418468

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Discount Factor from Spot
D_f.c1 = EXP (- (t_p.c1 - t_s) * r.c1) = 0.977584034
•

Coupon 2
Time to Payment
t_p.c2 = (dt_p.c2 - d_f) / B
1.658333333 = (2003/01/02 – 2001/05/15) / 360
MV Discount Factor
D_V.c2 = D_s * D_f.c2 = 0.933623285
PV Discount Factor
D_P.c2 = D_s * D_f.c2 = 0.933623285
Discount Factor from Spot
D_f.c2 = EXP (- (t_p.c2 - t_s) * r.c2) = 0.933781432

•

Coupon 3
Time to Payment
t_p.c3 = (dt_p.c3 - d_f) / B
2.672222222 = (2004/01/02 – 2001/05/15) / 360
MV Discount Factor
D_V.c3 = D_s * D_f.c3 = 0.885132268
PV Discount Factor
D_P.c3 = D_s * D_f.c3 = 0.885132268
Discount Factor from Spot
D_f.c3 = EXP (- (t_p.c3 - t_s) * r.c3) = 0.885282201

3.1.1.4.3 Valuation figures
The valuation method commonly used for a fixed-rate bond is the Theoretical method.
•

Principal flow figures
Market Value
V.p = A * D_V.p
885,132.27 = 1,000,000 * 0.8851322685
Clean Market Value
CMV.p = A * D_f.p
885,282.20 = 1,000,000 * 0.8852822015

•

Coupon 1 figures
Market Value
V.c1 = A.c1 * D_V.c1
48,870.92 = 50,000 * 0.977418468
Clean Market Value
CMV.c1 = A.c1 * D_f.c1 - Accrued_Interest_Spot
29,990.31 = 50,000 * 0.977584034 - 18,888.89

•

Coupon 2 figures
Market Value
V.c2 = A.c2 * D_V.c2
46,681.16 = 50,000 * 0.933623285
Clean Market Value
CMV.c2 = A.c2 * D_f.c2
46,689.07 = 50,000 * 0.933781432

•

Coupon 3 figures
Market Value
V.c3 = A.c3 * D_V.c3
44,256.61 = 50,000 * 0.885132280
Clean Market Value
CMVc3 = A.c3 * D_f.c3
44,264.11 = 50,000 * 0.885282201

•

Total transaction figures
Market Value
= V.p +V.c1 + V.c2 + V.c3
= 1,024,940.97

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Clean Market Value
= CMV.p + CMV.c1 + CMV.c2 + CMV.c3
=1,006,225.70

3.1.1.4.4 Result figures
The setup of the instrument impacts the way result figures are computed.
•

Principal flow figures
Total Profit
Total_Profit.p = V.p - V_b.p
-114,867.73 = 885,132.27 – 1,000,000
MtoM Profit
MtoM_Profit.p = A * D_f.p - V_b.p
-114,717.80 = 1,000,000 * 0.8852822015 – 1,000,000
Other Profit
Other_Profit.p = Total_Profit.p - MtoM_Profit.p
-149.93 = -114,867.73 – (-114,717.80)

•

Coupon 1 figures
Total Profit
Total_Profit.c1 = = V.c1 - V_b.c1
48,870.92 = 48,870.92 - 0
MtoM Profit
MtoM_Profit.c1 = A.c1 * D_f.c1 - V_b.c1 - Accrued_Interest.Spot
29,990.31 = 50,000 * 0.977584034 – 0 – 18,888.89
Accrued Interest
Accrued_Interest.c1 = A.c1 * (d_f - dt_i) / B
18,611.11 = 50,000 * (2001/05/15 – 2001/01/01) / 360
Other Profit
Other_Profit.c1 = Total_Profit.c1 - MtoM_Profit.c1 - Accrued_Interest.c1
269.50 = 48,870.92 - 29,990.31 - 18,611.11

•

Coupon 2 figures
Total Profit
Total_Profit.c2 = V.c2 - V_b.c2
46,681.16 = 46,681.16 - 0
MtoM Profit
MtoM_Profit.c2 = A.c2 * D_f.c2 - V_b.c2
46,689.07 = 50,000 * 0.933781432 - 0
Other Profit
Other_Profit.c2 = Total_Profit.c2 - MtoM_Profit.c2
-7.91 = 46,681.16 - 46,689.07

•

Coupon 3 figures
Total Profit
Total_Profit.c3 = V.c3 - V_b.c3
44,256.61 = 44,256.61 - 0
MtoM Profit
MtoM_Profit.c3 = A.c3 * D_f.c3 - V_b.c3
44,264.11 = 50,000 * 0.885282201 - 0
Other Profit
Other_Profit.c3 = Total_Profit.c3 - MtoM_Profit.c3
-7.50 = 44,256.61 - 44,264.11

•

Total transaction figures
Total Profit
= Total_Profit.p + Total_Profit.c1 +Total_Profit.c2 + Total_Profit.c3
= 24,940.97
MtoM Profit
= MtoM_Profit.p + MtoM_Profit.c1 + MtoM_Profit.c2 + MtoM_Profit.c3
= 6,225.70

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Accrued Interest
= Accrued_Interest.c1
= 18,611.11
Other Profit
= Total_Profit.total - MtoM_Profit.total - Accrued_Interest.total
= 104.16

3.1.1.4.5 Risk figures
The risk method commonly used for a bond is the Theoretical method.
•

Principal flow figures
IR Exposure 1bp
E_i.p = A * (- (t_p.p - t_s) * D_f.p * D_s - t_s * D_f.p * D_s) * 0.0001
-236.53 = 1,000,000*(-(2.6722222-0.005555556)*0.8852822015*0.9998306382-t_s*D_f.p*D_s)*0.0001
Effective Duration
U_eff.p = -E_i.p / V.p / 0.0001
2.672222 = -(-236.53) / 885,132.27 / 0.0001

•

Coupon 1 figures
IR Exposure 1bp
E_i.c1 = A.c1 * (- (t_p.c1 - t_s) * D_f.c1 * D_s - t_s * D_f.c1 * D_s) * 0.0001
-3.15 = 50,000 * (-(0.64444444–0.005555556)*0.977584034*0.9998306382–t_s*D_f.c1*D_s)*0.0001
Effective Duration
U_eff.c1 = -E_i.c1 / V.c1 / 0.0001
0.64444 = -3.15 / 48,870.92 / 0.0001

•

Coupon 2 figures
IR Exposure 1bp
E_i.c2 = A.c2 * (- (t_p.c2 - t_s) * D_f.c2 * D_s - t_s * D_f.c2 * D_s) * 0.0001
-7.74 = 50,000 * (-(1.658333333-0.005555556)*0.933781432*0.9998306382-t_s*D_f.c2* D_s)*0.0001
Effective Duration
U_eff.c2 = -E_i.c2 / V.c2 / 0.0001
1.65833 = -7.74 / 46,681.16 / 0.0001

•

Coupon 3 figures
IR Exposure 1bp
E_i.c3 = A.c3 * (-(t_p.c3 - t_s) * D_f.c3 * D_s - t_s * D_f.c3 * D_s) * 0.0001
-11.83 = 50.000*(-(2.672222222-0.005555556)*0.885282201*0.9998306382-t_s*D_f.c3* D_s)*0.0001
Effective Duration
U_eff.c3 = -E_i.c3 / V.c3 / 0.0001
2.672222222 = -11.83 / 44,256.61 / 0.0001

•

Total transaction figures
IR Exposure 1bp
= E_i.p +E_i.c1 + E_i.c2 + E_i.c3
= -259.24
Effective Duration
= -E_i.total / V.total / 0.0001
= 2.529357

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3.1.1.5 Norwegian government bond
Norwegian government bonds are based on annual coupon and Actual/365 accrual date basis. The
ex-coupon period starts 14 calendar days prior to the interest payment. Accrued interest is
calculated as shown in Equation 2-51 Accrued Interest: Norwegian on page 55.

3.1.1.5.1 Instrument setup
Norwegian bond instruments must be based on an instrument type derived from the class BOND.

•

Main characteristics
They are set up in a similar way to bonds (3.1.1 Fixed-rate bond on page 215), except for the
following.
Information

Description

Currency

NOK

AI Method

Norwegian. See Norwegian on page 77.

–

Schedule
Select a cashflow structure based on the Fixed, Bullet Repayment system template,
(FIXED-BULLET). See B.2.1.1.21 Fixed, Bullet Repayment on page 894.

•

Trading Yield
Information

Description

Yield Convention

GOVT-NO-ACT365 (Norwegian Government Actual365)

See A.2.323 Trading Yield on page 872.

•

Quoted parameters
Information

Description

Price Type

Yield

Quote Handling

Bond

Currency

NOK

See A.2.274 Quoted on page 849.

•

Result parameters
Information

Description

AI Method

Coupon %

See A.2.49 Base IR Setup on page 733.

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3.1.2 Floating rate note
Floating Rate Notes (FRNs) have interest payments linked to a reference rate which has to be fixed
for each coupon.

3.1.2.1 Instrument setup
Instrument setup for a floating rate note is similar to that of a fixed-rate bond (see 3.1.1 Fixed-rate
bond on page 215), except for the following:

•

Bond main characteristics
The coupon rate needs to be null.

•

Schedules
Select the cashflow structure template you want for the instrument and, for each set of
cashflows defined in the template, select the generation parameters.
One system template is provided for floating rate bonds (B.2.1.1.22 Floating, Bullet Repayment
on page 894); you can choose this template or any other template derived from it. Once the
template is applied to the instrument, the schedules are created and it is then possible to define
their characteristics.
One important set of characteristics in the case of a floating rate note are the fixing parameters:

–

Fixing Rate (the yield curve) optionally * by a factor and + a spread

–

Fixing period (3M, 6M, 1Y, and so on)

–

Price Scenario used to retrieve the price which will be used for fixing

–

Fixing offset and type (in advance or in arrears). If in advance, the rate of the first cashflow
is required.

See Appendix B Schedules on page 883.

•

Discount margin calculation
Most FRNs have a known first/next coupon payment, while subsequent coupons will usually be
set in terms of a margin over a specific reference rate (such as, LIBOR). As a result, a current
margin relative to the reference rate is often calculated.

–

Discount margin setup
Define the parameters used to calculate the discount margin if you want to take it into
account in the estimation of the instrument’s future flows.
See A.2.343 Z-DM/Spread Setup on page 882.

–

Quoted
It is necessary to specify how the FRN is quoted on the market.
Information

Description

Quote Handling

FRN

It will then be possible to use the Bid Z-DM/Spread and Ask Z-DM/Spread figures to convert
Price into Discount Margin in Rate Monitor.
See A.2.274 Quoted on page 849.

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3 Debt instruments
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–

Risk parameters
After the calculation of the discount margin, the payment discount factor of each flow is
adjusted. The derived risk structure is achieved by setting the following parameter:
Information

Description

Risk Profile

Plain Vanilla

See A.2.338 Valuation Setup (Floating) on page 879.

3.1.2.2 Deal capture
3.1.2.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
a floating-rate bond.
Information

Description

Deal Price

Price paid for the FRN as a percentage of the Nominal Amount.

Nominal Amount

Enter either the nominal amount or face amount, and the system will compute the
other automatically.

Face Amount
Value Date

Official date when money is transferred. This defaults to the spot date of the
transaction.

In addition, the following optional information can be captured:
Information

Description

Units

If the denomination of a bond instrument is specified at instrument setup, the deal
can be input in units, and the nominal and face amounts are computed by the system.

Trading Unit Size
Nominal/Spot Rate

Current "running" coupon can be entered in this field (if fixing of the first coupon has
not been carried out in Instrument Editor: see 3.1.2.3.1 Fixing on page 230).

3.1.2.2.2 Generated data
•

Transaction
Book Value (BV) = NA * price / 100
where:
NA = nominal amount
price = deal price

•

Cashflows
The system copies all the future cashflows of the bond and scales them according to the nominal
amount engaged (using rounding).
Additionally the system generates a settlement cashflow with amount = BV (see above) and an
accrued interest cashflow according to the AI Method.

Note: The bond must be fixed at instrument level in order for the accrued interest flow to be
generated (see 3.1.2.3.1 Fixing on page 230).

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The following cashflow structure is generated for a floating-rate bond:

3.1.2.3 Processing
This section describes the actions that can be done throughout the life of a floating-rate bond.

3.1.2.3.1 Fixing
The major process for a floating-rate note is the fixing of the flows.

•

Setup
Depending on the instrument setup (schedules) the fixing can be done in advance (the standard
case, at the beginning of each coupon period) or in arrears (at the end of each coupon period).
In both cases there can be an offset of n days (before the beginning or end of the coupon
period).

•

Execution
When fixing is executed, the rate is retrieved for the specified fixing rate and period according to
the designated fixing scenario. The scenario to be used for fixing is configured at the system
level, see TRM System Admin Guide. The fixing subscenario is specified at the cashflow level.
The following information is stored on the fixed cashflow:
The fixing date
The rate of the yield curve
The coupon rate which is the rate of the yield curve (and optionally * factor
+ spread)
The amount of the coupon.
The fixing process can be performed in two ways in TRM: the process itself is exactly the same in
each case: the coupon is fixed at both instrument and transaction level.
The methods of fixing are as follows:

–

Directly on the cashflow (in Instrument Editor’s Cashflow page) using the Fix Price action: the
fixing affects all deals on this instrument.

–

Using the Fixing Bond Cashflow activity: all instruments and their deals that need to be fixed
for a particular date are affected.
See the TRM User Guide for information on the activity parameters.

Note: The bond issue must be fixed at instrument level in order for the accrued interest flow to

be generated (for transactions captured between coupon fixing date and fixing value date).

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•

Cancellation
It is possible to cancel the cashflow fixing either manually, using the Undo Fixing action in
Instrument Editor; or automatically, using the Fixing Bond Cashflow - Undo activity.
See the TRM User Guide for information on the activity parameters.

3.1.2.4 Position monitoring
3.1.2.4.1 Setup
The cashflow discounting method used in IR risk calculation depends on the instrument set up:

•

•

Risk setup:

–

The default risk method is Zero-Coupon or you can select risk method Zero Discount Margin
(Z-DM). For more information about these methods, see A.2.289 Risk Setup (FRN) on page
858.

–

If discount margin is set up at the instrument level (see A.2.164 FRN Valuation on page
791), then the discount margin is used in the valuation and is added to the valuation curve
specified for the instrument, and the day count method and yield type used are taken from
the interpolation method of this valuation curve. For more information about Discount Margin
calculations, see 2.1.5 Discount Margin on page 66.

IR exposure setup:

–

By default, TRM uses the valuation curve interpolation settings (IR Quote and Yield Curve
Editor - Interpolation page). For example, if the interpolation settings are set up with Interest
Type Continuous Yield, then risk calculations use continuously compounding discounting of the
cashflows.

–

If IR Exposure is set up at the instrument level, then TRM uses these settings. For example,
if IR exposure is set up with yield type Periodic Rate, then risk calculations use periodic
discounting of the cashflows. See A.2.48 Base IR Exposure Setup on page 732.

For more information about these calculations, see 2.3 Key-figures on page 112.

3.1.2.4.2 Calculations - Discount Margin example
Let us consider a floating rate note with two coupons remaining, where the next coupon is fixed:

•

Input data
Data

Symbol

Example

Next coupon (fixed)

c1

0.0556111111111111

Last coupon (estimated)

c2

0.0232101439796721

Time from spot to next coupon (Act/365)

t1

13/365 = 0.035616438356164383

Time from spot to last coupon (Act/365)

t2

196/365 = 0.53698630136986303

Discount factor from spot to next coupon

D1

0.999066136779281

Discount factor from spot to last coupon

D2

0.981278683885205

Clean price from market quote

P

0.98

Accrued interest

Ia

0.05163888888888888

Dirty price

Pd

P + Ia = 1.0316388888888888

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Choosing continuous compounded rate as the discount margin yield type, we get the following
results:
Data

Calculation

Underlying rate to next coupon

r1 = - log[D1] / t1 = - log[0.999] / 0.0356 = 0.026232256389534768

Underlying rate to last coupon

r2 = - log[D2] / t2 = - log[0.981] / 0.0537 = 0.035194153518686676

Discount margin must satisfy the following equation:

from which we can solve numerically: m = 0.052423976963667664.

3.1.2.4.3 Calculations - FRN example
The numerical example in this section demonstrates how the different figures are calculated for a
floating-rate note.

Instrument data
•

•

Schedule page (Floating Coupon)
Interest Type

Periodic Rate

Date Basis (B)

Actual/360

Base Valuation page
(Valuation) Method

•

•

360

Theoretical

IR Exposure page
Date Basis (B_r)

Actual/360

Yield Type

Continuous Yield

360

Floating Valuation page
Risk Profile

Plain Vanilla

Transaction data

•

Nominal Amount

A = 1,000,000.00

Deal Price

p = 98.00%

Spot Date

d_v = 2002-02-26

Rate

r_c = 0.05

Calculated transaction data
Book Value

232

V_b = p*A = 980000

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3 Debt instruments
3.1 Bond

Market data
Coupon Period
(_p_c)

Time to Value
Date (_t_v)

Risk Date (_d_r)

Time to Risk
Date (_t_r)

Principal

1.713888889

2/22/2004

1.713888889

Coupon 1

0.188888889

8/22/2002

0.188888889

Coupon 2

0.7

Risk Cash Flow Start 2

177

8/22/2002

0.188888889

Risk Cash Flow End 2

184

2/22/2003

0.7

2/22/2003

0.7

8/22/2003

1.202777778

8/22/2003

1.202777778

2/22/2004

1.713888889

Coupon 3

1.202777778

Risk Cash Flow Start 3
Risk Cash Flow End 3

181

Coupon 4

1.713888889

Risk Cash Flow Start 4
Risk Cash Flow End 4

184

Valuation data
Figure or Valuation Date

d_f = 2002-06-15

Figure Market Value Spot
Discount Factor

D_s = 0.999746283358179

Valuation figures
•

•

•

Figure Market Value (_V_)
Principal

=_A_e*_D_p = 930990.3649

Coupon 1

=_A_e*_D_p = 24432.46813

Coupon 2

=_A_e*_D_p = 18638.33299

Coupon 3

=_A_e*_D_p = 20688.99262

Coupon 4

=_A_e*_D_p = 23545.42006

Transaction

V_Tr = SUM(_V) = 1018295.579

Figure Fixing Rate (_r_x)
Coupon 1

=r_c = 0.05

Coupon 2

=(INDEX(_D_p,A28,1)/(_D_p)-1)/(_p_c/360) = 0.037392717

Coupon 3

=(INDEX(_D_p,A29,1)/(_D_p)-1)/(_p_c/360) = 0.043109308

Coupon 4

=(INDEX(_D_p,A32,1)/(_D_p)-1)/(_p_c/360) = 0.049481851

Figure Amount (_A_e)
Principal

=A = 1000000

Coupon 1

=A*_r_x*_p_c/B = 24583.33333

Coupon 2

=A*_r_x*_p_c/B = 19111.8329

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3.1 Bond

•

Coupon 3

=A*_r_x*_p_c/B = 21674.4023

Coupon 4

=A*_r_x*_p_c/B = 25290.72367

Figure IR Exposure 1bp (_E_i1)
Principal

=_V_r*(-_t_r*_D_p)*0.0001 = -159.5614042

Coupon 1

=_V_r*(-_t_r*_D_p)*0.0001 = -0.461502176

Coupon 2
Risk Cash Flow Start 2

=_V_r*(-_t_r*_D_p)*0.0001 = -18.77296987

Risk Cash Flow End 2

=_V_r*(-_t_r*_D_p)*0.0001 = 68.26573443

Coupon 3
Risk Cash Flow Start 3

=_V_r*(-_t_r*_D_p)*0.0001 = -68.26573443

Risk Cash Flow End 3

=_V_r*(-_t_r*_D_p)*0.0001 = 114.809443

Coupon 4
Risk Cash Flow Start 4

=_V_r*(-_t_r*_D_p)*0.0001 = -114.809443

Risk Cash Flow End 4

=_V_r*(-_t_r*_D_p)*0.0001 = 159.5614042

Transaction

•

E_i1_Tr = SUM(_E_i1) = -19.23447204

Figure Risk Value (_V_r)
Principal

= A = 1000000

Coupon 1

= _A_e = 24583.33333

Coupon 2
Risk Cash Flow Start 2

= A = 1000000

Risk Cash Flow End 2

= -A = -1000000

Coupon 3
Risk Cash Flow Start 3

= A = 1000000

Risk Cash Flow End 3

= -A = -1000000

Coupon 4
Risk Cash Flow Start 4

= A = 1000000

Risk Cash Flow End 4

= -A = -1000000

Transaction

•

Figure Present Value (_V_p)
Principal

= _V_r*_D_p = 930990.3649

Coupon 1

= _V_r*_D_p = 24432.46813

Coupon 2
Risk Cash Flow Start 2

= _V_r*_D_p = 993863.1105

Risk Cash Flow End 2

= _V_r*_D_p = -975224.7775

Coupon 3

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3 Debt instruments
3.1 Bond

Risk Cash Flow Start 3

= _V_r*_D_p = 975224.7775

Risk Cash Flow End 3

= _V_r*_D_p = -954535.7849

Coupon 4
Risk Cash Flow Start 4

= _V_r*_D_p = 954535.7849

Risk Cash Flow End 4

= _V_r*_D_p = -930990.3649

Transaction

V_p_Tr = SUM(_V_p) = 1018295.579

Result figures
•

•

•

•

•

Figure MtoM Profit (_P_m)
Principal

=A*_D_p/D_s-V_b-_P_a = -51776.12227

Coupon 1

=_A_e*_D_p/D_s-_AI = 9299.779742

Coupon 2

=_A_e*_D_p/D_s-_AI = 18643.06305

Coupon 3

=_A_e*_D_p/D_s-_AI = 20694.24309

Coupon 4

=_A_e*_D_p/D_s-_AI = 23551.39544

Transaction

P_m_Tr = SUM(_P_m) = 20412.35905

Figure Accrued Interest (_AI)
Coupon 1

= (d_f-d_v)/(_d_v-d_v)*_A_e = 15138.88889

Transaction

AI_Tr = SUM(_AI) = 15138.88889

Figure Accrued Profit (_P_a)
Principal

= (d_f-d_v)/(_d_v-d_v)*(A-V_b) = 3002.754821

Transaction

P_a_Tr = SUM(_P_a) = 3002.754821

Figure Other Profit (_P_o)
Principal

= _P_T-_P_m-_P_a-_AI = -236.267694

Coupon 1

= _P_T-_P_m-_P_a-_AI = -6.200496936

Coupon 2

= _P_T-_P_m-_P_a-_AI = -4.73005535

Coupon 3

= _P_T-_P_m-_P_a-_AI = -5.250473862

Coupon 4

= _P_T-_P_m-_P_a-_AI = -5.975380961

Transaction

P_o_Tr = SUM(_P_o) = -258.4241011

Total Profit (_P_T)
Principal

=_V-V_b = -49009.63514

Coupon 1

=_V = 24432.46813

Coupon 2

=_V = 18638.33299

Coupon 3

=_V = 20688.99262

Coupon 4

=_V = 23545.42006

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3 Debt instruments
3.1 Bond

Risk figures
Figure Effective Duration

•

Transaction

U_eff_Tr = E_i1_Tr/V_Tr/0.0001 = -0.188888889

3.1.3 Australian floating rate note
An Australian floating rate note (FRN) is a medium-term bond that provides investors with the
ability to achieve returns at a fixed margin above a floating benchmark, usually the 90-day Bank Bill
Swap Rate (BBSW). BBSW rates are compiled daily by the Australian Financial Markets Association
using the mid-rates of 14 banks. Australian floating rate notes are traded at a trading margin and
swap rate, not at a price or yield. The interest margin is determined on the issue date by the credit
rating of the issuer, the term to maturity and the market perception of the issuer.
The official Treasury Adjustable Rate Bond Pricing Formula is as follows:
Price per $100 face value:
Equation 3-1 Official Treasury Adjustable Rate Bond Pricing formula

where:
C

0 if the next interest is not fixed at instrument level, otherwise 1.

b

The Index (as a percentage) from the last interest reset date to the next
interest payment date defined as the average three month Australian bank
bill swap reference mid-rate (BBSW) as indicated by Reuters, rounded to
four decimal places.

IM

Spread% defined at schedule level.

d

The number of days in the current interest period.

TM

Trading Margin (expressed as a percentage) to express the yield margin to
the Index.

an

v

n

236

The number of complete interest periods to maturity at the next interest
payment date.

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3 Debt instruments
3.1 Bond

i

s

The quarterly swap rate for the period starting on the settlement date and
ending on the maturity date. If the frequency of the swap rate is not
quarterly, the swap rate is converted to a quarterly compounding rate before
it is used. The conversion formula is given as follows:
Equation 3-2 Swap Rate Conversion

where:
•

r_in is the swap rate to be converted.

•

r_out is the resultant compounding rate, num_in and num_out are the
number of periods in a year for the frequencies related to r_in and
r_out respectively. For example, the number of periods in a year for a

quarterly frequency is 4.
•

r is the discount rate (expressed as a percentage) as determined on the
offering date for the period from the settlement date to the next interest
payment date, and rounded to four decimal places.

•

f is the number of days from the settlement date to the next interest
payment date.

3.1.3.1 Instrument setup
Australian FRN instruments must be based on an instrument type derived from the class BOND.
They are set up in a similar way to bonds, but require a different primary feature.

•

Main characteristics
Same set up as for a usual FRN, see 3.1.2 Floating rate note on page 228.
See A.2.30 Australian FRN on page 724.

•

Quotation information
Information

Description

Price Type

Select Trading Margin to trade Australian FRN instruments at a trading margin.

Quote Handling

Select FRN Australian to convert the quotation (trading margin) to the price of
the instrument. See Equation 3-1 on page 236.

See A.2.274 Quoted on page 849.

•

Yield Curve Default
The setup of the feature Quote Default (Australian FRN) is similar to the usual Quote Default
feature, except that it adds the Yield Curve Default page to select the Par rate yield curve to be
used for reference rate defaulting.
Information

Description

Currency

The currency that you want to specify. Select AUD.

Yield Curve

Select corresponding yield curve to be used instead of the yield curve defined
at the currency level (Currency Editor).

A.2.267 Quote Default (Australian FRN) on page 846.

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3.1 Bond

Valuation approach

•

To use the quoted valuation method, i.e. market value calculation using the trading margin to
price formula (Equation 3-1 on page 236).
A.2.31 Australian FRN Method on page 725.

3.1.3.2 Deal capture
3.1.3.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
an Australian FRN:
Information

Description

Trading Margin

Instrument quotation.

In addition, the following defaulted information can be modified:
Information

Description

Reference Rate

Quarterly swap rate for the period from settlement date to maturity date (from
the yield curve specified in Yield Curve Default page when provided, otherwise uses
the default yield curve defined at currency level).

Discount Rate

Computed from the settlement date and the next coupon date of the instrument
(from the default yield curve defined at currency level).

AU Rate Scenario

Scenario used to calculate the reference and discount rates. This scenario defaults
to the scenario defined at the instrument level (Quote Default page). You can
change the default scenario by selecting Quote Default Configuration from the Options
menu. See TRM User Guide for more information about changing this
configuration.

Deal Price

Computed using the trading margin to the price formula (Equation 3-1 on page

236).

3.1.3.2.2 Generated data
Same as for usual FRN, see 3.1.2.2.2 Generated data on page 229.

3.1.3.3 Processing
The actions that can be done throughout the life of an Australian FRN are the same ones as for a
usual FRN, see 3.1.2.3 Processing on page 230.

3.1.3.4 Position monitoring
There are two basic methods for valuation of Australian FRN instruments: Quoted or Theoretical.
When the Theoretical valuation method is used, the Australian FRN is valuated in the same way as a
usual FRN instruments. On the other hand, if you want to use the pricing formula (Equation 3-1 on
page 236) to compute the market value with the reference rate and discount rate taken on the
valuation date as described previously, then you need to attach feature Australian FRN Method (A.2.31
Australian FRN Method on page 725) and use the Quoted valuation method.
Swap and discount rates used in the pricing formula are retrieved as follows:

•

Reference Rate: The quarterly swap rate for the period from valuation date to maturity date is
computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature)
with Usage set to Valuation when provided, otherwise uses the valuation yield curve defined at
the currency level.

•

Discount Rate: Computed between valuation date and next coupon date of the instrument
(computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature)

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with Usage set to Discount when provided, otherwise uses the valuation yield curve defined at
currency level).

Note: For the valuation when the next coupon is not fixed, the estimation curve is used to

compute the next fixing rate and the discount rate in the pricing formula. If the estimation
curve is not defined at the instrument level, then the currency estimation curve is used
instead. If no currency estimation curve is defined, then the currency valuation curve will
be used.

See feature A.2.337 Valuation Curve Setup on page 878.

3.1.4 Zero-coupon bond
A zero-coupon bond does not pay any interest during its life, but is instead paid at a significant
discount and repays its entire face value at maturity.

3.1.4.1 Instrument setup
Instrument setup for a zero-coupon bond resembles a fixed-rate bond except for the following:

•

Bond main characteristics
The coupon rate needs to be null.

•

Schedules
Select the cashflow structure template you want for the instrument and, for each set of cashflow
defined in the template, select the generation parameters.
One system template is provided for zero-coupon bonds (B.2.1.1.46 Zero-Coupon on page 899);
you can choose this template or any other template derived from it. Once the template is applied
to the instrument, the schedules are created and it is then possible to define their
characteristics.
See Appendix B Schedules on page 883.

•

Trading yield
Specify how the yield/price conversion will be made when dealing the instrument.
Information
Yield Convention

Description
Select *ISMA-30E360-ANNUAL.
For more information about these conventions, see 2.1.4 Yield/price conversions on
page 38.
Note: *U.S.STREET can also be used when applicable. For example, use
*U.S.STREET-ACTACT-SEMIANNUAL for U.S. and UK STRIPS.

See A.2.323 Trading Yield on page 872.

3.1.4.2 Deal capture
3.1.4.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
a zero-coupon bond.
Information

Description

Deal Price or

If there is a yield/price convention set on the instrument, it is possible to enter either
a rate or a price and conversion is made automatically. If there is no convention set,
the deal must be entered in price.

Deal Rate

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Information

Description

Nominal Amount

Enter either the nominal amount or face amount, and the system will compute the
other automatically.

Face Amount
Value Date

Official date when money is transferred. This defaults to the spot date of the
transaction.

In addition, the following optional information can be captured:
Information

Description

Units

If the denomination of a bond instrument is specified at instrument setup, the deal
can be input in units, and the nominal and face amounts are computed by the system.

Trading Unit Size

3.1.4.2.2 Generated data
•

Transaction
Book Value (BV) = NA * price / 100
where:
NA = nominal amount
price = deal price

•

Cashflows
TRM generates a settlement cashflow with amount = BV (see above) and a principal payback
cashflow for the nominal amount.
The following cashflow structure is generated for a Zero-Coupon bond (bought):

3.1.4.3 Processing
This section describes the actions that can be done throughout the life of a zero-coupon bond.

3.1.4.3.1 Asset swap
It is possible to carry out the Asset Swap action on a zero-coupon bond (see 3.1.1.3.1 Asset swap on
page 218).
In this case, the Zero-Coupon Style switch is on by default (no interest flows) and the Book Value
instead of the Nominal Amount is used for the second leg of the swap.

3.1.4.3.2 Transaction conversion
It is possible to allow schedule conversion at predefined dates during a bond's life.

•

Setup (at instrument level)
This process is available on the transaction if the Transaction Conversion feature is associated
with the instrument.

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See A.2.325 Transaction Conversion on page 873.
Then, the user can attach conversion schedules (at the instrument level) in the Schedule page of
the Instrument Editor.

•

Execution

–

At instrument level:
To execute the conversion at a predefined date, in the Instrument Editor, Cashflow page, the
user selects the conversion flow and performs Convert action. After this conversion, when
capturing a transaction, cashflows are generated according to the converted schedules.

–

At transaction level:
When capturing a transaction before the conversion date, conversion events are also
generated in the transaction. To execute the conversion, the user right-clicks the row of the
corresponding transaction event and selects Transaction Conversion. The conversion inputs are
displayed.
See A.2.325 Transaction Conversion on page 873.
The execution generates a conversion transaction with the following attributes:

–

Kind: Conversion

–

Opening Date: Conversion opening date

–

Value Date: Conversion value date.
The remaining attributes are inherited from the initial transaction.
The conversion transaction generates closing cashflows for the initial transaction; and future
cashflows are reopened according to the conversion schedules defined at instrument level. If
the conversion price is different to the original deal price, then a P/L flow is generated,
showing the differences between the conversion price and the original deal price.

3.1.5 Amortizing bond
An amortizing bond repays the principal according to a pre-defined schedule.
Amortizing bonds can be fixed-rate or floaters.
A special case of an amortizing bond is the constant annuity. In this case, the rate is fixed and the
repayments, occurring at each coupon payment, are calculated so that the sum of the interest + the
repayment is constant during the life of the bond. In simple terms, this means that the interest
payments are decreasing, while the principal payments are increasing.

Note: TRM does not support repayments in the middle of a coupon period but only at coupon
payment dates.

3.1.5.1 Instrument setup
Most of the characteristics of an amortizing bond are the same as for a fixed/floating rate bond with the following differences.

•

Schedules
Select the cashflow structure template you want for the instrument and, for each set of cashflow
defined in the template, select the generation parameters.
Depending on whether the rate is floating or fixed, you need to apply either the Floating, Bullet
Repayment template (see B.2.1.1.22 Floating, Bullet Repayment on page 894), or the Fixed,
Bullet Repayment template (see B.2.1.1.21 Fixed, Bullet Repayment on page 894), or any other
template derived from them.
Then, for the principal schedule you have to specify the repayment frequency, the method used
for repayment calculation, and how much is repaid at each amortization.

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The most common methods are: linear, percentage, and amount. For the interest schedule, the
parameters are the same as those for fixed or floating rate bonds.
See Appendix B Schedules on page 883.
Note that for an annuity repayment, you have to select the Fixed, Annuity Repayment template
(see B.2.1.1.20 Fixed, Annuity Repayment on page 894).

3.1.5.2 Deal capture
3.1.5.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
an amortizing fixed-rate bond.
Information

Description

Deal Price or

If there is a yield/price convention set on the instrument, it is possible to enter either
a rate or a price, and conversion is made automatically. If there is no convention set,
the deal must be entered in price.

Deal Rate
Nominal Amount

Nominal amount of the deal.

Value Date

Official date when money is transferred. This defaults to the spot date of the
transaction.

In addition, the following optional information can be captured:
Information

Description

Trading Units

If the denomination of a bond instrument is specified at instrument setup, the deal
can be input in face amount/units and the Nominal Amount will be computed by the
system.

Face Amount

3.1.5.2.2 Generated data
•

Transaction
Book Value (BV) = NA * price / 100
where:
NA = nominal amount
price = deal price

•

Cashflows
The system copies all the future cashflows of the bond and scales them according to the nominal
amount engaged (using rounding).
Additionally, TRM generates a settlement cashflow with amount = BV (see above) and an
accrued interest cashflow according to the AI Method.

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The following cashflow structure is generated for an amortizing fixed-rate bond:

For a fixed annuity they are as follows:

3.1.6 Step-up bond
Step-up bonds have interest payments which increase during the life of the bond.

3.1.6.1 Instrument setup
Instrument setup for a step-up bond is similar to that of a fixed-rate bond, except for the following:

•

Schedules
The cashflow structure template assigned to the instrument can be the same one used for a
fixed-rate bond. However, you also have to specify the rate offset to be applied for each coupon.
See Appendix B Schedules on page 883.

3.1.6.2 Deal capture
3.1.6.2.1 Input data
The data required is the same as for a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215).

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3.1.6.2.2 Generated data
•

Transaction
Book Value (BV) = NA * price / 100
where:
NA = nominal amount
price = deal price

•

Cashflows
The following cashflow structure is generated for a step-up bond:

3.2 Structured bonds
3.2.1 Callable bond
A callable (or puttable) bond is modeled by adding a call or put event to an ordinary bond cashflow
structure template.

3.2.1.1 Instrument setup
Instrument setup for a callable bond is similar to that of a standard bond (see 3.1.1 Fixed-rate bond
on page 215 or 3.1.2 Floating rate note on page 228), except for the following:

•

Schedule
Select the cashflow structure template you want for the instrument. For each set of cashflows
defined in the template, select the generation parameters.
Call or put events are added to a cashflow structure using a secondary template. Several
system-defined secondary templates are provided for use with callable bonds: see B.2.1.2
Secondary templates on page 900; you can choose one of these templates or a user-defined
template derived from one of them.
Once the template is applied to the instrument, the schedules are created and it is then possible
to define their characteristics.
The call or put event should specify the following information:

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–

Any other characteristics, for example, whether the call/put option gives the issuer of the
bond the right to terminate (call: Transaction Sign = "+") or the holder (put: Transaction
Sign = "-").

–

If a call/put event has the attribute Special, the original call/put price can be overwritten at
call execution.

3.2.1.2 Processing
This section describes the processing actions that are specific to transactions on callable bonds.

3.2.1.2.1 Call/Put
•

Setup
To add call or put events to a cashflow structure, you need to select a system-defined secondary
template or a user-defined template derived from one of them.

•

Execution
The Execute Call/Put action performed in Transaction Manager's Event view allows you to specify
the following information:
Information

Description

Settlement Date

The settlement date of the selected event.

Amount to Call

Defaults to the amount left. Should be less than or equal to the amount left.

Counterparty

Defaults to the bond issuer. The counterparty of the call transaction.

Match with Parent at
Apply

Automatically matches the call transaction with the original transaction when
applied.

Executing the Call/Put action on a bond creates a transaction similar to a normal buyback or sell
transaction. In other words, the resulting transaction is generated with settlement and position
cashflows.
Call/Put transactions can be identified as follows:
Transaction Kind = Call/Put (Bond)
Closing and P/L cashflows are created as part of the end-of-day processing according to the
selling method (average balance, FIFO selling, or by manual matching).

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3.2.2 Dual-currency bond
Bond issues can be structured to involve several different currencies. With a dual-currency bond, the
currency in which the bond is issued (principal currency) differs from the currency in which the
principal is repaid (redemption currency). The currency of the coupon can be either the principal
currency, the redemption currency, or another currency.
The FX rate to apply can be known (determined on the date of issue) or unknown (determined a
number of days before the payment date of the interest cashflow or period start of the coupon).
Setting up a dual-currency bond in TRM involves specifying the Dual Currency feature in the
instrument definition. Schedule templates for known FX rates or unknown rates (whose rates will be
fixed at a defined date) are also applied at instrument level.

3.2.2.1 Instrument setup
Instrument setup for a dual-currency bond is similar to that of a standard bond (see 3.1.1 Fixed-rate
bond on page 215 or 3.1.2 Floating rate note on page 228), except for the following:

•

Bond main characteristics
Information

Description

AI Method

The method used by the system to compute settlement accrued interests.
The usual AI Methods (e.g. linear, and so on) are relevant. See 2.1.6.1 Accrued
interest calculations on page 67 for more information.
Note: The AI Settlement is generated when the fixing date method is set to In
Advance. However, when the fixing date method is set to In Arrears, the accrued
interest settlement is unknown and so no AI is calculated.

•

Dual-currency attributes
This information defines the characteristics of the principal cashflow.
Information

Description

Settlement
Currency

Currency in which the principal cashflow is settled.

Settlement FX
Rate

Rate used to calculate the settlement amount of the principal cashflow.

Need Fixing

Specify whether the FX rate needs to be fixed:
•

Select No when the FX rate is known

•

Select Yes, Unmarked when the FX rate is unknown.

Fixing Offset

Number of days’ offset allowed, that is, the difference in days between the fixing date
and the due date (default = 0).

Fixing Max. Offset

Maximum number of days’ offset allowed.

See A.2.125 Dual Currency on page 771.

•

Schedules
Select a suitable Dual Currency cashflow structure template for the instrument. For each set of
cashflows defined in the template, specify the generation parameters.
The following system templates are provided for dual-currency structures:

–

Dual-Currency Known FX
This is a fixed bullet structure used for dual currency instruments when the FX rate is known
when the deal is entered. For both interest and redemption schedules you can choose a
different settlement currency and specify the settlement FX rate.

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See B.2.1.1.15 Dual Currency, Known FX Rate on page 893.

–

Dual-Currency Known FX Floating
This is a floating bullet structure used for dual currency instruments when the FX rate is
known when the deal is entered. For both interest and redemption schedules you can choose
a different settlement currency and specify the settlement FX rate.
See B.2.1.1.16 Dual Currency, Known FX Rate, Floating on page 893.

–

Dual-Currency Unknown FX
This is a fixed bullet structure used for dual currency instruments when the settlement FX
rate is not known beforehand. For both interest and principal schedules you can choose a
different settlement currency.
See B.2.1.1.17 Dual Currency, Unknown FX Rate on page 893.

Note: This template covers fixed interest rates only. For floating rate issues, you also have to use
the Fixing Dates secondary template (see B.2.1.2.15 Fixing Dates on page 903).

You can choose one of these templates or any other template derived from them. After the
template is applied to the instrument, the schedules are created, it is then possible to define the
settlement currency characteristics, as well as other characteristics, such as date basis, payment
convention, calendars, and so on.
See Appendix A Features on page 713.

•

FX fixing
If the settlement FX rate is unknown when the deal is entered, then this feature needs to be
included in the instrument definition.
See A.2.174 FX Fixing on page 797.

3.2.2.2 Deal capture
3.2.2.2.1 Input data
Deals on dual-currency bonds are captured in the same way as a standard bond (see 3.1.1
Fixed-rate bond on page 215 or 3.1.2 Floating rate note on page 228).

3.2.2.2.2 Generated data
•

Cashflows
Settlement Currency = Settlement Currency (as defined in the schedule)
Settlement FX Rate = Settlement FX Rate (as defined in the schedule)
Settlement Amount = Amount * Settlement FX Rate

3.2.2.3 Processing
This section describes the actions that can be done throughout the life of a dual-currency bond.

3.2.2.3.1 FX fixing
When the settlement FX rate of a dual-currency bond is not known beforehand, the FX rates need to
be fixed at the agreed fixing date.

•

Setup
Depending on the instrument setup, the fixing can be done in advance (at the beginning of each
coupon period) or in arrears (the standard case, at the end of each coupon period).
In both cases there can be an offset of n days (before the beginning or end of the coupon
period).

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Execution

•

There are two ways to execute the FX Fixing action, one in the Instrument Editor, the other in
Transaction Manager as described further on.

–

The FX Fixing action performed in Instrument Editor's Cashflow page allows you to set the FX
rate. The following values can be input:
Information

Description

Settlement FX
Rate

Fixing market quote to be entered manually.
After the manual entry, the Fix Fx Rate action is available and should be performed
to fix the specified FX rate.

The fixing process is performed directly on an individual cashflow in the Cashflow page. It is
possible to modify the fixing values.

–

Alternatively, the FX Fixing action performed in Transaction Manager’s Cashflow view on the
cashflow allows you to set the FX rate. The following values can be input:
Information

Description

Fixing Date

Day the cashflow is fixed.

Reference FX Rate

Fixing market quote.
This is defaulted by the system to the FX cross rate between the actual currency and
the currency on the fixing date and can be changed by the user.

The fixing process is performed directly on an individual cashflow in the Cashflow view. It is
possible to modify the fixing values.
Cancellation

•

It is possible to undo the FX fixing using the Undo FX Fixing action.

3.2.2.3.2 Asset swap
It is possible to carry out the Asset Swap action on a dual-currency bond (see 3.1.1.3.1 Asset swap
on page 218).

3.2.2.4 Position monitoring
For the valuation of the dual-currency bond, an estimation of the future accrued interests can be
defined by setting up the feature Generic IR Valuation with the following parameters (see A.2.201
Generic IR Valuation on page 811 for more details):
Information

Description

AI Method

The method used by the system to compute accrued interests in the calculation of
the market value. For dual-currency bonds, there are two types of dual-currency
methods:
•

Dual Currency Estimated - The estimated accrued interest is calculated using the

•

Dual Currency Last - The accrued interest is calculated using the FX rate of the

forward FX rates.
previous FX fixing.
Note: Both methods round the figure value in the cashflow currency before
converting it into the settlement currency. See 2.1.6.1 Accrued interest
calculations on page 67 for more information.

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Information

Description

Settlement Switches

Activate the switches that apply to this instrument:
•

Dirty Price - determines whether price used for valuation includes accrued
interest (dirty price) or not.

Note: If it is on, the market value for accrued interest is not calculated, even if the
AI Method has been configured.
Method

For dual-currency bond, leave empty.

Valuation Modes

Valuation mode: Default, Benchmark, or Theoretical.

For information about dual currency calculations, see 2.3.5 Dual currency on page 147.

3.2.3 Credit step-up bond
Credit step-up bonds are corporate bonds that contain a provision stating that the coupon payment
increases as the credit rating of the issuer declines. When the credit rating of the issuer goes up
again, the coupon payment goes back down but is floored by the initial rate.
A credit-linked note usually offers a higher yield compared to a vanilla bond with a similar credit
rating. A Collateralized Debt Obligation (CDO), a common type of credit-linked note, represents a
leveraged position in a portfolio of credit risk and enables investors to gain exposure to a large
diversified pool of underlying credit risk.

3.2.3.1 Instrument setup
Credit step-up bonds are based on an instrument type derived from the class CREDIT-STEP-UP.
Instrument setup for a credit step-up bond is similar to that of a fixed-rate or floating-rate bond
(see 3.1.1 Fixed-rate bond on page 215 and 3.1.2 Floating rate note on page 228), except for the
following additional attributes.

•

Credit step-up characteristics
You set the credit event information at instrument level.
Information
Credit event type

Description
Select from Downgrade or Upgrade:
•

Downgrade when the credit rating deteriorates

•

Upgrade when the credit rating improves.

Date information

Date the step up/down action comes into effect and the date after which the coupons
are affected by the change in credit rating.

Offset parameters

Offset that applies to fixed rate or floating rate flows.

When the credit event information is saved, the coupon flows at transaction level are updated.
See A.2.115 Credit-Step-Up on page 765.

•

Schedule
The cashflow structure template assigned to the instrument can be the same one used for a
fixed-rate or floating-rate bond. However, you also have to specify the rate offset or spread
offset to be applied for each coupon.
See Appendix B Schedules on page 883.

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3.2.3.2 Deal capture
3.2.3.2.1 Input data
Deals on credit step-up bonds are captured in the same way as a standard bond (see 3.1.1
Fixed-rate bond on page 215 and 3.1.2 Floating rate note on page 228).

3.2.3.2.2 Generated data
Credit events (downgrade/upgrade) saved at instrument level trigger the recalculation of the
yield-to-maturity used for accruing discount (or amortizing premium) on transactions on credit
step-up bonds.

3.2.3.3 Processing
The processing actions that are available on credit step-up bonds are the same as those on standard
bonds (see 3.1.1 Fixed-rate bond on page 215 and 3.1.2 Floating rate note on page 228), except for
the following.

3.2.3.3.1 Credit event
Adding or removing a credit event on the instrument triggers the invalidation of the future cashflows
on all the existing deals. It also triggers the regeneration of a new set of cashflows with the new rate
or spread defined in the instrument setup.

3.3 Schuldscheindarlehen
Schuldscheindarlehen is a bond security representing collateralized ownership in a German loan,
with the lending bank participating in the underlying group of banks.
Schuldscheindarlehen is a special type of Bond and differs from a plain vanilla bond in the following
manner:

•

The Schuldscheindarlehen is traded without any accrued interest settlement by the buyer.
Instead, the issuer pays at the end of the coupon period the exact portion of the coupon that the
buyer is entitled to, on a pro-rata-temporis basis (e.g. if the owner buys the Schuldschein at half
year and the coupon is due at the end of the year, the owner will only receive half of the coupon
amount).

•

The issuer also pays any previous owners within the coupon period the interest amount on a
pro-rata-temporis basis to compensate them for holding the Schuldscheindarlehen for a given
period. The coupon amount is split between the different owners during the coupon period
according to their holding period.

3.3.1 Instrument setup
Schuldschein bonds are based on an instrument type derived from the class BOND.
Instrument setup for a Schuldscheindarlehen is similar to that of a fixed-rate bond (see 3.1.1
Fixed-rate bond on page 215), except for the following:

•

Schuldschein
This feature indicates that no accrued interest is settled, but the first coupon is adjusted to the
pro-rata-temporis ownership of the coupon, and is settled on the coupon payment date directly
by the issuer.
A.2.294 Schuldschein on page 860.

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3.3.2 Deal capture
3.3.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a
Schuldscheindarlehen (both primary and secondary markets):
Information

Description

Nominal Amount

Enter either the nominal amount or face amount, and the system will compute the
other automatically.

Face Amount
Value Date

Official date when money is transferred. This defaults to the spot date of the
transaction.

Deal Price

Price paid for the bond (expressed as a percentage of the nominal amount).

Note: If you need to monitor the ownership transfer, you must record and maintain the

subsequent transactions in the secondary market. You can then use standard TRM
monitoring and reporting tools to monitor the identity of the holders, the volume of the
bonds held by each holder, and the date of purchase and sale of the bonds by the holders.

3.3.2.2 Generated data
•

Transaction
Yields are calculated from the reduced coupon.

•

Cashflows

–

The first coupon is reduced and settled on the pro-rata-temporis of the ownership from the
transaction's value date to the coupon value date.
No accrued interest is generated.

–

On the coupon payment date, the Issuer of the Schuldschein calculates the interest for each
holder of the bond according to their holding period (from the purchase value date to the
sale value date).

3.3.3 Processing
The actions that can be done throughout the life of a Schuldschein bond are the same ones as for a
fixed-rate bond (see 3.1.1.3 Processing on page 218).

3.3.4 Position monitoring
This section describes how the Schuldschein bonds are calculated and provides a numerical example
that demonstrates the calculations of a Schuldschein bond instrument.

3.3.4.1 Setup
There are two basic methods for valuation of Schuldschein bond instruments: Quoted or Theoretical.
When the Theoretical method is used, the valuation is similar to the one used to calculate a
fixed-rate bond (3.1.1.4 Position monitoring on page 221). When the Quoted method is used, the
calculations are processed as described in section 3.3.4.2 Calculations on page 251.

3.3.4.2 Calculations
This section describes the model and calculations of Schuldschein bond instruments.

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3.3.4.2.1 Valuation model
The market value of a quoted Schuldschein (Quoted valuation method) is calculated as follows:
Equation 3-3 Quoted Schuldschein bond

where
P

The price of the deal.

A

The nominal amount.

Ia

The accrued interest is calculated according to the generic formula described in 2.1.6.1 Accrued
interest calculations on page 67.
where:

D_f

•

C is the coupon

•

t is the length of the accrual period (in years), calculated as follows:

•

T is the length of the coupon period (in years, calculated with the appropriate date basis)

The Discount Factor from figure spot to figure valuation date.

3.3.4.2.2 Numerical example
This section demonstrates how the different figures are calculated for a quoted
Schuldscheindarlehen.
This example shows a Schuldscheindarlehen EUR 1,000,000.00, 5%, issued on 2008-01-01, and
due on 2012-01-01.
Setup:

•

Data

Symbol

Example

Instrument Date Basis (30E/360)

B

360

Valuation Method

Quoted

First Coupon Payment

2009-01-01

Issue Date

dt_i

2008-01-01

Maturity Date

d_m

2012-01-01

Coupon Rate

c

5%

Coupon Frequency

1

Spot Days

3

Currency

EUR

AI Method

Linear

Schedule

Fixed, Bullet Repayment

•

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Transaction data (Schuldschein issue - primary market):

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3.3 Schuldscheindarlehen

On 2008-01-01, Bank1 issues 100,000,000.00 to Bank2.
Data

Symbol

Example

Opening Date

dt_o_1

2008-01-01

Nominal Amount

A_1

100,000,000.00

Issuer

Bank1

Counterparty

Bank2

Price

P

100%

Value Date

dt_v.p

2008-01-04

Issue Date

Formula

2008-01-01

Book Value

V_b.p

100,000,000.00

Coupon 1 Amount

A_1.c1

5,000,000.00

Coupon 1 Time to Value
Date

t_v.c1

360

=A

Transaction data (transfer of ownership - secondary market):

•

On 2008-01-02, Bank2 sells its position EUR 30,000,000 and EUR 70,000,000 to two different
holders: Holder1 and Holder2 respectively.
Data

Symbol

Example

Seller

Bank2

Counterparty

Holder1

Formula

Opening Date

dt_o_2

2008-01-02

Nominal Amount

A_2

30,000,000.00

Value Date

dt_v.p

2008-01-07

Book Value

V_b.p

30,000,000.00

=A_2

Symbol

Example

Formula

and
Data

•

Seller

Bank2

Counterparty

Holder2

Opening Date

dt_o_2

2008-01-02

Nominal Amount

A_3

70,000,000.00

Value Date

dt_v.p

2008-01-07

Book Value

V_b.p

70,000,000.00

=A_3

Data

Symbol

Example

Formula

Figure Date

d_f

2008-01-02

Time to Spot

d_s

2008-01-07

Valuation Figure:

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Data

Symbol

Example

Principal

A_1.P

100,000,000.00

Accrued Interest
(Coupon 1)

69,444.44

Formula

A_1.c1 * (d_s - d_f) / B

Calculated transaction data (first coupon payment):

•

2009-01-01, the issuer Bank1 pays the coupon amount pro-rata-temporis of the ownership to
each holder.
Data

Symbol

Example

Formula

Amount (Coupon 1)

A.c1

5,000,000.00

Value Date (Coupon 1)

dt_v.c1

2009-01-01

First coupon to Bank2

1c.p

13,888.89

A_1.c * (dt_0_2 – dt_0_1)/B

First coupon to Holder1

2c.p

1,495,833.33

A_2.c * (t_v.c1 -dt_0_2)/B

First coupon to Holder2

3c.p

3,490,277.77

A_3.c * (t_v.c1 -dt_0_2)/B

3.4 Denominated bond
Bonds (and swaps) with multiple denominations are traditionally a spin off from markets where
physical bonds or certificates were used. Some markets still trade bonds or certificates, and these
are physically delivered between parties. These certificates were used for secondary trading and
made it easier for traders to break down a large issue tranche, facilitating smaller value trades on
the back of the original issue. The denominations are aggregated into a single transaction but
denomination details are maintained and recorded.
In case of physical presentation of coupons, clearing houses and/or paying agents have to pay
investors (retail) the exact coupon amounts. However, with the advent of settlement houses the
practice of physical delivery is now the exception rather than the rule. The settlement agents merely
move electronic representations of the bonds or certificates between accounts.

3.4.1 Instrument setup
Denominated bonds must be based on an instrument type derived from the class BOND or SWAP.
The setup for multiple-denomination bonds and swaps is similar to that of a fixed-rate bond (see
3.1.1 Fixed-rate bond on page 215), except that you can define the denominations that can be used
when capturing transactions at the instrument or hedging swap leg level:

•

Bond main characteristics
Information

Description

Amount Rounding

Nearest number to which the coupon amount is rounded. By default, it is set
to 2 decimals (0.01).
Note: The rounding step applies to the accrued interest when the Settlement
Switch, Round Per Unit is activated (see below).

Rounding Method

Up, Down or Nearest. The amount is rounded up, down, or to the nearest figure
as calculated using the specified Amount Rounding number.

Settlement Switches

Round Per Unit
If the switch Round per Unit is activated, Accrued Interest is based on rounding
per denomination (see 3.4.4.2 Calculations on page 256).

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•

Denominated bond
If the denomination of a bond instrument is specified at instrument level using feature
Denominated Bond, the deal can be input in units and the Nominal Amount is computed by the
system.
A.2.120 Denominated Bond on page 767.

•

Bond Denominations Setup
The valid denominations can be defined at the instrument level. Only those denominations will
be allowed at deal capture.
A.2.60 Bond Denominations Setup on page 739.

Note: For monitoring purposes, you can view the positions by Trading Unit in Treasury Monitor,
Transaction grouping. For more information, see TRM User Guide.

3.4.2 Deal capture
3.4.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a
denominated bond:

•

Transaction view:
Information

Description

New Denomination

The deal is captured by selecting the denominations defined at the instrument
level.
To select a denomination, right-click the transaction, select the action New
Denomination from the drop-down list, and then select the relevant
denomination from the list.
A new row is added to the Denomination view. You need to populate the Unit
column.
Note: To delete a denomination, simply right-click the row you want to delete
and select Delete Denomination.

•

Denomination view:
Information

Description

Trading Unit

Displays the selected denomination.

Units

The deal can be input in units and the Nominal Amount is calculated by the
system.

Leg Group

Displays the number of the (Swap) leg group where the denomination applies.

3.4.2.2 Generated data
•

Transaction
Book Value (BV) = NA * price / 100
where:
NA = Nominal Amount
price = Deal Price

•

Cashflows

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When denominations are used at deal capture, the interest (coupon) payments are calculated
separately for each denomination according to the following formula:
Ic = Units * round[Denomination * Period Length * Coupon Rate,Amount Rounding]
where:
Ic = interest (coupon) payments
Amount Rounding = number of decimals to be used when rounding amounts.

3.4.3 Processing
This section describes the actions that can be done throughout the life of a denominated bond.

3.4.3.1 Buyback (sale) and Unwinding (early expiration)
When an issue is bought back (or a long position is sold), or when a swap is unwound
(early-expired), you enter the denominations and units in the same way as when entering a new
transaction. See 3.4.2.1 Input data on page 255 for more information about capturing
denominations and units.
This information is used the same way as for new transactions, to 'close' (offset) the future interest
and redemption payments accordingly.
For a swap, a net amount (amount to be settled between the parties) is entered in the same way as
in a swap without denominations. See 11.1.2 Asset swap on page 656.

Note: For accounting purposes: The fact that buybacks or corresponding issues may have

multiple denominations has no impact on realized results. The reason for this is that
buybacks are booked at par, and the difference between par and buyback price is recorded
directly into P/L. So, there is no linking between the issue price and the buyback price per
denomination.

3.4.4 Position monitoring
There are two basic methods for valuation of denominated bond instruments: Quoted or Theoretical.

3.4.4.1 Setup
The valuation setup for denominated is the same as for usual bonds. 3.1.1.4 Position monitoring on
page 221.

3.4.4.2 Calculations
The numerical example in this section demonstrates how the different figures are calculated for a
multiple denominated bond using the Theoretical method.
This example shows a multiple denominated bond with the following data:
Setup

•

Data

Symbol

Example

Issue Date

dt_i

2008-01-01

Maturity Date

2012-01-01

Currency

EUR

Valuation Method

Theoretical

Coupon

5.6333%

AI Method

Actual/Actual Annually

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Data

•

Symbol

Example

Amount Rounding

0.01

Rounding Method

Nearest

Schedule

Fixed, Bullet Repayment

Denominations Trading Units

1000 and 5000

Transaction data:

Note: When entering a transaction the coupon amount will be different in the two denominations.

•

Data

Symbol

Example

Formula

Opening Data

dt_o

2008-01-23

Value Date

dt_v

2008-01-25

Interest Rate

r

5.6333%

First Denomination

de_1

1000

Trading Units (First
Denomination)

n_m_1

100

Nominal Amount (First
Denomination)

A_1

100 000

de_1 * n_m_1

Coupon Amount (First
Denomination)

Ic_1

5633 (rounding to 2
decimals)

r* de_1=56.333 = 56.33 * n_m_1

Second Denomination

de_2

5000

Trading Units (Second
Denomination)

n_m_2

20

Nominal Amount
(Second Denomination)

A_2

= 100 000

de_1 * n_m_1

Coupon Amount
(Second Denomination)

Ic_2

5633.4 (rounding to 2
decimals)

r* de_2=281.665 = 281.67 * n_m_2

Accrued interest may be based on rounding per denomination or not depending on whether the
settlement switch Round Per Unit (Instrument Editor - Bond page) is activated at the instrument
level.

–

If the switch Round Per Unit is not activated, the accrued interest is calculated like any other
bond (Equation 2-71 Accrued interest (generic formula) on page 67):

Data

Symbol

Example

Date Basis

B

366

Time to Accrued
Interest

Formula

2008-01-25 2008-01-01 = 24

dt_v - dt_i

Accrued Interest (First
Denomination)

Ia _1

= 369.38 (rounded to 2
decimal places)

Ic_1*(dt_v - dt_i)/B= 369.377

Accrued Interest
(Second Denomination)

Ia _2

= 369.40 (rounded to 2
decimal places)

Ic_2*( dt_v - dt_i)/B= 369.4033

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–

"If the switch Round Per Unit is activated, the accrued interest is calculated using the
denomination rounding calculation:
Equation 3-4 Denomination rounding equation

Ia = Unit × round [ Denomination × Periodlength × CouponRate, AmountRounding ]

Data

Symbol

Example

Date Basis

B

366

Time to Accrued
Interest

Formula

2008-01-25 2008-01-01 = 24

dt_v - dt_i

Accrued Interest (First
Denomination)

Ia _1

= 369 (rounded to 2
decimal places)

r* de_1*(dt_v - dt_i)/B= 3.693967 =
3.69* n_m_1

Accrued Interest
(Second Denomination)

Ia _2

= 369.40 (rounded to 2
decimal places)

r* de_2*(dt_v - dt_i)/B= 18.46984 =
18.47 * n_m_2

Note: Accrued interest at settlement, and 'clean' settlement (principal) amount (i.e. the full

settlement amount minus accrued interest and fees/taxes) is calculated directly from the
total interest (coupon) amount and total nominal amount respectively, i.e. they are not
calculated separately for each denomination.

3.5 Convertible bond
Convertible bonds are fixed rate bonds that can be converted to equity, typically to shares of the
issuer. The bond can be converted on certain dates or during certain periods. Usually the holder of
the bond can decide to convert the bond but sometimes the issuer also has the right to force the
conversion. Some convertibles are also callable.
The conversion price (and ratio) may depend on time. Usually corporate actions (splits and
dividends) also affect the conversion price.

3.5.1 Instrument setup
Convertible bond instruments must be based on an instrument type derived from the class
CONVERTIBLE-BOND. They are set up in a similar way to fixed-rate bonds (see 3.1.1 Fixed-rate
bond on page 215), except for the following characteristics.

•

Schedules
Select a suitable schedule template that includes coupons, redemptions, call events (if the bond
is callable), and conversion events.
To define the conversion events, TRM provides a pre-defined secondary template designed for
this purpose (see B.2.1.2.11 Convertible Conversion on page 902).
See Appendix B Schedules on page 883.

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•

Convertible Bond
The conversion price (or ratio) is defined using this feature. Initially one entry is needed. If the
conversion price changes due to corporate actions, a new entry must be added each time.
Information

Description

Active From

Period during which this conversion price is applicable.

Active To
Type

Defines whether the user can enter conversion price or conversion ratio.

Par Value

If the convertible bond is traded using units, enter the par value of one unit.

Conversion Price

If Type = Conversion Price, you can enter the conversion ratio.
Otherwise, it is calculated using the conversion price and par value:
Conversion Price = Par Value/Conversion Ratio

Conversion Ratio

If Type = Conversion Ratio, you can enter the conversion price.
Otherwise it is calculated using the conversion ratio and par value:
Conversion Ratio = Par Value/Conversion Price

Underlying

The instrument into which the convertible can be converted.

Comment

Any comment you want to add about the instrument.

See A.2.103 Convertible Bond on page 759.

3.5.2 Deal capture
3.5.2.1 Input data
The data required is the same as for a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215).

3.5.2.2 Generated data
•

Cashflows
The following cashflow structure is generated for a convertible bond:
Interest flows

Accrued
interest

Nominal

Book value
Spot

Opening
date

Value
date

Maturity

Maturity
date

3.5.3 Processing
This section describes the actions that can be done throughout the life of a convertible bond.

3.5.3.1 Conversion
The convertible bond is converted to the underlying instrument using the Conversion action.

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•

Setup
Conversion parameters are defined in the instrument setup.

•

Execution
Conversion can be executed in Transaction Manager. The following parameters are used:
Information

Description

Conversion Date

Date on which the conversion is done.

Amount to
Convert

Nominal amount of the convertible to convert.

Delivery Type

Usually Delivery Type = Physical Delivery.
If the underlying is not delivered, but the profit/loss is settled instead, select Delivery
Type = Cash Settlement.

Scenario

Scenario from which you want to retrieve the market price of the underlying. This
parameter is used for cash settlement only.

Price

Price of the underlying. This parameter is used for cash settlement only.

Cash to Receive

Amount of cash to receive. This parameter is used for cash settlement or settling the
residual if the number of units to be delivered is rounded.
This field can be modified.

The execution of the action generates a conversion transaction which closes the existing
convertible position and replaces it with the appropriate number of units of the underlying
instrument.

•

Cancellation
Cancellation of the action is done by canceling the conversion transaction.

3.6 Index-linked bond
Index-linked bonds are linked in some way to a standard index.
The bond’s cashflows vary according to an underlying index. For example, in inflation index-linked
bonds, the coupon and principal payments are adjusted to compensate for changes in inflation.
These payments are adjusted in relation to a Consumer Price Index (CPI) value or a Retail Prices
Index (RPI) value for a country.
A period of time usually elapses between the measurement of price levels and the publication of an
index, therefore the index value associated with a given cashflow will be the index as published for a
time in the past. This time difference is called the indexation lag.
The way in which the index-linked bonds are traded and valued varies according to market
conventions.
Index-linked bonds must be based on an instrument type derived from the class
INDEX-LINKED-BOND.

3.6.1 Instrument setup
The following information is relevant to any kind of index-linked bond.
Index-linked bonds are set up in a similar way to fixed-rate bonds (see 3.1.1 Fixed-rate bond on
page 215) or zero-coupon bonds (see 3.1.4 Zero-coupon bond on page 239), depending on whether
there are any coupon payments.
The additional values required to set up index-linked bonds are described in the following sections.

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•

Index-linked bond main characteristics

–
•

The primary feature A.2.210 Index-Linked Bond on page 818.

Trading characteristics
Each index-linked bond type has its own specific trading feature. Special risk characteristics

•

Special risk characteristics
Interest sensitivity of index-linked bonds is, by default, calculated in the same way as for similar
fixed rate bonds. However, you can capture a factor (e.g. yield beta, a number between 0 and 1)
for scaling the IR sensitivity of the instrument, which is then used as a multiplier for scaling IR
exposure and duration figures. Effective convexity is scaled by the factor squared. This factor
can be entered either as a static sensitivity scaling factor at instrument level using the
instrument feature Base IR Exposure Setup, or as Beta for the instrument in Rate Monitor
allowing time-dependent scaling factors.
For more information relating to the setup and structure of specific types of index-linked bond,
see:

•

–

3.6.4 Australian index-linked annuity bond on page 263

–

3.6.5 Australian index-linked bond on page 267

–

3.6.6 Brazilian (LFT) selic-linked security on page 270

–

3.6.7 Brazilian FX-linked NBC-E/NTN-D on page 271

–

3.6.8 Brazilian inflation-linked NTN on page 272

–

3.6.9 Canadian real return bond on page 273

–

3.6.10 French OAT€i on page 274

–

3.6.11 Greek index-linked bond on page 277

–

3.6.12 Israeli index-linked bond on page 279

–

3.6.13 Italian BTP €i on page 281

–

3.6.14 Japanese index-linked bond on page 282

–

3.6.15 Swedish index-linked bond on page 283

–

3.6.16 UK index-linked gilt on page 287

–

3.6.17 US Tips on page 292.

Schedules
Select the cashflow structure template that is appropriate for the instrument.
System templates are provided for several types of index-linked bonds; you can choose one of
these templates or any other template derived from them. Once a template is applied to the
instrument, the schedules are created and it is then possible to define their characteristics, such
as, date basis, payment convention, calendars, and so on.
See Appendix B Schedules on page 883.

•

Quoted
It is necessary to specify how the index-linked bond is quoted on the market. Each index-linked
bond type has its own specific quote handler.
See A.2.274 Quoted on page 849.

•

Valuation approach
Each index-linked bond type has its own specific valuation approach feature.

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3.6.2 Deal capture
3.6.2.1 Input data
In addition to the standard deal parameters, the information required to enter a deal on an
index-linked bond is similar to the data required for a fixed-rate bond (see 3.1.1 Fixed-rate bond on
page 215).
Information

Description

Deal Price or

If there is a yield/price convention set on the instrument, it is possible to enter either
a rate or a price and conversion is made automatically. If there is no convention set,
the deal must be entered in price.

Deal Rate
Nominal Amount
Face Amount

Enter either the nominal amount or face amount, and the system will compute the
other automatically.

Value Date

Official date when money is transferred. This defaults to the spot date of the
transaction.

Index

Value of the index (to which the instrument is index-linked) at trade date.

In addition, the following optional information can be captured:
Information

Description

Units

If the denomination of a bond instrument is specified at instrument setup, the deal
can be input in units, and the nominal and face amounts are computed by the system.

Trading Unit Size
Index Prolong Rate

(For UK index-linked bonds only)
Interest rate by which the index rate is prolonged into the future.

Index Ratio

Index ratio used to adjust the coupon and redemption flows of the bond.
Note: If this is defined at instrument level, this is used as the default in the
transaction and cannot be modified: for example, see 3.6.7 Brazilian FX-linked
NBC-E/NTN-D on page 271.

3.6.2.2 Generated data
•

Cashflows
The following cashflows are generated:

–

Principal

–

Interest (unless it is a zero-coupon index-linked bond)

–

Redemption.

3.6.3 Processing
This section describes the actions that can be done throughout the life of an index-linked bond.

3.6.3.1 Fixing
The major process for an index-linked bond is the fixing of the coupon and the redemption flows.
These need to be adjusted to account for changes in the index.

•

Setup
Depending on the instrument setup (schedules) the fixing can be done in advance or in arrears.
In both cases there can be an offset of n days (before the beginning or end of the coupon
period).
The fixing parameters that define how the fixing rate is calculated are defined in the schedule.

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•

Execution
When fixing is executed, the rate is retrieved for the specified fixing rate and period according to
the designated fixing scenario. The fixing scenario is configured at the system level, see TRM
System Admin Guide. The fixing subscenario is specified at the cashflow level.
The expression value gives the current value of the expression and is used to calculate the index
value.
The following information is stored on the fixed cashflow:
The
The
The
The

fixing date
fixing quote
expression and expression value
amount of the coupon or redemption flow.

The fixing process can be performed in two ways in TRM: the process is exactly the same in each
case: the coupon is fixed at both instrument and transaction level.
The methods of fixing are as follows:

–

Directly on the cashflow (in Instrument Editor’s Cashflow page) using the Fix Price action: the
fixing affects all deals on this instrument.

–

Using an activity (Fixing Bond Cashflow): all instruments and their deals which need to be
fixed for a particular date are affected.

Note: The bond issue must be fixed at instrument level in order for the accrued interest flow to

be generated (for transactions captured between coupon fixing date and fixing value date).

•

Cancellation
It is possible to cancel the cashflow fixing either manually, using the Undo Fixing action in
Instrument Editor; or automatically, using the Fixing Bond Cashflow - Undo activity.

3.6.4 Australian index-linked annuity bond
The following sections describe the characteristics that are specific to Australian index-linked
annuity bonds.

3.6.4.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following:

•

Trading characteristics - issue index parameters
The Australian CPI is published quarterly and is applied to settlement calculations and valuations
starting from the publication date. The index is set up similarly to other indexes.
Information
Index

Description
Select the Instrument ID of the underlying index you previously defined.
See 7.1 Index types on page 425.

Issue Index

Enter the value of the underlying index at issue. This value is used to adjust the
coupon and redemption flows of the bond.

See A.2.32 Australian IAB on page 725 or A.2.34 Australian IAB (Round to 3) on page 725.

•

Bond characteristics
Information

Description

Currency

AUD

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•

Information

Description

AI Method

Australian Index Linked (IAB), or for three decimal places rounding, Australian Index Linked
(IAB) (3 dec).

Settlement
Switches

Dirty Price.

Coupon Rate

Coupon rate of the bond.

Schedule parameters
Select the cashflow structure template BOND-AU-IAB (Australian Indexed Annuity Bond). See
B.2.1.1.4 Australian Indexed Annuity Bond on page 890.
In the Interest Adjustment schedule, set the parameter Factor equal to the rounded value of the
annuity payment.

Note: For rounding to three decimal places, change the expression in the Interest Adjustment
schedule to: round((ixau/divider)*factor,0.001)*100 - 100 * factor

Set the required fixing characteristics as follows:
Information

Description

Factor

Enter the annuity payment percentage.
Note: The Fixing Rate and Divider fields default to the values you selected in the
Issue Index page.

Method

Select 4th Wednesday (M) as the index is published (and index adjustment
cashflows fixed) on the 4th Wednesday of the publishing month.

Frequency

Enter 3.

First Date

Enter the first publishing (fixing) date applicable to this instrument. The
subsequent publishing dates are calculated from this date onwards using the
monthly frequency specified in the Frequency field.

After you have generated the cashflows, remove the default value from the field Amount
Rounding in the Schedule page and leave the field Amount Rounding empty for all Interest
Adjustment cashflows in the Cashflow page.

•

•

Trading yield parameters
Information

Description

Yield Convention

Australian Government Index Annuity - GOVT-AU-IX-ANNUITY

Quoted
Information

Description

Price Type

Yield (w/o rounding)

Quote Handling

Depending on how you want to round the adjusted annuity, select one of the
following:

Currency

264

•

Index-Linked Annuity Bond (Australian): six decimal places rounding

•

Index-Linked Annuity Bond (Australian 3 Digits Rounding): three decimal places rounding

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•

•

Result parameters
Information

Description

AI Method

Australian Index Linked (IAB), or for three decimal places rounding, Australian Index Linked
(IAB) (3 dec).

Valuation approach
Australian Indexed Annuity Bonds can be valuated either using a direct (yield) quote, or taken
from the yield curve.

–

For a direct quote, see A.2.33 Australian IAB Valuation on page 725), or if adjusted annuities
are to be rounded to 3 decimal places, see A.2.35 Australian IAB Valuation (Round to 3) on
page 726.

–

For a valuation taken from the yield curve (loans only), see A.2.36 Australian IAB Par Curve
Valuation on page 726, or if adjusted annuities are to be rounded to 3 decimal places, see
A.2.37 Australian IAB Par Curve Valuation (Round to 3) on page 727.

Note: To use a yield curve, you must first set one up in the IR Quote and Yield Curve Editor. For
general information about setting up yield curves, see TRM User Guide.

3.6.4.2 Deal capture
3.6.4.2.1 Input data
In addition to standard deal parameters, the information required to enter a deal on an australian
index-linked bond is similar to usual index-linked bonds (see 3.6 Index-linked bond on page 260).
Information

Description

Face Amount

Enter the face amount. The Nominal Amount is automatically calculated by the
system.

Nominal Amount

Shows the remaining amount taking into account the annuity payments.

In addition, the following optional information can be captured:
Information

Description

Index

The system automatically fetches the latest available CPI value for the settlement
date. You may change the index value.
Note: In Rate Monitor, the index value of a given quarter is associated with the
first day of the quarter (Jan. 1, Apr. 1, Jul. 1, Oct. 1). The publication date is
given in the field Period From.

Deal Rate

Enter the trade yield.

3.6.4.2.2 Generated data
•

Transaction
The formula used to calculate the price depends on whether the CPI value that will determine
the next coupon is known or not.

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–

If the value is not known, we use the inflation rate (q) for coupon estimation:
Equation 3-5 Coupon estimation: CPI value unknown

–

If the value is known, the formula is:
Equation 3-6 Coupon estimation: CPI value known

where
Br – 1

Previous annuity payment

B0

Original unadjusted annuity payment

h

Rounding precision, 3 or 6, depending on the issue

q

Quarterly inflation factor

Ii

CPI for quarter I: where I = 0 corresponds to the quarter
before the issue date of the bond, and I = 1 corresponds to
the latest quarter for which the CPI has been issued on the
settlement date

y

Trading yield

v

•

n

Number of full quarters from the next annuity payment to
maturity

f

Number of days from settlement to the next annuity
payment date

d

Number of days in the full quarter ending on the next
annuity payment date

Z

1 if there is an annuity payment to the purchaser at the
next annuity payment date, otherwise 0.

Cashflows
The following cashflows are generated:

266

–

Principal

–

Interest

–

Interest Adjustment

–

Amortization

–

Delivery.

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•

Fixing
In the fixing of Australian index-linked annuity bonds, rounding is carried out at the total annuity
payment level. To make sure that the total of the fixed interest and amortization payments are
correct, one of the cashflows takes into account the rounding of the other.

Note: In Rate Monitor, the index value of a given quarter is associated with the first day of the

quarter (Jan. 1, Apr. 1, Jul. 1, Oct. 1). The publication date is given in the field Period From.

3.6.4.3 Processing
3.6.4.3.1 Fixing
The fixing of the inflation adjustment (Interest Adjustment cashflow) is carried out at the instrument
level in Instrument Editor - Cashflow page.

•

Execution
Information

Description

Fixing Quote

Select action Fix Price. The appropriate CPI value is displayed and the amount
of the inflation adjustment is automatically calculated. You can also first set
the relevant CPI value, and then select the action Fix Price.

Update the cashflows (click Update) and save the instrument.

3.6.5 Australian index-linked bond
The following sections describe the characteristics that are specific to Australian index-linked bonds.

3.6.5.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following:

•

Trading characteristics
See A.2.29 Australian CIB on page 724.

–

Issue Index parameters
Information

Description

Index

Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

(Not used for Australian index-linked bonds)
However, a value must be entered as 100.00 for calculation purposes only.

•

Bond characteristics
Information

Description

Currency

AUD

Settlement
parameters

Dirty Price.

Coupon Rate

Coupon rate of the bond.

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Schedule parameters

•

Select the cashflow structure template BOND-AU-CIB (Australian Capital Indexed Bond). See
B.2.1.1.3 Australian Capital Indexed Bond on page 890.
Trading yield

•

Information

Description

Yield Convention

Australian Government Index - GOVT-AU-IX

Quoted

•

Information

Description

Price Type

Yield (w/o rounding)

Quote Handling

Index-Linked Bond (Australian)

Currency

AUD

Valuation approach

•

See A.2.38 Australian Index-Linked Bond Valuation on page 727.

3.6.5.2 Position monitoring
In this section, numerical examples demonstrate how the different figures are calculated for
Australian Treasury index-linked bonds.
If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.
This example shows an Australian Treasury index-linked bond, with the following deal data:
Setup data
First interest payment date

1994-08-20 (Q3 / 1994)

First reference quarter

Q4 / 1993

Maturity date

dt_m

2015-08-20

Interest

r

4.00%

Face amount

1,000.00

Transaction data
Settlement date

dt_s

2007-01-23

Next coupon date

dt_c

2007-02-20 (Q1 / 2007)

Yield

y

2.76%

Current quarter length

dp

92

Index factor

p

1.25

Adjustment factor

K_t

141.270 (Q3 / 2006)

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Other important deal data is calculated by the system as follows:
•

Quarters left
n = FLOOR(YEARFRAC(dt_s, st_m, 0) * 4, 1)
= 34

•

Reference index
v = ROUND (1 / (1 + y / 4), 9)
= 99.31%

•

Days to next coupon
dc = dt_c - dt_s
28 = 2007/02/20 - 2007/01/23

•

Time to next coupon
t_n = dc / dp
0.3043478 = 28 / 92

•

Unadjusted dirty price
Pdu =ROUND (POWER (v, t_n) * (ROUND (r / 4,9) * (1 + ROUND ((1 - POWER (v., n)) / (y / 4), 9)) +
POWER (v, n)) * POWER (1 + p / 100, -t_n.), 9)
= 109.71994%

•

Adjusted dirty price
P_d = ROUND (K_t. * Pdu / 100,5)
= 155.001%

•

Accrued interest
I_a = ROUND ((r / 4) * K_t / 100 * (dp - dc) / dp, 5)
= 0.98300000000%

•

Clean price
P_c = P_d - I_a
= 154.018%

3.6.5.2.1 Settlement figures
Settlement flows for the transaction are calculated as follows:
•

Nominal amount
A.s = 10,000,000.00

•

Clean price
P_c.s = A * P_c
15,401,800.00 = 10,000,000.00 * 1.54018

•

Accrued interest
I_a.s = A * I_a
98,300.00

•

Total
= 15,500,100.00

3.6.5.2.2 Fixing figures
Fixing flows for the transaction are calculated using the following data:
Fixing data
Coupon date

2007-05-20

Fixing date

2007-02-20

Reference quarter

141.82 (Q4 / 2006)

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•

Index adjustment factor
cf = 141.82 / 100
= 1.41820

•

Nominal coupon
cn = r / 4
0.0100000 = 0.04 /4

•

Adjusted amount
Ap = A * cn *cf
141,820.00 = 10,000,000 * 0.010000 * 1.41820

3.6.5.2.3 Valuation figures
Unless otherwise stated, the figure date used in the calculations is 2007-01-20. On this date, the
market data is as follows:
Market data on 2007-01-20
Market quote (dirty, adjusted)

p_q

155.00

Figure D

D_s

0.99960191

•

Market value
= p_q / 100 * A * D_s
15,493,829.60 = 155.00 / 100 * 10,000,000 * 0.99960191

3.6.6 Brazilian (LFT) selic-linked security
Brazilian LFT (Letra Financeira do Tesouro) instruments are zero-coupon bonds linked to the O/N
SELIC interest rate. The maturities can be over two years.
These instruments are traded and quoted in 1000’s (Date Basis = BRL/252) and have a unique
security ID (ISIN number), issue and maturity date.

3.6.6.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics
See A.2.52 Bond - Brazilian LFT on page 737.

•

•

Bond characteristics
Information

Description

Currency

BRL

Schedule parameters
The Brazilian LFT Bond system-defined primary template is provided for this type of index-linked
bond, where:

–

Fixing parameters
Need Fixing = Yes
Fixing Date Method = In Arrears
Expression = iix/trading unit
where:
iix = instrument-specific index entered in Rate Monitor together with Bid and Ask (select the
Rate Monitor figure Index Value).

See B.2.1.1.7 Brazilian LFT Bond on page 891.

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•

•

•

Trading yield
Information

Description

Yield Convention

Brazilian LFT - BOND-BR-LFT

Quoted
Information

Description

Price Type

Yield

Quote Handling

Index-Link Bond (LFT)

Currency

BRL

Valuation approach
See A.2.53 Bond - Brazilian LFT Valuation on page 737.

3.6.7 Brazilian FX-linked NBC-E/NTN-D
NBC-E/NTN-D instruments are fixed-rate bonds linked to the PTAX-index (FX rate). The maturities
are 2Y, 3Y, and 5Y. The fixed rate is 12% pa.
These instruments are traded and quoted in 1000’s and have a unique security ID (ISIN number),
issue date, and maturity date.
The coupons and redemption cashflows are adjusted by the index ratio, and the fixing dates are the
coupon/redemption value dates.

3.6.7.1 Instrument setup
Instrument setup for these index-linked bonds is the same as for other index-linked bonds (see 3.6
Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics
See A.2.54 Bond - Brazilian FX-Linked NBC on page 737.

–

Issue index parameters
Information

Description

Index

Instrument ID of the underlying index: PTAX-index (FX rate).
See 7.1 Index types on page 425.

Issue Index

•

•

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

Bond characteristics
Information

Description

Currency

BRL

Settlement
parameters

Dirty Price

Coupon Rate

Coupon rate is 12% and the coupon is paid semi-annually.

Schedule
The Brazilian FX-Linked Bond (NBC) system-defined primary template is provided for these
index-linked bonds, where:

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–

Fixing parameters
Need Fixing = Yes
Fixing Date Method = In Arrears
Expression = ixlag_d/divider*price
where:
ixlag_d = lagged index value of one day
divider = index value on the transaction’s opening date inserted on deal capture
price = quoted bond price

See B.2.1.1.5 Brazilian FX-Linked Bond (NBC) on page 890.

•

•

•

Trading yield
Information

Description

Yield Convention

Brazilian NBC - BOND-BR-NBC

Quoted
Information

Description

Price Type

Yield

Quote Handling

Index-Link Bond (NBC)

Currency

BRL

Valuation approach
See A.2.55 Bond - Brazilian FX-Linked NBC Valuation on page 737.

3.6.8 Brazilian inflation-linked NTN
Brazilian NTN-B/NTN-C (Nota do Tesouro Nacional) instruments are inflation-linked securities, setup
as fixed-rate bonds, linked to the IGPM-index (NTN-C) or the ICPA-index (NTN-B). The maturities
are 2Y, 3Y, and 5Y. The fixed rate is 12% p.a. or 6% p.a.
These instruments are traded and quoted in 1000’s and have a unique security ID (ISIN number),
issue date, and maturity date.
The coupons and redemption cashflow are adjusted by the index ratio and the fixing dates are the
coupon/redemption value dates.

3.6.8.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics
See A.2.56 Bond - Brazilian Inflation-Linked NTN on page 738.

–

Issue Index parameters
Information

Description

Index

Instrument ID of the underlying index: IGPM-index (NTN-C) or the ICPA-index
(NTN-B).
See 7.1 Index types on page 425.

Issue Index

272

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

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3 Debt instruments
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•

Schedule
Information

Description

Fixing parameters

•

•

•

•

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = ix/divider*price

Bond characteristics
Information

Description

Currency

BRL

Settlement
parameters

Dirty Price

Coupon Rate

Coupon rate is 6% or 12% and the coupon is paid semi-annually.

Trading yield
Information

Description

Yield Convention

Brazilian NTN - BOND-BR-NTN

Quoted
Information

Description

Price Type

Yield

Quote Handling

Bond

Currency

BRL

Valuation approach
See A.2.57 Bond - Brazilian Inflation-Linked NTN Valuation on page 738.

3.6.9 Canadian real return bond
The following sections describe the characteristics that are specific to Canadian real return bonds.

3.6.9.1 Instrument setup
Instrument setup for Canadian real return bonds is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics

–

Issue Index parameters
Information
Index

Description
Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

See A.2.58 Bond - Canadian RRB on page 738.

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•

Bond characteristics
Information

Description

AI Method

Canadian
See Canadian on page 73.

Currency

CAD

Coupon Rate

Coupon rate of the bond.

See A.2.210 Index-Linked Bond on page 818.

•

Schedule parameters
The Canadian real return bonds system-defined primary template is provided for these
index-linked bonds, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = ixratio*price

See B.2.1.1.8 Canadian Real Return Bond on page 891.

•

Trading yield
Information

Description

Yield Convention

Canadian Government
See 2.1.4.2.18 GOVT-CA (financial/instrument/canadian@price) on page 51.

•

•

Quoted
Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (Canadian)

Currency

CAD

Valuation approach
See A.2.59 Bond - Canadian Index-Linked Bond Valuation on page 738.

3.6.10 French OAT€i
The following sections describe the characteristics that are specific to French OAT€i bonds.

3.6.10.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics
See A.2.65 Bond - French OAT€i on page 741.

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–

Issue Index parameters
Information

Description

Index

Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

•

•

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

Bond characteristics
Information

Description

Currency

EUR

Coupon Rate

Coupon rate of the bond.

Schedule parameters

–

The French Index-Linked Bond (OAT) system-defined primary template is provided for this
type of index-linked bond, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = max (ixratio, 1) * price

See B.2.1.1.24 French Index-Linked Bond (OAT) on page 895.

•

•

•

Trading yield
Information

Description

Yield Convention

French Government OAT - GOVT-FR-OAT

Quoted
Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (French)

Currency

EUR

Valuation approach
See A.2.66 Bond - French Index-Linked Bond Valuation on page 742.

3.6.10.2 Position monitoring
In this section, numerical examples demonstrate how the different figures are calculated for French
OAT€i linked bonds.
If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.

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This example shows a French OAT€i linked bond, with the following deal data:
Setup data
Index at issue

v_0

92.98393

Maturity date

dt_m

2012-07-25

Interest

c_m

3.00%

Rounding

decimals

5

Yield rounding

y_round

6

Settlement date

dt_s

2007-06-20

Next coupon date

dt_c

2007-07-25

Yield

y

2.40% (= round(2.396461364098%, 2))

Last index (2007-03)

v_1

103.39

Current index (2007-04)

v_2

104.05

Day of month

d_1

20

Transaction data

Other important deal data is calculated by the system as follows:
•

Coupons left
n_c = FLOOR (YEARFRAC (dt_s, dt_m, 4), 1) +1
=6

•

Reference index
v = ROUND (v_1 + (d_1 - 1) / DAY (EOMONTH (dt_s, 0)) * (v_2 - v_1), decimals)
= 103.80800

•

Dirty price
p_d_n = (POWER (1 + y, -n_c. + 1) + c_m * ((1 + y) * (1 - POWER (1 + y, -n_c))) / (y)) *
POWER (1 + y, -d_c / 365)
= 105.57230%

•

Accrued interest unadjusted
I_a_n = c_m * (365 - d_c) / 365
2.7123288% = 0.03 * (365 - 35) / 365

•

Accrued interest
I_a = g_i * I_a_n
3.0280710% = 1.1164100000 * 0.027123288

•

Clean price unadjusted
p_c_n = p_d_n - ROUND (I_a_n, y_round)
= 102.8600%

•

Clean price
p_c = p_c_n * g_i
114.83393259% = 1.028600 * 1.1164100000

•

Days to next coupon
dcv = DAYS360 (dt_s, dt_c)
= 35

•

Index adjustment factor
g_i = ROUND (v / v_0, decimals)
= 1.1164100000

3.6.10.2.1 Settlement figures
Settlement flows for the transaction are calculated as follows:
•

276

Nominal amount
A = 1,000,000.00

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3 Debt instruments
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•

Clean price
p_c.s = A * p_c
1,148,339.33 = 1,000,000.00 * 1.1483393259

•

Accrued interest
I_a.s = A * I_a
30,280.71 = 1,000,000.00 * 0.03280710

•

Total
= 1,178,620.04

3.6.10.2.2 Fixing figures
Fixing flows for the transaction are calculated using the following data:
Fixing data
Fixing date
Index on 2007-04-25

2007-07-25
vf

•

Index adjustment factor
gf = ROUND (vf / v_0, decimals)
1.12923 = 105 / 92.98393

•

Nominal coupon
cn = ROUND(c_m * gf, 7)
0.033876900 = ROUND (0.03 * 1.12923, 7)

•

Adjusted amount
Ap = A * cn
33,876.00 = 1,000,000 * 0.033876900

105

3.6.10.2.3 Valuation figures
Unless otherwise stated, the figure date used in the calculations is 2007-06-18. On this date, the
market data is as follows:
Market data on 2007-06-18
Figure date

2007-06-18

Figure spot date

d_s.f

2007-06-20

Market quote (clean unadjusted)

p_q

102.86%

Index adjustment factor

gv

1.11641

Spot discount factor

Ds

0.9998027

Days to next coupon

dcv

35

•

Accrued interest
ai.f = A * c_m * (365 - dcv) / 365 * gv * Ds
30,274.73 = 1,000,000 * 0.03 * (365 / 35) / 365 * 1.11641 * 0.9998027

•

Clean price
= A * p_q * gv * Ds
1,148,112.72 = 1,000,000 * 1.0286 * 1.11641 * 0.9998027

3.6.11 Greek index-linked bond
The following sections describe the characteristics that are specific to Greek index-linked bonds.

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3.6.11.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics
See A.2.71 Bond - Greek Index-Linked Bond on page 744.

–

Issue Index parameters
Information

Description

Index

Instrument ID of the underlying index.
See 7.2.1 Simple Index on page 426.

Issue Index

•

•

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

Bond characteristics
Information

Description

Currency

EUR

AI Method

Greek (3 decimals). See Greek (3 decimals) on page 74.

Coupon Rate

Coupon rate of the bond.

Schedule parameters

–

The Greek Index-Linked Bond system-defined primary template is provided for this type of
index-linked bond, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Expression = ixratio*price

See B.2.1.1.25 Greek Index-Linked Bond on page 895.

•

•

•

Trading yield
Information

Description

Yield Convention

GOVT-EUROZONE

Quoted
Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (Greek)

Currency

EUR

Valuation approach
See A.2.72 Bond - Greek Index-linked Bond Valuation on page 744.

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3.6.12 Israeli index-linked bond
Israeli index-linked bond instruments must be based on an instrument type derived from the class
INDEX-LINKED-BOND. The following sections describe the characteristics that are specific to Israeli
index-linked bonds.

3.6.12.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics - Issue Index parameters
Information
Index

Description
Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

Value of the underlying index at issue. This value is used to adjust the coupon and
redemption flows of the bond.

See A.2.73 Bond - Israeli Index-Linked Bond on page 744.

•

Bond characteristics
Information

Description

Currency

ILS

AI Method

Israeli (Linear, 5 decimals)
See Israeli (Linear, 5 decimals) on page 76.

•

Settlement
Switches

Dirty Price.

Coupon Rate

Coupon rate of the bond.

Note: According to the market convention, the deal price of Israeli index-linked bonds
is treated not just as Dirty Price but as an inflation-adjusted dirty price. At deal
entry, this means that you should capture the dirty price as well as the index
ratio. The settlement amount is equal to the deal price times the nominal
amount.

Schedule parameters
The Israeli Index-Linked Bond system-defined primary template (BOND-IL-IX) is provided for
this type of index-linked bond, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = round(ixratio*price,0.0000001)

See B.2.1.1.28 Israeli Index-Linked Bond on page 895.

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For Israeli GALIL Index-Linked Bond, the system-defined primary template (BOND-IL-IX-GALIL)
is provided for this type of index-linked bond, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression =

round((max(ixratio,1)*((1+price/100)^(years)-1)),0.0000001)*nom
inal
•

Fixing rate Type = Amount

See B.2.1.1.29 Israeli Index-Linked Bond Galil on page 896.

•

Trading yield
Information

Description

Yield Convention

*U.S.STREET-ACTACT-SEMIANNUAL
See 2.1.4.2.12 *U.S.STREET-ACTACT-ANNUAL
(financial/instrument/us-street@price-1) on page 45.

•

•

Quoted
Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (Israeli)

Currency

ILS

Optionally, time-dependent index value
Complete the following parameters:
Information

Description

Date

Date when rebasing is done.

Type

Choices are: Value or Factor
•

Value - When you select this option, the New / Old Value fields are available for
editing, the Factor field is no longer available.

•

Factor - When you select this option, only the Factor field is available for editing,
the New / Old Value fields are no longer available.

Old Value

Index value before the rebase. Defaults to the same value as specified in the Factor
field when type Factor is selected.

New Value

Index Value after the rebase. Defaults to 1 when type Factor is selected.

Factor

Rebase factor. When type Value is selected, this field displays Old Value / New
Value, rounded to 9 decimals (i.e. trailing zeros are not displayed).

See A.2.214 Index Rebase (Index-Linked Bond) on page 820.

•

Valuation approach
See A.2.74 Bond - Israeli Index-Linked Bond Valuation on page 745.

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3.6.12.2 Deal capture
In addition to standard deal parameters, the information required to enter a deal on an Israeli
index-linked bond is similar to usual index-linked bonds (see 3.6 Index-linked bond on page 260).

3.6.12.2.1 Input data
Index at Issue and Index Ratio columns (take into account all the rebases that took place from the
bond's issue date until (and including) the transaction's opening date).
Information

Description

Index at Issue

The Index at Issue column is calculated according to the issue index value defined at
instrument level (Issue Index page), divided by each published rebase factor
between the bond's issue date and the transaction's opening date:
Equation 3-7 Israel index-linked bonds: Index at Issue calculations

Where
-

V0 is the base index of the bond on the issue day as defined in the Issue

Index page of the index-linked bond.
-

rbti is the rebase factor at time ti between the issue date and the

opening date of the transaction, as defined in the Rebase page of the
index.
Index Ratio

The Index Ratio takes into account the rebased index at issue and and the latest
index value. For Israeli index-linked bond the Index Ratio is rounded to 7
decimals. For information about this calculation, see D.4.3.4.3 Calculation for
Israeli index-linked bonds on page 925.

3.6.12.3 Processing
The processing of an Israeli index-linked bond is the same as for a standard index-linked bond, see
3.6 Index-linked bond on page 260.

3.6.13 Italian BTP €i
The following sections describe the characteristics that are specific to Italian BTP€i bonds.

3.6.13.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics
See A.2.75 Bond - Italian BTP€i on page 745.

–

Issue Index parameters
Information

Description

Index

Instrument ID of the underlying index.
See 7.2.1 Simple Index on page 426.

Issue Index

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

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•

•

Bond characteristics
Information

Description

Currency

EUR

AI Method

Italian (5 decimals). See Italian (5 decimals) on page 77.

Coupon Rate

Coupon rate of the bond.

Schedule parameters

–

The Italian Index-Linked Bond (BTP) system-defined primary template is provided for this
type of index-linked bond, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Expression = max (ixratio, 1) * price

See B.2.1.1.30 Italian Index-Linked Bond (BTP) on page 896.

•

•

•

Trading yield
Information

Description

Yield Convention

Italian Government - GOVT-IT

Quoted
Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (Italian)

Currency

EUR

Valuation approach
See A.2.76 Bond - Italian Index-Linked Bond Valuation on page 745.

3.6.14 Japanese index-linked bond
The following sections describe the characteristics that are specific to Japanese index-linked bonds.

3.6.14.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics

–

Issue Index parameters
Information
Index

Description
Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

See A.2.225 Japanese JGBi on page 825.

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•

Bond characteristics
Information

Description

Currency

JPY

AI Method

Japanese Yield (7 decimals)
See Japanese Yield (7 decimals) on page 77.

Coupon Rate

•

Coupon rate of the bond.

Schedule parameters
The Japanese Index-Linked Bond system-defined primary template is provided for this type of
index-linked bond, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = ixratio*price

See B.2.1.1.31 Japanese Index-Linked Bond on page 896.

•

Trading yield
Information

Description

Yield Convention

Japanese Government
See 2.1.4.2.29 GOVT-JP (financial/instrument/simple-yield@price) on page 59.

•

•

Quoted
Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (Japanese)

Currency

JPY

Valuation approach
See A.2.226 Japanese Index-Linked Bond Valuation on page 826.

3.6.15 Swedish index-linked bond
The following sections describe the characteristics that are specific to Swedish index-linked bonds.

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3.6.15.1 Instrument setup
Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see
3.6 Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics

–

Issue Index parameters
Information

Description

Index

Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

See A.2.317 Swedish Index-Linked Treasury Bond on page 869.

•

•

Bond characteristics
Information

Description

Currency

SEK

Coupon Rate

Coupon rate of the bond (unless it is a zero-coupon bond).

Schedule parameters

–

The Swedish Index-Linked Bond system-defined primary template is provided for this type of
index-linked bond, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = round (ixse / divider * price, 0.0000001)
ixse = expression specific to Swedish index-linked bonds, see D.4.3.6
Swedish CPI market reference - ixse on page 926.

See B.2.1.1.38 Swedish Index-Linked Bond on page 898.

–

For zero-coupon bonds, the Swedish Index-Linked Zero-Coupon Bond system-defined
primary template is provided, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = max (ixse / divider, 1) * price
ixse = expression specific to Swedish index-linked bonds.

See B.2.1.1.39 Swedish Index-Linked ZC Bond on page 898.

•

284

Trading yield
Information

Description

Yield Convention

Swedish Government - GOVT-SE

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Quoted

•

Information

Description

Price Type

Yield

Quote Handling

Index-Linked Bond (Swedish)

Currency

SEK

Valuation approach

•

See A.2.318 Swedish Index-Linked Bond Valuation on page 870.

3.6.15.2 Position monitoring
In this section, numerical examples demonstrate how the different figures are calculated for
Swedish index-linked bonds.
If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.
This example shows a Swedish index-linked bond, with the following deal data:
Setup data
Index at issue

v_0

245.1

Maturity date

dt_m

2008-12-01

Interest

c_m

4.00%

Settlement date

dt_s

2003-04-30

Next coupon date

dt_c

2003-12-01

Yield

y

2.30%

Nominal amount

A

1,000,000.00

Last index (2003-01-01)

v_1

276.0

Current index (2003-02-01)

v_2

278.4

Day of month

d_1

30

Transaction data

Other important deal data is calculated by the system as follows:
•

Coupons left
n_c = FLOOR (YEARFRAC (dt_s, dt_m, 4), 1) + 1
=6

•

Dirty price
p_d = (POWER (1 + y, -n_c + 1) + c_m * ((1 + y) * (1 - POWER (1 + y, -n_c))) / (y)) *

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POWER (1 + y, -d_c / 360) * g_i
= 125.43308%
•

Accrued interest
I_a = g_i * (360 - d_c) / 360 * c_m
= 0.018799437871

•

Clean price
p_c = p_d - I_a
= 123.55313963%

•

Reference index
v = v_1 + (MIN(d_1, 30) -1) / 30 *(v_2 - v_1)
= 278.32

•

Days to next coupon
d_c = DAYS360 (dt_s, dt_c)
= 211

•

Index adjustment factor
g_i = v / v_0
= 1.1355365157

3.6.15.2.1 Settlement figures
Settlement flows for the transaction are calculated as follows:
•

Principal flow
P = A * P_c
1,235,531.40 = 1,000,000 * 1.2355313963

•

Accrued interest flow
AI = A * I_a
18,799.44 = 1,000,000 * 0.018799437871

3.6.15.2.2 Fixing figures
Fixing flows for the transaction are calculated using the following data:
Fixing data
Fixing date
Index on 2002-09-01

2002-12-01
vf

•

Index adjustment factor
gf = vf / v_0
1.11995104 = 274.50 / 245.1

•

Nominal coupon
cn = ROUND(c_m * gf, 7)
0.0447980 = ROUND (0.04 * 1.11995104, 7)

•

Adjusted amount
Ap = A * cn
44,798.00 = 1,000,000 * 0.0447980

274.50

3.6.15.2.3 Valuation figures
Unless otherwise stated, the figure date used in the calculations is 2003-04-28. On this date, the
market data is as follows:
Market data on 2003-04-28
Figure date

2003-04-28

Figure spot date

d_s.f

2003-04-30

Market quote (real yield)

y_f

2.30%

Index adjustment factor

g_f

1.135536516

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Market data on 2003-04-28
Spot discount factor

D_s.f

1.00

•

Days to next coupon
d_c.f = DAYS360 (d_s.f, dt_c)
= 211.00

•

Dirty price
d_p.f = (POWER(1 + y_f, -n_c. + 1) + c_m * ((1 + y_f) * (1 - POWER (1 + y_f, -n_c))) / (y_f.)) *
POWER (1 + y_f,- d_c.f / 360) * g_f
1.254330834

•

Accrued interest
ai.f = g_f * (360 - d_c.f) / 360 * c_m
= 0.018799438

•

Clean price
= p_d.f - ai.f
= 1.235531396

•

Market value
= A * ai.f * D_s.f + A * p_c.f * D_s.f
= 1,254,330.83

3.6.16 UK index-linked gilt
The following sections describe the characteristics that are specific to UK (3 month and 8 month)
index-linked gilts.

3.6.16.1 Instrument setup
Instrument setup for UK index-linked gilts is the same as for index-linked bonds (see 3.6
Index-linked bond on page 260) except for the following parameters:

•

Trading characteristics
See A.2.329 UK ILG (3M) on page 876 and A.2.330 UK ILG (8M) on page 876.

–

Issue Index parameters
Information

Description

Index

Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

•

•

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

Bond characteristics
Information

Description

Currency

GBP

Coupon Rate

Coupon rate of the bond.

Schedule parameters
Select the appropriate cashflow structure template, BOND-UK-IG-3M or BOND-UK-IG-8M.
See B.2.1.1.42 United Kingdom Index-Linked Gilt (3M) on page 898 or B.2.1.1.43 United
Kingdom Index-Linked Gilt (8M) on page 899.

Note: These templates correspond to rounding down to 4 decimal places. Some issues (both 8M
and 3M) use different rounding conventions. To round down to 2 decimal places, replace

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the function round ( , 0.000001, -1) by round ( ,0.0001, -1). To round to nearest 6
decimal places, use round ( , 0.00000001).
Trading yield

•

Information

Description

Yield Convention

UK Government - GOVT-UK

Quoted

•

Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (UK 3M) or Index-Linked Bond (UK 8M)

Currency

GBP

Valuation approach

•

See A.2.331 UK Index-Linked Bond (3M) Valuation on page 876 and A.2.332 UK Index-Linked
Bond (8M) Valuation on page 877.

3.6.16.2 Position monitoring
In the following sections, numerical examples demonstrate how the different figures are calculated
for UK 3 month and 8 month index-linked gilts.
If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.

3.6.16.2.1 Calculations - UK 3 month
This example shows a UK 3 month index-linked gilt, with the following deal data:
Setup

•

Data

Symbol

Example

Index at issue

v_0

193.725

Maturity date

dt_m

2012-11-22

Interest

c_m

1.25%

Rounding

decimals

5

Yield rounding

y_round

6

Dividend rounding

decimals_div

6

Data

Symbol

Example

Settlement date

dt_s

2007-06-18

Previous coupon date

dt_p

2007-05-22

Next coupon date

dt_c

2007-11-22

Coupons left

n_c

21

Yield

y

2.19%

Transaction data

•

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Data

Symbol

Example

Last index (2007-03)

v_1

204.40

Current index (2007-04)

v_2

205.40

Day of month

d_1

18

Other important deal data is calculated by the system as follows:
•

Dirty price
d_p = (POWER (1 + y / 2, -n_c + 1) + c_m / 2 * ((1 + y / 2) * (1 - POWER (1 + y / 2, -n_c))) / (y / 2)) *
POWER (1 + y / 2, -d_c / 183)
= 91.37171%

•

Accrued interest unadjusted
I_u = c_m / 2 * (p_c - d_c) / p_c = 0.0917120%

•

Accrued interest
I_ a = g_i * I_u = 0.0970340%

•

Clean price unadjusted
p_cu = d_p - I_u = 91.2800%

•

Clean price
Pca =p_cu * g_i = 96.57697839%

•

Reference index
v = ROUND (v_1 + (d_1 - 1) / DAY(EOMONTH (dt_s, 0)) * (v_2 - v_1), decimals) = 204.96667

•

Coupon period
p_c = dt_c - dt_p = 184

•

Days to next coupon
d_c = dt_c - dt_s = 157

•

Index adjustment factor
g_i = ROUND (v / v_0, decimals) = 1.0580300000

Settlement figures
Settlement flows for the transaction are calculated as follows:
•

Nominal amount
A = 1,000,000.00

•

Clean price
Pca.s = A * Pca = 965,769.78

•

Accrued Interest
I_a.s = A * I_a = 970.34

•

Total
= 966,740.12

Fixing figures
Fixing flows for the transaction are calculated using the following data:
Data

Symbol

Fixing date
Index on 2007-08-22

Example
2007-11-22

vf

205.40

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•

Index adjustment factor
gf = ROUND (vf / v_0, decimals) = 1.06027

•

Nominal coupon
cn = ROUND (c_m / 2 * gf, decimals_div + 2) = 0.006626690

•

Adjusted amount
Ap = A * cn = 6,626.69

Valuation figures
Unless otherwise stated, the figure date used in the calculations is 2007-06-16. On this date, the
market data is as follows:
Market data on 2007-06-16

•

Data

Symbol

Figure date

Example
2007-06-16

Figure spot date

d_s.f

2007-06-18

Market quote (clean unadjusted)

Pcu

91.28%

Index adjustment factor

gv

1.05803

Spot discount factor

Ds

0.999564

Days to next coupon

dnv

157

•

Accrued interest
= A * (c_m / 2) * (p_c - dnv) / p_c * gv * D_s = 969.92

•

Principal
= A * Pcu * gv * D_s = 965,348.87

3.6.16.2.2 Calculations - UK 8 month
This example shows a UK 8 month index-linked gilt, with the following deal data:
Setup data

•

Data

Symbol

Example

Issue date

1982-01-28

Index at issue (5/1981)

294.10

Rebasing index (2/1983)

394.50

Index at issue rebased

v_0

74.55006337136

Maturity date

dt_m

20011-08-23

Interest

r

2.50%

Rounding decimals

dec

0.0001000

Symbol

Example

Transaction data

•

Data
Opening date

2007-03-28

Settlement date

d.s

2007-03-29

Previous coupon date

d.pc

2007-02-23

Next coupon date

dt.c

2007-08-23

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Data

Symbol

Example

Reference index for next coupon

v

202.70

Latest published index

v_l

203.10

Forecast delay months

m_d

2

Next but one coupon date

2008-02-23

Coupons left

n

8

Index Prolong Rate

pi

3%

Note: Index Prolong Rate (for the underlying index) is shown in Rate Monitor under key figure
Index Rate. If the index rate is not given, the default value is 3%.

Other important deal data is calculated by the system as follows:
•

Index forecast factor
g_f = (v_l / v0) * POWER (u, m_d * 2 / 12) = 2.710955377

•

Next but one coupon amount estimate
d2 = (r / 2) * g_f / u = 3.4391490%

•

Days to next coupon
d.n = dt.c - d.s = 147

•

Current coupon period
p = dt.c - d.pc = 181

•

Time to next coupon
t_n = d.n / p = 0.81215

Price from real yield
•

Yield (real)
y = 2.2656270%

•

Semi-annual real discount factor)
w = 1 / (1 + y. / 2) = 0.988798754

•

Semi-annual inflation factor)
u = POWER (1 + pi, -0.5) = 0.985329278

•

Dirty price
P_d = (d1 + d2 * u * w + (g_f * r * w * w) / (2 * (1 - w)) * (1 - POWER (w, n -1))) *
POWER (u * w, d.n / p) + g_f * POWER (u, d.n / p) * POWER (w, n + d.n / p)
= 271.106796%

•

Accrued interest (adjusted)
I_a = d1 * ((p - d.n) / p) = 0.63679558%

•

Clean price (adjusted)
p_c = P_d - I_a = 270.4700%

•

Nominal from real
= 2 * ((y / 2 + 1) * SQRT(1 + pi) - 1) = 5.2771916%

Settlement figures
Settlement flows for the transaction are calculated as follows:
•

Nominal amount
A = 10,000,000.00

•

Clean price
p_c.s = A * p_c = 27,047,000.00

•

Accrued interest
I_a.s = I_a * A = 63,679.56

•

Total
= 27,110,679.56

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Fixing figures
Fixing flows for the transaction are calculated using the following data:
Fixing data
Coupon date

2007-08-23

Index on 2006-12-01

vf

•

Index adjustment factor
g_i = v / v0 = 2.718978239

•

Adjusted coupon
d1 = FLOOR ((r / 2) * g_i, dec) = 3.3900%

•

Adjusted amount
Ap = A * d1 = 339,000.00

202.70

Valuation figures
Unless otherwise stated, the figure date used in the calculations is 2007-03-28. On this date, the
market data is as follows:
Market data on 2007-03-28
Figure date

2007-03-28

Figure spot date

d_s.f

2007-03-29

Discount factor for spot date

Ds

0.999854679

Market quote

Pc

270.47%

Days to next coupon

dvc

147

•

Principal market value
= A * Pc * Ds = 27,043,069.49

•

Accrued interest market value
= A * d1 * (p - dvc) / p * Ds = 63,670.30

3.6.17 US Tips
The following sections describe the characteristics that are specific to US Treasury index-linked
bonds.

3.6.17.1 Instrument setup
Instrument setup for US Tips is the same as for other index-linked bonds (see 3.6 Index-linked bond
on page 260) except for the following parameters:

•

Trading characteristics
See A.2.334 US TIPS on page 877.

–

Issue Index parameters
Information
Index

Description
Instrument ID of the underlying index.
See 7.1 Index types on page 425.

Issue Index

292

Value of the underlying index at issue. This value is used to adjust the coupon
and redemption flows of the bond.

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•

•

Bond characteristics
Information

Description

Currency

USD

Coupon Rate

Coupon rate of the bond.

Schedule parameters
The US Treasury Inflation Protected Security system-defined primary template is provided for
these index-linked bonds, where:
Information

Description

Fixing parameters

•

Need Fixing = Yes

•

Fixing Date Method = In Arrears

•

Expression = ixratio*price

See B.2.1.1.44 US Treasury Inflation Protected Security on page 899.

•

•

•

Trading yield
Information

Description

Yield Convention

U.S. Treasury - *U.S.TREASURY

Quoted
Information

Description

Price Type

Price %

Quote Handling

Index-Linked Bond (US TIPS)

Currency

USD

Valuation approach
See A.2.333 US Index-Linked Bond Valuation on page 877.

3.6.17.2 Position monitoring
In the following sections, numerical examples demonstrate how the different figures are calculated
for US Treasury index-linked bonds, both at the time of issue and at trading.
If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.

3.6.17.2.1 Calculations - at issue
This example shows a US Treasury index-linked bond, with the following deal data (at issue):
Setup data
Issue date

1998-01-15

Index at issue

v_0

161.55484

Maturity date

dt_m

2008-01-15

Interest

r

3.625%

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Transaction data
Opening date

1998-10-13

Spot days

2

Settlement date

dt_s

1998-10-15

Previous coupon date

dt_c0

1998-07-15

Next coupon date

dt_c

1999-01-15

Yield

y

3.650%

Last index

v_1

163.20

Current index

v_2

163.40

Day of month

d_1 (= dt_s)

15

Length of month

m_1

31

Other important deal data is calculated by the system as follows:
•

Coupons left
c_n = FLOOR (YEARFRAC (dt_c, dt_m, 0) * 2, 1) = 18

•

Yield factor
vy = 1 / (1 + y / 2) = 0.9821

•

Dirty price unadjusted
P_u = (r / 2 + (1 - POWER (vy, c_n)) / (y / 2) * (r / 2) + POWER (vy, c_n)) / (1 + (d / p) * (y / 2))
= 100.7032666%

•

Accrued interest unadjusted
I_u = ROUND ((pn - dn) / pn * r / 2, 8) = 0.00906250

•

Accrued interest adjusted
I_a = ROUND (I_u * g_i, 8) = 0.0091598300

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•

Clean price unadjusted
P_cu = ROUND (P_u - I_u, 5) = 99.79700%

•

Clean price adjusted
P_a = ROUND (P_cu * g_i, 5) = 100.86900%

•

Reference index
v = ROUND (v1 + (d_1 - 1) / m_1 * (v2 - v1), 5) = 163.2903200

•

Index adjustment factor
g_i = ROUND (v / v_0, 5) = 1.0107400000

•

Days to next coupon
d = dt_c - dt_s = 92

•

Current coupon period
p = dt_c - dt_c0 = 184

Settlement figures
•

Nominal amount
An = 1,000,000.00

•

Clean price
= An * P_a = 1,008,690.00

•

Accrued interest
= An * I_a = 9,159.83

•

Total
= 1,017,849.83

Fixing figures
Fixing flows for the transaction are calculated using the following data:
Fixing data
Coupon date
Index on 2002-09-01

1999-01-15
vf

•

Index adjustment factor
gf = ROUND (vf / v_0, 5) = 1.01514

•

Nominal coupon
cn = r / 2 * gf = 0.0183994

•

Adjusted amount
Ap = cn * An = 18,399.41

164

Valuation figures
Unless otherwise stated, the figure date used in the calculations is 1998-10-13. On this date, the
market data is as follows:
Market data on 1998-10-13
Figure date

1998-10-13

Figure spot date

d_s.f

1998-10-15

Market quote
(clean unadjusted price)

Pq

99.7970%

Index adjustment factor

g_v

1.010740

Spot discount factor

D_s

1

Days to next coupon

dcv

92

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•

Accrued interest
= An * ROUND ((pn - dcv) / pn * r / 2, 8) * g_v * D_s = 9,159.83

•

Principal
= An * Pq * g_v = 1,008,688.20

3.6.17.2.2 Calculations - at trading
This example shows a US Treasury index-linked bond, with the following deal data (at trading):
Setup data
Index at issue

v_0

198.47742

Maturity date

dt_m

2016-01-15

Interest

r

2.00%

Settlement date

dt_s

2007-06-18

Previous coupon date

dt_c0

2007-01-15

Next coupon date

dt_c

2007-07-15

Yield

y

2.783%

Last index

v_1

205.35200

Current index

v_2

206.68600

Day of month

d_1 (= dt_s)

18

Length of month

m_1

30

Transaction data

Other important deal data is calculated by the system as follows:
•

Coupons left
c_n = FLOOR (YEARFRAC (dt_c, dt_m, 0) * 2, 1) = 17

•

Yield factor
vy = 1 / (1 + y / 2) = 0.9863

•

Dirty price unadjusted
P_u = (r / 2 + (1 - POWER (vy, c_n)) / (y / 2) * (r / 2) + POWER (vy, c_n)) / (1 + (d_1 / m_1) * (y / 2))
= 94.9133290%

•

Accrued interest unadjusted
I_u = ROUND ((pn - dn) / pn * r / 2, 8) = 0.00850829

•

Accrued interest adjusted
I_a = I_u * g_i = 0.0088354338

•

Clean price unadjusted
P_a = P_u - I_u = 94.06250%

•

Clean price adjusted
P_a = P_cu * g_i = 97.67920%

•

Reference index
v = ROUND (v1 + (d_1 - 1) / m_1 * (v2 - v1), 5) = 206.1079300

•

Index adjustment factor
g_i = ROUND (v / v_0, 5) = 1.0384500000

•

Days to next coupon
dn = dt_c - dt_s = 27

•

Current coupon period
pn = dt_c - dt_c0 = 181

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Settlement figures
•

Nominal amount
An = 1,000,000.00

•

Clean price
= An * P_a = 976,792.03

•

Accrued Interest
= An * I_a = 8,835.43

•

Total
= 985,627.47

3.7 Asset backed security
With normal bonds, the investor is dependent on the creditworthiness of the issuer for payment of
the coupons and repayment of the original investment. In contrast, asset-backed securities have a
pool of assets that collateralize the bond and generate the cashflows.
Asset-backed securities (ABS) are backed by assets such as consumer loans, credit card receivables,
royalties, and leases. However, the majority of the market consists of securities backed by
residential mortgage loans with mortgage-backed securities (MBS).
The main risk for the investor is the risk of repayment.
When an individual asset is repaid (repayment), the security is amortized by the principal amount of
that mortgage or loan. The structure of the security determines precisely how this amortization is
passed on to investors; however it is done, it is impossible to predict the cashflows precisely for
fixed or floating-rate instruments.

Note: TRM does not support repayments in the middle of a coupon period but only at coupon
payment dates.

3.7.1 Instrument setup
Asset-backed security instruments must be based on an instrument type derived from the class
ABS.
They are set up in a similar way to standard bonds (see 3.1 Bond on page 215).
The additional values required to set up ABS instruments are described in the following sections.

•

ABS main characteristics
The main characteristics of an ABS are defined in the same way as a Bond instrument, but using
the primary feature ABS: see A.2.1 ABS - Asset Backed Security on page 713.

•

Schedules
Select the cashflow structure template that is appropriate for the instrument.
System templates are provided for both fixed-rate ABS (see B.2.1.1.1 ABS-MBS, Fixed Rate on
page 890) and floating-rate ABS (see B.2.1.1.2 ABS-MBS, Floating Rate on page 890); you can
choose one of these templates or any other template derived from them.

Note: It is possible to modify the Start Date value for the redemption cashflow to reflect any
restrictions on the date when repayments are allowed to begin on the ABS.

•

Repayment estimation
The estimations of future repayments are defined and stored in the Repayment Estimates page. To
define a new set of repayments, click Generate to open the resulting dialog and enter the
following parameters:

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Important: Do not use the Add/Remove and Clear buttons in the Repayment Estimates page.
Information

Description

Estimation Date

Date from when the estimation is valid.

Outstanding

Read-only. Percentage of the initial nominal amount which is outstanding (the current
repayment included) on the Estimation Date.

Legal Maturity

Read-only. Legal maturity of the instrument.

Expected Maturity

Expected maturity of the instrument.
The date must be later than the estimation date and earlier or equal to the legal
maturity date. Default is the legal maturity date.

Method

Defines which method to use to generate the estimate:
•

Annuity does a fixed annuity calculation.

•

Copy Previous + Fixed % copies the previous estimation, if it exists, and adds %
between % From and % To.

•

Fixed % creates a repayment of % between % From and % To.

•

Linear performs linear amortization of the outstanding principal until the date
specified in the Expected Maturity field.

•

WAL Date allow the user to enter an expected maturity date different from the
coupon date. The selected WAL (Weighted Average Life) date is displayed in WAL
Date field of the Repayment Estimates page. When this method is used, two
repayments are automatically created from this date, by splitting the redemption
amount between previous and next coupon dates (according to the WAL date) as
follows:
-

PrevCD is the first coupon value date immediately before the WAL date:
P*OutstandingAmount is prepaid at PrevCD.

-

NextCD is the first coupon value date immediately after the WAL date:
(1-P)* OutstandingAmount is paid at NextCD.
where

P = (WAL date - PrevCD)/(NextCD - PrevCD)
Note: WAL Date is visible in Transaction Manager.
Interest Rate

The last known fixed rate (only used for annuity calculation).

% From

Date from when % should apply in Copy Previous + Fixed % and Fixed % methods.

% To

Date until when % should apply in Copy Previous + Fixed % and Fixed % methods.

%

Percentage to use in Copy Previous + Fixed % and Fixed % methods.

Click OK to display the repayments generated for this date. The information displayed is as
follows:

298

Information

Description

Outstanding

Read-only. Percentage of the initial nominal amount which is outstanding (the current
repayment included).

WAL Date

This date is used when the expected maturity date is different to the coupon date, i.e.
when the method WAL Date is selected during the generation.

Value Date

Read-only. Date on which the repayment may occur for the selected row, valid for the
specified estimation date.

Estimation Date

Date from when the estimation is valid.

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Information

Description

Percentage

For the selected row, the percentage of the principal which is estimated to be repaid
on a specified estimation date.

Active From/To

Read-only. First and/or last date that the estimation is valid.

Each row displayed consists of a repayment estimate, valid for a given period (defined by the
fields Active From/Active To).

–

To refine the repayment estimate for this value date, you can edit the percentage of a row.
Click Update to validate the modification.

–

To generate a new set of estimates for a different date, enter this date in Estimation Date and
generate again as described above.

–

To remove a set of estimations, click Delete. All the estimates with Active From included in the
period defined in the Delete dialog are removed.

Alternative repayment parameters

•

Optionally, you can add the feature Alternative Repayment Estimates to override the repayment
parameters set up in the Repayment Estimates page. This feature adds two pages, Alternative
Repayment Estimate Setup and Alternative Repayment Estimates. The Alternative Repayment Estimates
page is set up in the same way as the Repayment Estimates page.
A.2.27 Alternative Repayment Estimates on page 723.

Note: For accounting: Alternative repayments should not be used for the valuation modes used

in accounting. Accounting should use the set of estimates defined in the Repayment Estimates
page to ensure that the accrual figures are consistent with the yield calculation. (The yield
is calculated based on the estimates defined in the Repayment Estimates page.)

3.7.2 Deal capture
A deal involving an asset-backed security is entered in a similar way to a bond deal.

3.7.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
an asset-backed security.
Information

Description

Price or Rate

If there is a yield/price convention set on the instrument, it is possible to enter either
a rate or a price, and conversion is made automatically. If there is no convention set,
the deal must be entered in price.

Face Amount

The deal can be input in face amount or units, in which case, the Nominal Amount is
computed by the system.

or
Units
Amount

Nominal amount of the deal. This amount is computed by the system when the face
amount or units are entered.

3.7.2.2 Generated data
•

Cashflows
Only definite cashflows are generated on a deal with an ABS instrument:

–

Position cashflow

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–

Known future amortization flows and corresponding interest flows (no uncertain cashflows
are generated)

–

Accrued interest flow

–

Delivery flow (pseudo)

3.7.3 Processing
This section describes the actions that can be done throughout the life of an ABS.

3.7.3.1 Fixing repayment flows
Repayment flows for an ABS are not known in advance and can only be estimated. Therefore, when
you know a repayment is definitely going to take place, the cashflow needs to be fixed.
The following information is needed to fix a repayment:
Fixing Rate = Real percentage of principal

•

Execution
There are two ways to execute fixing of repayment flows. In both cases, the results of the action
are identical. The action parameters are defaulted from the repayment percentage specified in
the Repayment page. If the WAL (Years) is provided, then it is used to calculate the expected
maturity in the subsequent estimate regeneration.
The methods of fixing are as follows:

–

Directly on the cashflow (in Instrument Editor’s Cashflow page) using the Fix Repayment action:
the fixing affects all deals on the instrument by updating the cashflows at transaction level
when the instrument is saved.

–

Using the activity Fixing ABS Repayment: all instruments and their deals which need to be fixed
for a particular date are affected by the activity.

Note: See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

When the fixing of the repayment is done, the cashflows are updated as follows:

–

The repayment flow and the next interest flow are added to the deal.

–

The position flow is added to reflect the outstanding principal amount.

Additionally, after the fixing of the repayment, the system automatically prompts to re-estimate
the repayment estimate based on the result of the fixing. The action parameters are defaulted
from the previous estimation.
Click OK to accept these defaults.

Note: This action can be executed automatically using the Selling Values activity. See the TRM
User Guide for information on the activity parameters.

In case of Floating Rate ABS, the next interest should be fixed before the repayment can be
fixed. This is required to ensure the correct recalculation of yield accrual and regeneration of
estimates for a annuity repayment.

3.7.3.2 Full Repayment
When an ABS is fully repaid, the current position of the corresponding ABS is closed by creating a
Sell transaction with the outstanding amount as the nominal amount.

•

Execution
There are two ways for full repayment of an ABS, in both cases, the results are identical.

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Directly on the cashflow at the instrument level (Instrument Editor - Cashflow page) using the
Full Repayment action. This closes the current position on the corresponding ABS as follows:

–

A Sell transaction is generated (consolidated per Portfolio/Counterparty/Result mode) with a
nominal amount equal to the amount left at the full repayment date. The Sell transaction has
a position flow that closes the current position and a settlement flow to repay the ABS.

Note: No delivery flow is generated in this transaction in order to reflect the market practice

where the issuer may call back the security, usually after the full repayment date. You can
generate the security settlement (delivery flow) at a later date as described in the next
section.
Using the activity Fixing ABS Repayment (Full Repayment), see TRM User Guide for more
information about this activity.

–

After a full repayment, you can generate the security settlement (delivery flow) by right-clicking
the previously generated Sell transaction and selecting ABS Custody Account Clearing. This action
also clears the custody balance.
Enter the following parameters in the resulting dialog:
Information

Description

Opening Date

Defaults to the opening date of the Sell transaction.

Value Date

Defaults to the opening date plus the spot date.

From

(Read-only) Defaults to the owner of the original transaction.

From Custodian

Custody account defined for the owner. Only the accounts with Custody account kind
are available for selection.

From Account

Account from the custody account you selected in the From Custodian field.

To

Defaults to the issuer of the ABS. You can modify the issuer.

To Custodian

Custody account defined for the issuer you selected in the To field. Only the accounts
with Custody account kind are available for selection.

To Account

Account from the custody account you selected in the To Custodian field.

Click OK.
A transfer transaction is created to generate a delivery cashflow between the Owner of the
transaction and the Issuer of the ABS.

Note: You can cancel the transfer transaction by clicking the Cancel command at the transaction
level.

•

Cancellation
You can cancel a full repayment by selecting the Cancel Full Repayment action on the
corresponding redemption flow (Instrument Editor - Cashflow page).

3.7.3.3 Fixing coupon flows
The unknown interest flows for a floating-rate ABS need to be fixed. The procedure for fixing these
flows is the same as the one used for floating-rate notes.
See 3.1.2.3.1 Fixing on page 230 for more information.

3.7.3.4 Selling Values activity
If yield accrual is used, you can set up an activity (using type Selling Values) to have accrued profit
available for the selling process. You must run the activity before processing the selling. This can be

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done by setting activity to run automatically, for example, at the end of each day, before the end of
day accounting processing.

Note: See the TRM User Guide for information about how to set up and use activities in general.

3.7.4 Position monitoring
3.7.4.1 Setup
The presence of the valuation method feature ABS Valuation in the instrument definition determines
that the instrument is valuated as an asset-backed security.
See A.2.2 ABS Valuation on page 714.

3.7.4.2 Calculations
TRM values an asset-backed security according to the current valid estimates on the valuation
dates. It does so by expanding a cashflow structure matching the estimated repayment structure
according to the parameters defined at the instrument level.

Note: The expanded repayment estimate of an ABS that can be seen in Treasury Monitor

corresponds to the cashflow structure of an equivalent bond instrument. Therefore, ABS
valuation behaves in exactly the same way as valuation of an equivalent bond.

3.7.5 Australian MBS
Australian MBS are similar to other MBS instruments already handled by TRM, except that they are
quoted in trading margin, and that the formula used to compute the price is specific. This specific
formula is used to convert the trading margin (market quote) to the instrument's price:
Equation 3-8 Trading Margin conversion - Australian MBS

then
MarketValue = Price * Outs tan ding Principal
where:
C

Next coupon amount per $100 FV

IM

Spread% defined at schedule level.

TM

Quoted yield in %

f

Number of days from settlement to next coupon date.

d

Number of days between previous and next coupon dates.

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a

Annuity Factor

i

s

Quarterly Swap Rate between settlement date and maturity date, this rate is
interpolated on the yield curve defined in the Quote Default page at the instrument
level. The corresponding frequency is retrieved from the Yield Type field of the
yield curve.
Note: If not quarterly, the corresponding rate is converted according to the
Equation 3-2 on page 237.

r

Discount Rate between settlement date and next coupon date (interpolated on the
default yield curve defined at currency editor level).

n

Number of coupon periods between the next coupon date and the Weighted
Average Life (WAL) date with the appropriate ’n’ rounding convention applied (see
3.7.5.1 Instrument setup on page 303 for information about this setup):
Equation 3-9 Number of coupon periods

where:
•

WAL is calculated as shown in 3.7.5.2.1 Input data on page 304.

•

365.25 or 365 corresponds to the Days Divisor selected at the instrument level
in the Bond page.

3.7.5.1 Instrument setup
Australian MBS must be based on an instrument type derived from the class ABS. They are set up in
a similar way to ABS, but require a different primary feature.

•

Main characteristics
Same setup as for usual ABS with the following additional parameter:
Information

Description

N-Periods’ Rounding

Nearest number to which the number of coupon periods ’n’ (as calculated in
Equation 3-9 on page 303) between the next coupon date and the Weighted
Average Life date is rounded.
For example, 0 for none, 1 for an integer, or 0.1 for a rounding to the first
decimal.

N-Periods’ Rounding
Method

Up, Down or Nearest. The amount is rounded up, down, or to the nearest
figure as calculated using the specified N-Periods’ Rounding number.

Days Divisor

The divisor used in the pricing (valuation) formula . Choices are:
•

365

•

365.25.

See A.2.39 Australian MBS on page 727.

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Quotation information

•

Information

Description

Price Type

Select Trading Margin to trade Australian MBS at a trading margin.

Quote Handling

Select MBS (Australian) to convert the quotation (trading margin) to the price of
the instrument. See Equation 3-8 on page 302.

See A.2.274 Quoted on page 849.
Yield Curve Default

•

The setup of the feature Quote Default (Australian MBS) is similar to the usual Quote Default
feature except that it adds the Yield Curve Default page to select the Par rate yield curve to be
used for reference rate defaulting.
Information

Description

Currency

The currency that you want to specify. Select AUD.

Yield Curve

Select corresponding yield curve to be used instead of the yield curve defined
at the currency level (Currency Editor).

A.2.268 Quote Default (Australian MBS) on page 846.
Valuation approach

•

To allow quoted valuation of market value calculation instead of the usual valuation of ABS.
A.2.40 Australian MBS Valuation on page 728.

3.7.5.2 Deal capture
3.7.5.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
an Australian MBS:
Information

Description

Trading Margin

Instrument quotation.

In addition, the following defaulted information can be modified:
Information

Description

Reference Rate

Quarterly swap rate for the period from settlement date to maturity date (from
the yield curve specified in Yield Curve Default page when provided, otherwise uses
the default yield curve defined at currency level).

Discount Rate

Computed from the settlement date and the next coupon date of the instrument
(from the default yield curve defined at currency level).

AU Rate Scenario

Scenario used to calculate the reference and discount rates. This scenario defaults
to the scenario defined at the instrument level (Quote Default page). You can
change the default scenario by selecting Quote Default Configuration from the Options
menu. See TRM User Guide for more information about changing this
configuration.

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Information

Description

WAL Date

If repayments were created with the WAL Date method at the instrument level,
then the entered date is automatically populated according to that date, otherwise
the WAL date is computed as follows for each row of repayments according to the
value date to the transaction settlement date:
Equation 3-10 WAL Date

Deal Price

Computed using the trading margin to the price formula (Equation 3-8 on page
302).

3.7.5.3 Processing
The actions that can be done throughout the life of an Australian MBS are the same ones as for a
usual MBS (see 3.7.3 Processing on page 300).

3.7.5.4 Position monitoring
There are two basic methods for valuation of Australian MBS instruments: Quoted or Theoretical.

3.7.5.4.1 Setup
When the Theoretical valuation method is used, the Australian MBS is valuated in the same way as a
usual MBS. On the other hand, if you want to use the pricing formula (Equation 3-8 on page 302) to
compute the market value, then you need to attach the feature Australian MBS Method (A.2.40
Australian MBS Valuation on page 728) and use the Quoted valuation method.
Swap and discount rates used in the pricing formula are retrieved as follows:

•

Reference Rate: The quarterly swap rate for the period from valuation date to maturity date is
computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature)
with Usage set to Valuation, when provided, otherwise uses the valuation yield curve defined at
the currency level.

•

Discount Rate: Computed between valuation date and next coupon date of the instrument
(computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature)
with Usage set to Discount, when provided, otherwise uses the valuation yield curve defined at
currency level).

Note: For the valuation when the next coupon is not fixed, the estimation curve is used to

compute the next fixing rate and the discount rate in the pricing formula. If the estimation
curve is not defined at the instrument level, then the currency estimation curve is used
instead. If no currency estimation curve is defined, then the currency valuation curve will
be used.

See feature A.2.337 Valuation Curve Setup on page 878.

3.8 Short term loan
Deposits and short-term loans are usually fixed-rate agreements to deposit or borrow a specified
amount for a specified period. They are basically the same instrument, with the name simply
depending on whether they are seen from the borrower's (loan) or the depositor's (deposit)
standpoint. A buy transaction is made by the lender while a sell transaction is made by the
borrower. The maturity is usually less than one year and the principal and interest are paid out at
expiration.

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3.8.1 Instrument setup
Short-term loans must be based on an instrument type derived from the class SHORT-LOAN.

•

Main characteristics
The following basic information may be captured when defining the instrument. This information
is relevant to any kind of short term loan/deposit.
Information

Description

Currency

Currency of the instrument. If the currency is not defined at instrument level, it needs
to be specified separately for each transaction.

Date Basis

Date basis of the instrument. If the date basis is not defined at instrument level, it
can be specified separately for each transaction.

Rounding
parameters

Method and precision used to round cashflow amounts.

Interest Type

Interest rate type used to calculate the cashflows of the instrument.

Transaction Sign

Sign of the transaction. If the sign is not defined at instrument level, it needs to be
specified separately for each transaction.

Principal Subtype

Type of repayment and interest cashflows (default values are Redemption and
Interest).

Interest Subtype

See A.2.299 Short Term Loan on page 862.

•

Maturity definition
It is possible to set up maturity information at instrument level.
Information

Description

Calendar
parameters

Calendars used to calculate the maturity date.

Gap Set

Gap set used for supplying the available maturity periods.

Maturity Date
Period

If defined, this maturity period is applied to each transaction.

See A.2.230 Maturity Date Setup on page 827.

•

Short loan margin definition
It is possible to input margins when entering a loan.
See A.2.300 Short Term Loan Margin Result on page 863.

For a short-term loan/deposit it is also possible to set up:

•

Spot date calculation

•

Value date calculation to enable easy entry of forward deals with this instrument

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes

•

Deal rate defaulting when entering the transaction

See Appendix A Features on page 713.

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3.8.2 Deal capture
3.8.2.1 Input data
Note: For margin loans, make sure that the columns Margin and Margin (bp) are visible in the
Transaction view.

In addition to the standard deal parameters, the following information is required to enter a
short-term loan/deposit:
Information

Description

Currency

Currency of the transaction.

Value Date

Date when the loan/deposit starts, and from which interest starts to accrue. This
defaults to the spot date of the transaction.

Maturity Date

Date when the transaction matures. If you enter a maturity code, the date is
calculated automatically; otherwise you can enter the date manually.

Maturity Code

If the maturity definition parameters are defined at instrument level, these are used
by default and cannot be modified.
Nominal Amount

Amount deposited/lent, that is, the amount exchanged on the value date of the
transaction, and the amount on which interest is calculated.

Deal Rate

Rate at which interest is calculated for the transaction.

In addition, the following optional information can be captured:
Information

Description

Value Date Code

If the Value Date Setup feature is applied at instrument level, you can enter the value
date period you want to use to calculate the value date for the transaction, for
example, 3M (3 months).
This can be used to compute the value date for a forward purchase of a short-term
loan/deposit.
Note: If you specify a value date period in the instrument setup, this is used as the
default in the transaction and cannot be modified: see A.2.339 Value Date
Setup on page 879.

Date Basis

Date basis of the transaction. If the date basis is not defined at instrument level, it can
be specified separately for each transaction.

Margin

You can enter the margin as a percentage in the Margin column or as basis points in
the Margin (bp) column, in which case, the margins are stored as a percentage but
displayed as basis points (multiplied by 100).

Margin (bp)

The margin added or subtracted from the Nominal/Spot Rate to get Deal Rate. Positive
margins are always in favor of the portfolio owner and negative margins against the
portfolio owner. Thus, for short-term loans placed, the margin will be added to
Nominal/Spot Rate to get Deal Rate, and for short-term loans taken, the margin will
be subtracted from Nominal/Spot Rate to get Deal Rate. The exact calculation is the
following:

Deal Rate = Nominal / Spot Rate + Transaction Sign * Margin
Nominal Spot / Rate

The interest rate excluding margins.

3.8.2.2 Generated data
•

Transaction

–

Book value of the transaction is automatically defaulted to the nominal amount.

–

Issuer is determined by the transaction direction:

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Transaction Sign = Buy, Issuer = Counterparty
Transaction Sign = Sell, Issuer = Portfolio Owner

•

Cashflows
The following cashflow structure is generated for a bought transaction (depositor side).

The interest amount is calculated as follows:
rounder (A * (1 / D - 1))
where:
D = discount factor
A = nominal amount
rounder depends on the instrument’s rounding parameters

–

Margin cashflows
A Margin cashflow is generated if a transaction margin rate is entered and the instrument
has the feature Short Term Loan Margin. The Margin cashflow is only used for calculating
Margin Profit. The Margin cashflow is calculated in the same way as the interest, using the
captured margin rate. This cashflow effectively represents the margin rates contribution in
the final interest amount.

3.8.3 Processing
This section describes the actions that can be done throughout the life of a short-term loan/deposit.

3.8.3.1 Early expiration
Short-term loans/deposits can be matured earlier than their agreed maturity date. This process is
referred to as early expiration. However, the action is only enabled for transactions that have
reached a certain state in the transaction flow.

•

Execution
Early expiration of short-term deposits/loans can be done in two different ways. In both cases,
the following information is needed to process the early-expiration:

308

Information

Description

Opening Date

Date when the early expiration is executed. By default, this is today’s date.

Value Date

Date when the early expiration is settled. This must be earlier than the original
maturity date and later than the original value date of the initial transaction.

Amount to Expire

Amount to be early expired. This defaults to the amount still available to be early
expired, taking into account previous partial early expirations and roll overs.

Rate

Rate at which the early expiration is done.

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The execution generates an early expiration transaction with the following attributes:
Transaction sign = opposite of initial transaction
Nominal amount = amount to expire
Rate = early expiration rate
Opening date = date when the early expiration is done
Value date = date when the early expiration is settled
Kind = Early Expiration
The remaining attributes are inherited from the initial transaction.

•

Cancellation
You can undo the early expiration by canceling the early expiration transaction.

3.8.3.2 Early expiration with margins
You can also specify margins when you early expire short term loans.
See A.2.300 Short Term Loan Margin Result on page 863.

•

Execution
When early expiring a short loan with margin, the following information is displayed/ calculated
instead of the Rate field:
Information

Description

Nominal Rate

Defaulted from the original deal.

Margin

Defaulted from the original deal and cannot be modified. Margin is added to or
subtracted from the Nominal Rate to get the Deal Rate.

Deal Rate

Rate at which the early expiration is done. Defaulted from the original deal.

When a transaction being early expired has margin cashflows (i.e. instrument has feature Short
Term Loan Margin), the margin accrued from the value date of the underlying deposit until the
settlement date of the early expiration is realized.

•

Cancellation
You can undo the early expiration by canceling the early expiration transaction.

3.8.3.3 Roll over
You can defer the maturity of a short-term loan/deposit to a later date. This process is referred to as
a roll-over.
See A.2.14 Allow Roll Over (Short Loan) on page 719.

•

Setup
It is possible to restrict the use of the roll-over methods at instrument level (see below for
methods description). It is also possible to specify the default method for the instrument.

•

Execution
Roll-over of short-term deposits/loans can be done in four different ways. In all cases, the
following information is needed to process the roll-over:
Information

Description

Roll Over Date

Date when the roll-over is executed.

Value Date

Date of the roll over transaction. Corresponds to the maturity date of the initial
transaction.

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Information

Description

Roll Over Method

Method used for the roll over: Settle All, Settle Interest, Delay Interest, Compound
Interest, Settle Interest and Allow Increase, Capitalize Interest and Allow Increase.
The outcome of the roll over depends on the chosen method, see further on in this
section for more information.

Nominal Amount

Amount of the roll-over. This defaults to the amount left of the initial transaction but
you can override this if you want to perform a partial roll-over.

Additional Amount

Amount to be added to the initial principal amount if you want to increase capital at
roll over.
This field becomes available when one of the Allow Increase roll over methods has
been selected.

New Nominal
Amount

Original nominal amount plus interest (if interest is capitalized) plus the additional
amount.
This field becomes available when one of the Allow Increase roll over methods has
been selected.

Gap
Maturity Date

Gap set used for supplying the available maturity periods.
The maturity date for the loan/deposit. The defaulting is defined as follows:
•

If the parent transaction was defined with a maturity period, the roll over maturity
date defaults according to that period, otherwise you have to enter the maturity
date.

•

If the switch No Maturity Defaulting is selected at the instrument level (Roll Over
page), then the maturity date of the rollover is never defaulted and you must
enter it.

Note: If the specified maturity date does not fall on a business day, you can choose to
keep the non business day or to change it.
Deal Rate

(Mandatory) New interest rate for the roll-over, that is, the rate at which interest is
calculated from the old maturity date until the new maturity date.
By default, the rate is defaulted from the initial transaction however it is possible to
disable this defaulting by selecting the switch No Rate Defaulting at the instrument level
(Roll Over page).

The outcome of the roll-over depends on the method chosen as follows:
Method

Description

Settle All

The initial transaction is paid in its entirety at the initial maturity date. The default
nominal amount of the roll-over transaction equals the sum of the interest and
principal cashflows of the initial transaction.

Settle Interest

The interest of the initial transaction is paid at the initial maturity date, but the
principal payment is deferred. The part of the principal which is rolled over is paid
back at the end of the roll-over transaction.
The default nominal amount of the roll-over transaction equals the principal cashflow
of the initial transaction but can be reduced (partial roll-over).

Settle Interest,
Allow Increase

This method allows the user to provide additional capital (increase the principal) as
part of the roll over process.
The interest from the underlying deposit/loan is settled, and the original principal
amount (plus the additional capital) is rolled over.

Capitalize
Interest, Allow
Increase

310

This method allows the user to provide additional capital (increase the principal) as
part of the roll over process.
The interest from the underlying deposit/loan is capitalized (that is, realized and
added to the initial nominal amount) and included with the additional capital in the roll
over.

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Method

Description

Delay Interest

Nothing is paid at the initial maturity date: both the interest and principal payments
are deferred. The parts of the principal and interest cashflows which are rolled over
are paid back at the end of the roll-over transaction.
The default nominal amount of the roll-over transaction equals the principal cashflow
of the initial transaction but can be reduced (partial roll-over).

Compound
Interest

This method is the same as Delay Interest, but the closed interest of the initial
transaction is reinvested in the roll-over. New interest accrues on top of the initial
transaction’s interest.
The default nominal amount of the roll-over transaction equals the principal cashflow
of the initial transaction but can be reduced (partial roll-over).

The execution generates a new transaction with the following attributes:
Nominal amount = amount (can be smaller than the initial transaction)
Rate = roll-over rate
Opening date = date when the roll-over is done
Value date = maturity date of the initial transaction
Maturity date = maturity of the roll-over
Kind = Roll-over

•

Cancellation
You can undo the roll-over by canceling the roll-over transaction.

3.8.3.4 Roll over with margins
You can specify margins in case you roll over short term loans.
See A.2.15 Allow Roll Over (Short Loan - Margin Result) on page 719.

•

Execution
This roll over behaves exactly as the roll over without margins, except that instead of just the
Deal Rate field, the following fields are available:

•

Information

Description

Nominal Rate

Defaulted from the original deal.

Margin

Defaulted from the original deal. Added to or subtracted from the Nominal Rate to get
Deal Rate.

Cancellation
You can undo the roll-over by canceling the roll-over transaction.

3.8.4 Position monitoring
3.8.4.1 Setup
The presence of the valuation method feature Short Term Loan Valuation in the instrument
definition determines that the instrument is valuated as a short term loan.
See A.2.301 Short Term Loan Valuation on page 863.

3.8.4.2 Calculations
In this section, numerical examples demonstrate how the different figures are calculated for
short-term deposit/loan transactions.

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If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.
This example shows a 6 month USD deposit with a 3% Periodic Rate, with the following deal data:
Setup data
Instrument Date Basis

Act/360

Instrument Yield Type

Periodic

Valuation Method

Theoretical

Risk Method

Theoretical

Valuation Date

Figure Date

Result IR: AI Method

Linear

Result IR: Accrual Method

Linear Accrual

Accrual Yield: Interest Type

Periodic Rate

Accrual Yield: Date Basis

Actual/360

Result FX: Profit Method

FX Forward

FX Exposure Offset

e_fx

0.01

IR Risk Rate

e_ir

0.0001

Transaction data
Opening Date

2004-06-01

Spot Date

d_p

2004-06-03

Maturity Date

d_m

2004-12-03

Nominal Amount

c_m

1,000,000

Deal Rate

r_b

3%

Base Book FX Rate (EUR/USD)

S_b

1.18710

Currency

USD

Portfolio Currency

EUR

Other important deal data is calculated by the system as follows:
•

Period
t_p = (d_m - d_p) / B
0.508333333 = (2004/12/03 – 2004/06/03) / 360

•

Discount Factor
D_b = 1 / (1 + t_p * r_b)
0.984979069 = 1 / (1 + 0.508333333 * 0.03)

•

Interest Cashflow
c_I = c_m * r_b * t_p
15,250.00 = 1,000,000 * 0.03 * 0.508333333

•

Book Value (Local)
V_b = (c_m + c_I) * D_b
1,000,000.00= (1,000,000 + 15,250) * 0.984979069

•

Book Value
V_bp = ROUND(V_b / S_b ,2)
842,389.02 = ROUND(1,000,000 / 1.18710 ,2)

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Unless otherwise stated, the figure date used in the calculations is 2004-08-17. On this date, the
market data is as follows:
Market data on 2004-08-17
Figure Date

d_f

2004-08-17

Days to Spot

d_fs

2

Interest Rate

r_f

1.105695%

Discount Rate

r_d

1.044985%

FX Spot Rate

S

1.20000

FX Spot CCY Base Rate

S_p

1.2

Other figures are calculated by the system as follows:
•

Days to Maturity
= d_m - d_f
108 = 2004/12/03 – 2004/08/17

•

Time to Maturity
t_m = (d_m - d_f) / B
0.30000 = 108 / 360

•

Time to Spot
t_s = d_fs / B
0.00555556 = 2 / 360

•

Market Value Discount Factor
D_V = D_s * D_I = 0.9966917723

•

Present Value Discount Factor
D_P = D_s * D_I = 0.9966917723

•

Market Value Spot Discount Factor
D_s = EXP(-t_s * r_d) = 0.9999419470

•

Discount Factor From Spot
D_I =EXP(-(t_m - t_s)* r_f) = 0.9967496366

3.8.4.2.1 Valuation figures
The valuation method commonly used for a short-term loan/deposit is the Theoretical method.
•

Principal flow figures
Local Market Value
V_lp = c_m * D_V
996,691.77 = 1,000,000 * 0.9966917723
Market Value
V_p = V_lp / S
830,576.48 = 996,691.77 / 1.200
Clean Market Value
CMV_p = V_p / D_s
830,624.70 = 830,576.48 / 0.9999419470

•

Interest flow figures
Local Market Value
V_li = c_I * D_V
15,199.55 = 15,250 * 0.9966917723
Market Value
V_i = V_li / S
12,666.29 = 15,199.55 / 1.200
Clean Market Value
CMV_i = (c_I * D_V / D_s - (c_I * (t_p - t_m + t_s)) / t_p) / S
7,319.80 = (15,250 * 0.9966917723 - (c_I * (0.50833333 - 0.3 + 0.00555556)) / t_p) / 1.2

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•

Transaction figures
Local Market Value
= V_lp + V_li
1,011,891.32 = 996,691.77 + 15,199.55
Market Value
= V_p + V_i
843,242.77 = 830,576.48 + 12,666.29
Clean Market Value
= CMV_p + CMV_i
837,944.50 = 830,624.70 + 7,319.80

3.8.4.2.2 Result figures
The setup of the instrument impacts the way result figures are computed.
•

Principal flow figures
Total Profit (Local)
P_tlp = V_lp - V_b
-3,308.23 = 996,691.77 – 1,000,000
MtoM Profit (Local)
P_mlp = c_m * D_V / D_s - V_b
-3,250.36 = 1,000,000 * (0.9966917723/0.9999419470) – 1,000,000
Accrued Interest (Local)
I_alp = 0
Accrued Profit (Local)
P_alp = 0
Other Profit (Local)
P_olp = P_tlp - P_mlp
-57.86 = (-3,308.23) – (-3,250.36)
FX Profit
P_fxp = V_b * (1 / S_p) - V_bp
-9,055.68 = 1,000,000 * (1 / 1.2000) – 842,389.02
Total Profit
P_tp = V_p - V_bp
-11,812.54 = 830,576.48 – 842,389.02
MtoM Profit
P_mp = P_mlp / S
-2,708.64 = -3,250.36 / 1.2
Accrued Interest
I_ap = 0
Accrued Profit
P_ap = 0
Other Profit
P_op = P_tp - P_fxp - P_mp
-48.22 = (-11,812.54) – (-9,055.68) – (-2,708.64)

•

Interest flow figures
Total Profit (Local)
P_tli = V_li
= 15,199.55
MtoM Profit (Local)
P_mli = =c_I * D_V / D_s - (c_I * (t_p - t_m + t_s)) / t_p
8,783.77 = 15,250 * (0.9966917723 / 0.9999419470) – (c_I * (0.508333333 - 0.3 + 0.00555556)) / t_p
Accrued Interest (Local)
I_ali = c_I * (t_p - t_m) / t_p
6,250.00 = 15,250 * (0.508333333 – 0.3) / 0.508333333
Other Profit (Local)
P_oli = P_tli - P_mli – I_ali
165.78 = 15,199.55 – 8,783.77 – 6,250.00

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Total Profit
P_ti = V_i
= 12,666.29
MtoM Profit
P_mi = P_mli / S
7,319.80 = 8,783.77 / 1.2
Accrued Interest
I_ai = I_ali / S
5,208.33 = 6,250.00 / 1.2
Other Profit
P_oi = P_ti - P_mi – I_ai
138.15 = 12,666.29 -7,319.80 – 5,208.33
•

Transaction figures
Total Profit (Local)
= P_tlp + P_tli
11,891.32 = -3,308.23 + 15,199.55
MtoM Profit (Local)
= P_mlp + P_mli
5,533.40 = -3,250.36 + 8,783.77
Accrued Interest (Local)
= I_ali
= 6,250.00
Other Profit (Local)
= P_olp + P_oli
-58.75 = (-57.86) + (-0.88)
FX Profit
= P_fxp
= -9,055.69
Total Profit
= P_tp + P_ti
853.75 = -11,812.54 + 12,666.29
MtoM Profit
= P_mp + P_mi
4,611.17 = -2,708.64 + 7,319.80
Accrued Interest
= I_ap + I_ai
5,208.33 = 0 + 5,208.33
Other Profit
= P_op + P_oi
89.93 = (-48.22) + 138.15

3.8.4.2.3 Risk figures
The risk method commonly used for a short-term loan/deposit is the Theoretical method.
•

Principal flow figures
IR Exposure 1bp
E_ip = (c_m) * (-(t_m - t_s)*D_I*D_s - t_s*D_I*D_s) / S * e_ir
-24.92 =
1,000,000*(-(0.3-0.005555556)*0.9967496366*0.9999419470-0.005555556*D_I*D_s) /1.2*0.0001
FX Exposure
E_fxp = V_p * e_fx
8,305.76 = 830,576.48 * 0.01
Effective Duration
U_eff = -E_ip / V_p / 0.0001
0.300000 = -(-24.92) / 830,576.48 / 0.0001

•

Interest flow figures
IR Exposure 1bp
E_ipi = (c_I) * (-(t_m - t_s)* D_I * D_s - t_s * D_I * D_s) / S * e_ir
-0.38 =
15,250.00 *(-(0.3 - 0.005555556) * 0.9967496366 * 0.9999419470 - t_s * D_I * D_s) / 1.2 * 0.0001

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FX Exposure
E_fxi = V_i * e_fx
126.66 = 12,666.29 * 0.01
Effective Duration
U_eff = -E_ipi / V_i / 0.0001
0.300000 = -(-0.38) / 12,666.29 / 0.0001
•

Transaction figures
IR Exposure 1bp
= E_ip + E_ipi
-25.30 = (-24.92) + (-0.38)
FX Exposure
= E_fxp + E_fxi
8432.43 = 8,305.76 + 126.66
Effective Duration
U_eff = -(E_ip + E_ipi) / (V_p + V_i) / 0.0001
0.300000 = -((-24.92) + (-0.38)) / (830,576.48 + 12,666.29) / 0.0001

3.9 Discount paper
A discount paper is a short-term instrument which pays its face amount at maturity and is
purchased at a discount price. Most discount papers are listed instruments. The most commonly
traded discount paper is the US Treasury-Bill.

3.9.1 Instrument setup
Discount papers are based on an instrument type derived from the class DISCOUNT.

•

Main characteristics
The following basic information may be captured when defining the instrument. This information
is relevant to any kind of discount paper.
Information

Description

Currency

Currency of the discount paper (that is, if it is a listed discount paper).
Leave this field blank if you want to specify the currency when you enter the deal in
Transaction Manager when you are defining an OTC discount paper.

Date Basis

Date basis of the instrument. If the date basis is not defined at instrument level, it
needs to be specified separately for each transaction.

Rounding
parameters

Method and precision used to round cashflow amounts.

Yield Type

Yield type of the discount paper, typically a discount rate.

Transaction Sign

Sign of the transaction. If the sign is not defined at instrument level, it needs to be
specified separately for each transaction.

Principal Subtype

Type of principal or interest cashflows.

Interest Subtype
Issuer

Issuer of the instrument.

See A.2.121 Discount Paper on page 768 or A.2.122 Discount Paper OTC on page 770.

–

Date details
For listed discount papers, you must specify the issue date and maturity date of the
instrument.

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For OTC discount papers, you can set up maturity information.

–

Information

Description

Calendar

Calendars used to calculate the maturity date.

Gap Set

Gap set used for supplying the available maturity periods.

Maturity Date Period

If defined, this maturity period is applied to each transaction.

Trading unit details
It is possible to define a minimum bid size or trading units of a discount paper. If a minimum
denomination is defined, deal entry is available either in units or amount and TRM ensures
that the amount is a multiple of the denomination size.

•

Quoted
If you want to enter quotes for a discount paper, this must be specified at instrument level.
Information

Description

Price Type

Select Yield.
Select Discount Paper to display yields and prices in Rate Monitor.

Quote Handling

See A.2.274 Quoted on page 849.

•

Valuation approach
Discount papers can be valuated using either Fixed IR Valuation or Discount Valuation features.
See A.2.150 Fixed IR Valuation on page 784 or A.2.123 Discount Valuation on page 770.
Examples of calculations using these methods are provided in section 3.9.4 Position monitoring
on page 320.

It is also possible to set up:

•

Spot date calculation

•

Value date calculation to enable easy entry of forward deals with this instrument

•

Cashflow and transaction charge rules

•

Collateral

•

Branch codes

•

Quotation information.

See Appendix A Features on page 713.

3.9.2 Deal capture
3.9.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a discount
paper:
Information
Currency

Description
Currency of the transaction.
If you specified the currency in the instrument setup (for example, for a US T-Bill),
this is used as the default currency in the transaction and cannot be modified.

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Information

Description

Maturity Date

Date for the maturity of the contract. If you enter a maturity code, the date is
calculated automatically; otherwise you can enter the date manually.

Maturity Code

Note: For listed discount papers, the maturity date defaults from the instrument setup
and cannot be changed.
Value Date

Date when the transaction starts. This defaults to the spot date of the transaction.

Nominal Amount

Amount of the discount paper. This is equal to the principal (the amount on which the
interest is calculated).

Units

For listed discount papers, the nominal amount must be a multiple of the minimum
contract size defined in the instrument setup.
Deal Rate

Rate used to discount the nominal amount (the book rate).

In addition, the following optional information can be captured:
Information

Description

Deal Price

Deal price of the transaction (expressed as a percentage of the nominal amount) used
to calculate the book value and the settlement amount.

Value Date Code

If the Value Date Setup feature is applied at instrument level, you can enter the value
date period you want to use to calculate the value date for the transaction, for
example, 3M (3 months).
This can be used to compute the value date for a forward purchase of a discount
paper.
Note: If you specify a value date period in the instrument setup, this is used as the
default in the transaction and cannot be modified: see A.2.339 Value Date
Setup on page 879.

Issuer

Issuer of the discount paper.
If Issuer is defined at instrument level, this is used by default and cannot be modified.

Date Basis

Date basis of the transaction.
If this value is defined at instrument level, this is used by default and cannot be
modified at deal entry.

3.9.2.2 Generated data
•

Transaction
A discount paper is bought or sold at a discount price. This means that the Book Value (BV) is
equal to the nominal amount discounted with the deal rate.
BV = NA * D

•

Cashflows
The following cashflows are generated:

318

–

The principal/settlement cashflow is generated with amount = book value

–

There is only one payback cashflow (principal/payback)

–

There is no interest cashflow.

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The figure below illustrates the cashflows which are established in TRM when a discount paper is
purchased.

3.9.3 Processing
This section describes the actions that can be done throughout the life of a discount paper.

3.9.3.1 Early expiration
Discount papers can be matured earlier than their agreed maturity date. This process is referred to
as early expiration. However, the action is only enabled for transactions that have reached a certain
state in the transaction flow.

•

Execution
The following information is needed to process the early-expiration:
Information

Description

Opening Date

Date when the early expiration is executed. By default, this is today’s date.

Value Date

Date when the early expiration is settled. This must be earlier than the original
maturity date and later than the original value date of the initial transaction.

Amount to Expire

Amount to be early expired. This defaults to the amount still available to be early
expired, taking into account previous partial early expirations and roll overs.

Rate

Rate at which the early expiration is done.

The execution generates an early expiration transaction with the following attributes:
Transaction sign = opposite of initial transaction
Nominal amount = amount to expire
Rate = early expiration rate
Opening date = date when the early expiration is done
Value date = date when the early expiration is settled
Kind = Early Expiration
The remaining attributes are inherited from the initial transaction.

•

Cancellation
You can undo the early expiration by canceling the early expiration transaction.

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3.9.4 Position monitoring
3.9.4.1 Setup
In addition to the basic valuation setup which can be set up for every instrument (see A.2.50 Base
Valuation Setup on page 734) it is possible to set up the following:
Information

Description

AI Method

It is possible to override the standard linear method in order to accrue interest
differently for the valuation figures (see A.2.49 Base IR Setup on page 733, Chapter 1
Concepts on page 21, A.2.337 Valuation Curve Setup on page 878).

Spread Curve

It is possible to add spread curves to correspond to the credit risk (see A.2.305
Spread Curve Setup on page 865, Chapter 1 Concepts on page 21, A.2.337 Valuation
Curve Setup on page 878).

3.9.4.2 Calculations - Theoretical
In this section, numerical examples demonstrate how the different figures are calculated for
discount papers.
See Chapter 2 Market standards and calculations on page 33.
This example shows a US T-Bill, with the following deal data:
Setup data
Instrument Date Basis

Act/360

Instrument Yield Type

Discount

Valuation Method

Theoretical

Valuation Date

Figure Date

Risk Date

Figure Date

Risk Yield Type

Continuous

Result IR: Accrued Interest

Linear

Result IR: Accrual Method

Linear Accrual

Accrual Yield: Interest Type

Periodic Rate

Accrual Yield: Date Basis

Actual/360

FX Exposure Offset

e_fx

0.01

Transaction data
Opening Date

2004-02-02

Nominal Amount

c_m

1,000,000

Deal Rate

r_b

3%

Base Book FX Rate (EUR/USD)

S_b

1.2

Maturity Date

d_m

2004-07-01

Value Date

d_a

2004-02-04

Currency

USD

Portfolio Currency

EUR

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Other important deal data is calculated by the system as follows:
•

Book Value (Local)
V_b = c_m * D_b
987,750.00 = 1,000,000 * 0.98775

•

Book Value
V_p = V_b / S_b
823,125.00 = 987,750.00 / 1.2

•

Period
t_p = DAYS360(d_a,d_m,TRUE) / B
0.408333333 = (2004/02/04,2004/07/01,TRUE) / 360

•

Discount Factor
D_b = 1 – t_p * r_b
0.98775 = 1 – 0.408333333 * 0.03

Unless otherwise stated, the figure date used in the calculations is 2004-03-01. On this date, the
market data is as follows:
Market data on 2004-03-01
Figure Date

d_f

2004-03-01

Interest Rate

r_f

1.113119%

Days to Spot

d_fs

2

Discount Rate

r_d

1.044985%

FX Conversion Rate

S

1.260000

Other figures are calculated by the system as follows:
•

Days to Maturity
= d_m - d_f
122 = 2004/07/01 – 2004/03/01

•

Time to Maturity
t_m = (d_m - d_f) / B
0.33888889 = 122 / 360

•

Time to Spot
t_s = d_fs / B
0.005555556 = 2 / 360

•

Market Value Discount Factor
D_V = D_s * D_I = 0.996238639

•

Present Value Discount Factor
D_P = D_s * D_I = 0.996238639

•

Spot Discount Factor
D_s = EXP(-t_s*r_d) = 0.999941947

•

Spot-Maturity Discount Factor
D_I =EXP(-(t_m-t_s)*r_f) = 0.996296478

Valuation figures
The valuation method commonly used for a discount paper is the Theoretical method.
•

Local Market Value
V_l = c_m * D_V
996,238.64 = 1,000,000 * 0.996239

•

Market Value
V = V_l / S
790,665.59 = 996,238.64 / 1.2600

•

Clean Market Value
= V / D_s
790,711.49 = 790,665.59 / 0.999941947

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Result figures
The setup of the instrument impacts the way result figures are computed.
•

Total Profit (Local)
P_tl = V_l – V_b
8,488.64 = 996,238.64 – 987,750.00

•

MtoM Profit (Local)
P_ml = -c_m * ((1 - r_b * (t_m - t_s)) - (D_I))
6,296.48 = 1,000,000*((1 - 0.03 *(0.33888889-0.005555556)) - 0.996296478

•

Accrued Profit (Local)
P_al = = -c_m * (D_b -(1 - (t_m - t_s) * r_b))
2,250.00 = -1,000,000*(0.98775-(1-(0.33888889-0.005555556)*0.03))

•

Other Profit (Local)
P_ol = P_tl - P_ml - P_al
-57.84 = 8,488.64 – 6,296.48 – 2,250

•

FX Profit
P_fx = V_b * (1/S - 1/S_b)
-39,196.43 = 987,750.00*(1 / 1.260000 – 1 / 1.20000)

•

Total Profit
P_t = V – V_p
-32,459.41 = 790,665.59 – 823,125.00

•

MtoM Profit
P_m = P_ml / S
4,997.20 = 6,296.48 / 1.260000

•

Accrued Profit
P_a = P_al / S
1,785.71 = 2,250.00 / 1.260000

•

Other Profit
P_o = P_t - P_m - P_a - P_fx
-45.90 = -32,459.41 - 4,997.20 - 1,785.71 – (-39,196.43)

Risk figures
The risk method commonly used for a discount paper is the Theoretical method.
•

IR Exposure 1bp
E_ip = c_m * (-(t_m-t_s) * D_I*D_s - t_s *D_I* D_s) /S * 0.0001
-26.79 =
1,000,000*(-(0.33888889-0.005555556)*0.996296478*0.999941947-t_s*(D_I*D_s)/1.26*0.0001

•

IR Exposure 1bp from spot
E_is = c_m * (-(t_m - t_s) * D_I) / S * 0.0001
-26.357050 = 1,000,000 * (-(0.33888889-0.005555556)*0.996296478 / 1.26 * 0.0001

•

FX Exposure
E_fx = e_fx * V
7,906.66 = 0.01 * 790,665.59

•

Effective Duration
U_eff = -E_ip / V / 0.0001
0.338889 = -(-26.79) / 790,665.59 / 0.0001

3.9.4.3 Calculations - Discount Yield
Discount yield is calculated from quoted market value at spot, using Yield Type and Date Basis
defined in IR Exposure page in the Instrument Editor:
Equation 3-11 Discount yield

where

–
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–

t v is time between spot date and value date calculated using the IR Exposure date basis

–

R[] is the function that converts discount factor into rate, according to the Yield Type defined
for IR Exposure .

3.9.4.3.1 Example
Instrument data
•

Discount Paper page
Date Basis

Actual/365

Interest Type

Periodic Rate

Price Rounding

0.001 (3 decimal places)

pr = 3
•

Dates page
Maturity Date

•

•

2009-08-05

Base Valuation page
Method

Quoted

Switches

To Spot

IR Exposure page
Date Basis

Actual/365

Yield Type

Continuous Yield

Switches

To Spot

Transaction data
Nominal Amount

A = 100000

Valuation data
Valuation Date

2008-08-05

Figure Market Quote

rm = 5
d v = 365
ds = 2

Days to Maturity Date
Days to Spot

Calculated data
•

Price (P)
Let [ X ] k mean rounding to k decimal places. Then
Equation 3-12 Discount Yield Price

= 95.263

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•

Discount Yield (y)
Using
Equation 3-13 Discount Yield: Discount Yield (y)

= 0.994520547945206
The discount yield (Figure Interest Rate) is:
Equation 3-14 Discount Yield: Figure Interest Rate

= 0.0487960741031

•

IR Exposure (E1)
Figure Risk Value is:

Vr = A
= 1000000
Sensitivity of discount factor is (for continuous yield):
Equation 3-15 Discount Yield: IR Exposure (E1)

= -0.947410109589
Figure IR Exposure 1bp is:
Equation 3-16 Discount Yield: IR Exposure (1bp)

E 1 = V r D r × 0.0001
= -94.7410109589

3.9.4.4 Calculations - Modified Duration / Effective Duration
The following numerical example demonstrates how Modified Duration and Effective Duration figures
are calculated for depo/discount papers. For more information about Duration key figures, see
2.3.4.9 Duration figures on page 142.

3.9.4.4.1 Example: Depo/Discount Paper
The example in this section shows an overnight paper of 100,000,000 at 0.70 with a price of
99,998,088.89.

Transaction data
•

On November 9th, the Principal cashflow was equal to -99 998 088.89

•

On November 10th, the Principal cashflow was equal to 100,000,000.00

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Valuation data
Valuation Date

2009-11-09

Valuation Mode

Theoretical

Date Basis

Actual/365

Risk figures
•

Principal cashflow (risk date = 2009-11-09)
Equation 3-17 Time to maturity of the cashflow

dr – dv
t i = ---------------- = 0
365

•

Present Value Discount Factor

Dp = 1

Present Value

Vp= -99,998,088.89

IR Exposure

E { i1 } = 0

Amortization cashflow (risk date = 2009-11-10)
Equation 3-18 Time to maturity of the cashflow

dr – dv
t i = ---------------- = 1 ⁄ 365
365

Present Value Discount Factor

Dp = 0.999964445709

Present Value

Vp = -99,996,444.57

IR Exposure

E { i1 } = – V p × t i × 0.0001 = 27.39628618

Transaction figures
IR Exposure

E { i1 } = – V p × t i × 0.0001 = 0 + 27.39628618 = 27.39628618
Present Value
Modified Duration

Effective Duration

Vp = -99,998,088.89+99,996,444.57 = -1644.3
Sett

Pos

1000 × [ Ei1 + E i1 ]
10000 × [ 27.39628618 ]
U Mod = ------------------------------------------------------= ------------------------------------------------------------------------------------------------------------- = 0.002739704
Sett
Pos
0.5
×
(
–
99
, 998, 088.89 + 99, 996, 444.57 )
0.5 × ( V p
+ Vp )
– E { i1 }
– 27.39628618
U eff = ⎛⎝ ----------------⎞⎠ × 10000 = ⎛⎝ ----------------------------------⎞⎠ × 10000 = 166.6117372
Vp
– 1644.3191

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3.10 Loan
In TRM, loans are agreements to lend or borrow money for a medium/long term with multiple
interest (and potentially principal) payments occurring during the life of the deal.
The key concept concerning loans is that of the cashflow schedule. Several schedules must be
attached to a loan deal, and they drive the generation of the cashflow structure for the deal.
For the simplest types of loans, two schedules are associated with the deal: one schedule for
interest flows; and one schedule for principal flows. For more complex deals, there will be additional
schedules for optional events, additional interest cashflows, and so on.
Loans belong to the instrument class LOAN. This class covers a diverse set of instruments: from
fixed annual interest / bullet repayment loans to more complex, exotic structures. Therefore, this
chapter is organized into the following sections:

–

How TRM handles fixed-rate loans

–

How TRM deals with floating-rate loans

–

A list of more exotic deals that can be set up in TRM.

3.10.1 Fixed-rate loan
Fixed-rate loans pay interest at a pre-defined (fixed) rate.

3.10.1.1 Instrument setup
•

Loan main characteristics
The following basic information may be captured when defining the instrument. This information
is relevant to any kind of fixed-rate loan.
Information
Currency

Description
Currency of the loan.
Leave this field blank if you want to specify the currency when you enter the deal in
Transaction Manager.

Transaction Sign

Sign of the transaction. If the sign is not defined at instrument level, it needs to be
specified separately for each transaction.

AI Method

Method used to calculate accrued interest if interest starts to accrue before the value
date of the transaction.

Settlement
Switches

Dirty Price: Switch on to use the dirty price for the instrument, that is, to include
accrued interest in the instrument’s price.

Par: Switch on in order to have the deal price defaulted to 100.
Rounding
Parameters

Method and precision used to round cashflow amounts.

Structure

Schedule template to be used for the loan.
If a structure is not defined at instrument level, a schedule needs to be specified for
each transaction. Usually the structure is defined at the instrument level. If this is not
the case, then you have to define it for each transaction at transaction level.

See A.2.202 Generic Loan on page 812.

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•

Maturity definition
It is possible to set up maturity information at instrument level.
Information

Description

Calendar
parameters

Calendars used to calculate the maturity date.

Gap Set

Gap set used for supplying the available maturity periods.

Maturity Date
Period

If defined, this maturity period is applied to each transaction.

See A.2.230 Maturity Date Setup on page 827.

•

Selectable cashflow structures
With this option, you can limit the choice of schedules available to assign to a loan in Transaction
Manager by associating one or several schedule template groups to the instrument. At deal
entry, only the templates belonging to these groups will be available for selection.
If a cashflow structure is already set up in the instrument’s main characteristics, it will override
any schedule groups.
See A.2.293 Schedule Template Setup on page 859.

It is also possible to set up:

•

Spot day calculations

•

Manual charges

•

Cashflow and transaction charge rules

•

Branch codes.

See Appendix A Features on page 713.

3.10.1.2 Deal capture
Depending on the selected cashflow structure, the information needed to deal the instrument and
the generated cashflows are very different.
The transaction level information is the same.

3.10.1.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
a fixed rate loan:
Information
Currency

Description
Currency of the transaction.
If you specified the currency in the instrument setup, this is used as the default
currency in the transaction and cannot be modified.

Maturity Date

Date for the maturity of the contract.
If you use maturity date setup, the date is calculated automatically from the selected
maturity period, otherwise you can enter the date manually.

Nominal Amount

Amount of the loan. This is equal to the principal (the amount on which the interest is
calculated).

Deal Price

Deal price of the transaction (expressed as a percentage of the nominal amount) used
to calculate the book value and the settlement amount. In order to have the deal
price defaulted to 100, you should set the settlement switch Par in Instrument Editor.

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These values alone are not sufficient to define the deal. To complete the creation of a fixed-rate
loan, the cashflow structure of the deal also needs to be specified, either in the instrument setup, or
at deal entry, by applying a schedule template.
The following sections explain how the system handles standard fixed-rate cashflow structures.

3.10.1.2.2 Generated data
•

Book Value (clean price):
BV = A * p /100
where:
A = Nominal Amount
p = deal price

•

Book Value (dirty price):
BV = (A * p /100) - AI
where:
A = Nominal Amount
p = deal price
AI = Accrued Interest

3.10.1.2.3 Bullet repayment structure
A fixed-rate loan with periodic interest and total repayment of the principal at maturity represents a
bullet repayment structure.

•

Input data
To define this kind of structure, a template is required which contains at least one schedule for
fixed-rate interest flows, and one schedule for repayment flows. TRM provides a pre-defined
system template designed for this: see B.2.1.1.21 Fixed, Bullet Repayment on page 894.
For each set of cashflows, the following information must be supplied at deal entry:

–

–

Interest flows
Information

Description

Frequency Method
and Period

The frequency method/period for the interest cashflows (for example, Years/1
generates one interest flow per year).

Interest Rate

The fixed interest rate (for example, 5%).

Repayment flows
No information required.

•

Generated data

–

Schedule
When a template is selected, one schedule is created for each item in the template. Some of
the values are automatically defaulted from the transaction parameters (see Appendix B
Schedules on page 883), while others can be modified at deal entry (see above).

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–

Cashflows
For a fixed-rate loan with repayment at maturity, the cashflows generated are as follows:

3.10.1.2.4 Fixed-rate loan - amortizing structure
A fixed-rate loan with periodic interest and repayment of the principal in several steps during the
deal represents an amortizing structure.

•

Input data
To define this kind of structure, a template which contains at least one schedule for fixed-rate
interest cashflows, and one schedule for repayment cashflows is required. TRM provides a
pre-defined system template (B.2.1.1.21 Fixed, Bullet Repayment on page 894) designed for
this purpose.
For each set of cashflows, the following information must be supplied at deal entry:

–

–

Interest flows
Information

Description

Frequency Method
and Period

The frequency method/period for the interest cashflows (for example, Years/1
generates one interest flow per year).

Interest Rate

The fixed interest rate (for example, 5%).

Repayment flows
Information

Description

Frequency Method
and Period

The frequency method/period for the repayment cashflow (for example,
Times/Year-1 means that one repayment will occur every year).

Calculation Method
and Repayment %

Defines how the repayments have to be generated.

Start Date

•

For example, using percentage 10% as the method means 10% of the initial
capital at each repayment, with the remaining capital being repaid at maturity.
Start date can be moved forward in order to start amortizing later.

Generated data

–

Schedule
When a template is selected, one schedule is created for each item in the template. Some of
the values are automatically defaulted from the transaction parameters, while others can be
modified at deal entry.

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–

Cashflows
For an amortizing loan, the cashflows generated are as follows:

3.10.1.2.5 Fixed-rate loan - fixed annuity structure
A fixed-rate loan with a fixed amount of principal and interest over the life of the deal represents a
fixed annuity structure.

•

Input data
To define this kind of structure, TRM provides a pre-defined system template (B.2.1.1.20 Fixed,
Annuity Repayment on page 894) designed for this purpose.
For each set of cashflows, the following information must be supplied at deal entry:

–

–

Interest flows
Information

Description

Frequency Method
and Period

The frequency method/period for the interest cashflows (for example, Years/1
generates one interest flow per year).

Interest Rate

The fixed interest rate (for example, 5%).

Repayment flows
No information required.

•

Generated data

–

Schedule
When a template is selected, one schedule is created for each item in the template. Some of
the values are automatically defaulted from the transaction parameters (see Appendix B
Schedules on page 883), while others can be modified at deal entry (see above).

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–

Cashflows
For a fixed-annuity loan, the cashflows generated are as follows:

3.10.1.2.6 Fixed-rate loan - irregular annuity
With an irregular annuity, the flows are computed equally throughout the life of the loan except for
the final payment, which is adjusted according to how much of the loan remains outstanding.

•

Input data
To define this kind of structure, the following information must be supplied at deal entry in the
Schedule view:

–

•

Principal schedule
Information

Description

Interest Rate

The fixed interest rate (for example, 5%).

Generated data

–

The annuity is computed equally across all flows, except the last one.

–

The remaining principal is repaid on the final cashflow (100 - rate).

3.10.1.2.7 Fixed-rate loan - margin
It is possible to specify a margin when entering a fixed rate loan. As well as the standard fixed-rate
loan input data and generated cashflows there are input data and generated cashflows for margins.

•

Input data
For margin loans, you need to attach a secondary schedule Margin to the interest schedule and
specify the margin in the Spread schedule field (of the Margin schedule).

•

Generated data

–

Margin flows
A Margin cashflow is generated if a margin schedule is attached to the transaction and a
margin rate is entered (in the Spread field). The Margin cashflow is only used for calculating
Margin Profit. The Margin cashflow is calculated in the same way as the interest, using the
captured margin rate. This cashflow effectively represents the margin rates contribution in
the final interest amount.

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3.10.1.3 Processing
This section describes the actions that can be done throughout the life of a loan.

3.10.1.3.1 Early expiration
Loans can be matured earlier than their agreed maturity date. This process is referred to as early
expiration.

•

Execution
Early expiration of loans requires the following information:
Information

Description

Opening Date

Date when the early expiration is executed.
By default, this is today’s date unless a Fixing/Action Date was specified at transaction
level.

Value Date

Date when the early expiration is settled. This must be earlier than the original
maturity date and later than the original value date of the initial transaction.

Settlement Date

Date when early-expiration price is paid.

Amount to Expire

Amount to be early expired. This defaults to the amount still available to be early
expired, taking into account previous partial early expirations and roll overs.

Price

The premium or discount the early expiration is made at.

Settlement Price
Method

Clean Price: AI is created as Payable cashflow and P/L flow is the difference between
early-expiration price and original deal price.
Dirty Price: AI is created as Not Payable cashflow, and P/L flow is reduce by the AI
amount.

Accrued Interest

The accrued interest that will be paid in the early expiration transaction. This value
can be modified.

Options

•

Amortize P/L
Switch on to amortize the P/L from the value date until the original maturity date.
If this switch is off, the Sell P/L flow created by the early expiration (arising from
Net Amount – Accrued Interest) occurs on the early expiration value date.

•

No Fee Realization
Switch on to continue to amortize fees to maturity. For example, this can be used
in the case of an asset swap, which mirrors the issue fees, to keep the fees
amortizing even when the asset swap is fully unwound.
If this switch is off, at early expiration, the fees that were amortizing until the
maturity date are closed.

•

Delay Interest (only available when the settlement price method is set to Clean Price)
Switch on to delay the accrued interest payment to the next interest payment
date.

The execution generates an early expiration transaction with the following attributes:
Transaction sign = opposite of initial transaction
Nominal amount = amount to expire
Price = early expiration rate
Opening date = date when the early expiration is done
Value date = date when the early expiration is settled
Kind = Early Expiration
The remaining attributes are inherited from the initial transaction.
The early expiration transaction generates closing cashflows for the initial transaction and P/L
cashflows if there is a difference between the early expiration price and the original deal price.

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•

Cancellation
You can undo the early expiration by canceling the early expiration transaction.

3.10.1.3.2 Roll over
You can defer the maturity of a loan to a later date. This process is referred to as a roll-over.
See A.2.9 Allow Roll Over on page 716.

•

Setup
It is possible to restrict the use of the roll-over methods at instrument level (see below for
methods description).
It is also possible to specify the default roll over method for the instrument.

•

Execution
Roll-over of loans can be done in four different ways. In all cases, the following information is
needed to process the roll over:
Information

Description

Roll Over Date

Date when the roll over is executed.

Maturity Date

New maturity date for the loan. This must be later than the maturity date of the initial
transaction. The maturity date is calculated automatically from the maturity period of
the initial transaction.

Nominal Amount

Amount of the roll over. This defaults to the amount left of the initial transaction but
you can override this if you want to perform a partial roll over.

Additional Amount

Amount to be added to the initial principal amount if you want to increase capital at
roll over.
This field becomes available when one of the Allow Increase roll over methods has
been selected.

New Nominal
Amount

Original nominal amount plus interest (if interest is capitalized) plus the additional
amount.
This field becomes available when one of the Allow Increase roll over methods has
been selected.

Rate

A new interest rate for the roll over, that is, the rate at which interest is calculated
from the old maturity date until the new maturity date.
By default, the rate displayed is taken from the interest schedule information, and is
used to generate the interest schedule of the new roll over transaction.

Roll Over Method

Method used for the roll over.

The outcome of the roll-over depends on the method chosen as follows:
Method

Description

Settle All

The initial transaction is paid in its entirety at the initial maturity date. The default
nominal amount of the roll over transaction equals the sum of the interest and
principal cashflows of the initial transaction.

Settle Interest

The interest of the initial transaction is paid at the initial maturity date, but the
principal payment is deferred. The part of the principal which is rolled over is paid
back at the end of the roll over transaction.

Settle Interest,
Allow Increase

This method allows the user to provide additional capital (increase the principal) as
part of the roll over process.
The interest from the underlying loan is settled, and the original principal amount
(plus the additional capital) is rolled over.

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Method

Description

Capitalize
Interest, Allow
Increase

This method allows the user to provide additional capital (increase the principal) as
part of the roll over process.

Delay Interest

Nothing is paid at the initial maturity date: both the interest and principal payments
are deferred. The parts of the principal and interest cashflows which are rolled over
are paid back when the first interest payment of the roll over transaction occurs.

Compound
Interest

This method is the same as Delay Interest, but the closed interest of the initial
transaction is reinvested in the roll over. New interest accrues on top of the initial
transaction’s interest.

The interest from the underlying loan is capitalized (that is, realized and added to the
initial nominal amount) and included with the additional capital in the roll over.

The execution generates a new transaction with the following attributes:
Nominal amount = amount (can be smaller than initial one)
Rate = roll-over rate
Opening date = date when the roll-over is done
Value date = maturity date of the initial transaction
Maturity date = maturity of the roll-over
Kind = Roll-over

•

Cancellation
You can undo the roll over by canceling the roll over transaction.

3.10.1.3.3 Trade assignment
Trade assignments are changes of ownership of transactions.

•

Execution
Change of ownership during the life of a transaction can be performed in two steps:

–

Right-click the existing transaction and choose Assignment(sale) action. This action closes the
existing transaction, and when required, exchanges settlement amounts between the old
and new owners of the transaction.

–

Right-click the generated transaction and choose Assignment (purchase) action. This action
creates the new transaction with the new owner.

Assignment (sale) of a transaction to another client requires the following information:
Information

Description

Opening Date

Date when the early expiration is executed.
By default, this is today’s date unless a Fixing/Action Date was specified at transaction
level.

Value Date

Date when the early expiration is settled. This must be earlier than the original
maturity date and later than the original value date of the initial transaction.

Settlement Date

Date when assignment price is paid.

Amount Left

Read-only. Remaining amount of the initial transaction.

Assignee

New owner of the transaction

Settlement Price
Method

Clean Price: AI is created as Payable cashflow and P/L flow is the difference between
assignment price and original deal price.
Dirty Price: AI is created as Not Payable cashflow, and P/L flow is reduce by the AI
amount.

Currency

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Information

Description

Settlement Price

The price of the assignment.

Accrued Interest

Read-only. Interest accrued on specified date.

Options

•

Amortize P/L
Switch on Amortize P/L to amortize the P/L from the value date until the original
maturity date. If this switch is off, the Sell P/L flow created by the assignment
(arising from Net Amount – Accrued Interest) occurs on the assignment value
date.

•

No Fee Realization
Switch on No Fee Realization so that fees keep amortizing to maturity.
If this switch is off at assignment, the fees that were amortizing until the maturity
date are closed.

Execution generates an Assignment transaction with following cashflows:

–

Cashflows to close the future cashflows of the original transactions (closing of cashflows
where payment date is after the assignment value date)

–

Settlement flows between the assignor and the assignee, reflecting the settlement amounts.

The generated transaction has the following attributes:
Information

Description

Transaction Sign

Opposite of the original transaction sign.

Nominal Amount

Amount to assign.

Opening Date

Opening date of action.

Value Date

Value date of action.

Kind

Assignment.

The original transaction remains unchanged.
The assignee can then select the Assignment (purchase) action on the generated closing
transaction. Selecting the portfolio from the resulting dialog generates a new transaction,
reflecting the future cashflows of the original transaction and settlement flows between assignee
and assignor.

Note: The Counterparty field is open, to allow Counterparty change if required.
•

Cancellation
You can undo the assignment action by canceling the generated assignment transaction.

3.10.1.3.4 Changing the counterparty of a transaction
You can terminate the existing transaction against one counterparty and reopen it against another
counterparty. The following information is required:
Information

Description

Opening Date

Date when the transfer is executed. By default, this is today’s date unless a
Fixing/Action Date was specified at transaction level.

Value Date

Date when the transfer is settled. This must be earlier than the original maturity date
and later than the original value date of the initial transaction.

Counterparty

New counterparty for the transaction.

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A transaction will be generated whose Kind is Counterparty Conversion. The characteristics of the
new transaction will be the same than the old one, except for Counterparty and opening/value date.
This action generates closing cashflows for the future cashflows from the original transaction, and
futures cashflows between the original owner and the new counterparty.
No settlement/result flows will be affected to the generated transaction, as the assignment is
between the counterparties only.
The generated transaction can be canceled to undo the action.

3.10.1.3.5 Transferring transactions between portfolios
You can transfer the transaction from one portfolio to another. This is effectively a sale in one
portfolio and a purchase in another. Portfolio transfer of an existing transaction can be performed at
transaction level by right-clicking and choosing Transfer. Transfer of a transaction to another
portfolio requires the following information:
Information

Description

Opening Date

Date when the transfer is executed. By default, this is today’s date unless a
Fixing/Action Date was specified at transaction level.

Value Date

Date when the transfer is settled. This must be earlier than the original maturity date
and later than the original value date of the initial transaction.

Settlement Date

Payment date for settlement flows.

New Portfolio

New portfolio for the transaction

No Settlement
switch

If On, the generated settlement amount is marked as pseudo (i.e. not bookable, not
payable).

Settlement Price
Method

Clean Price: AI is created as Payable cashflow and P/L flow is the difference between
transfer price and original deal price.
Dirty Price: AI is created as Not Payable cashflow, and P/L flow is reduce by the AI
amount.

Currency

Read-only. Currency of loan.

Settlement Price

The price of the assignment.

Accrued Interest

Read-only. Interest accrued on specified date.

Options

•

Amortize P/L

•

No Fee Realization

Two Transfer transactions are generated:
1. A sale is created in the source portfolio of the transfer, i.e. closing cashflows of the original
transaction and settlement flows (real or pseudo, depending on inputs).
2. A purchase is then created in the receiving portfolio, with future flows and settlement flows (real
or pseudo, depending on inputs).
The original transaction remains unchanged. The user can undo the portfolio transfer action by
canceling the generated transactions.

3.10.1.3.6 Transaction Conversion
To allow schedule conversion at predefined dates during transaction's life.

•

Setup
This process is available on the transaction if the Transaction Conversion feature is associated
with the instrument.
See A.2.325 Transaction Conversion on page 873.

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Then, the user is allowed to attach the Conversion schedule to the existing schedule and to
define conversion events and converted schedules.

•

Execution
When conversion schedules are defined, the user is allowed to execute generated conversion
events. The conversion inputs are displayed.
See A.2.325 Transaction Conversion on page 873.
The execution generates a conversion transaction with the following attributes:

–

Kind: Conversion

–

Opening Date: Conversion opening date

–

Value Date: Conversion value date.

The conversion transaction generates closing cashflows for the initial transaction.
If the conversion price is different to the original deal price, then a P/L flow is generated,
showing the differences between the conversion price and the original deal price.

3.10.1.4 Position monitoring
3.10.1.4.1 Setup
The cashflow discounting method (periodic, continuously compounded) used in IR risk calculation
depends on the instrument set up.
By default, TRM uses the valuation curve interpolation settings (IR Quote and Yield Curve Editor Interpolation page). For example, if the interpolation settings are set up with Interest Type Continuous
Yield, then risk calculations use continuously compounding discounting of the cashflows.
If IR Exposure is set up at the instrument level, then TRM uses these settings. For example, if IR
exposure is set up with Yield Type Periodic, then risk calculations use periodic discounting of the
cashflows.
For more information about risk calculations, see 2.3 Key-figures on page 112.

3.10.2 Floating-rate loan
Interest cashflows for a floating-rate loan are linked to a market reference. The market reference
has to be observed for each interest period. The fixing of the interest rate can be done before
interest starts accruing (classical in-advance fixing), or at the end of the period (in-arrears fixing).

3.10.2.1 Instrument setup
Floating-rate loans are set up in a similar way to fixed-rate loans, but refer to a different type of
cashflow structure: the structure you choose needs to generate floating interest cashflows.
You can pre-define the cashflow structure in the main characteristics of the loan, or restrict the
available schedule templates at deal entry using the Schedule Groups option.
See A.2.293 Schedule Template Setup on page 859.

3.10.2.2 Deal capture
Depending on the selected cashflow structure, the information needed to deal the instrument and
the generated cashflows are very different.
The transaction level information is always the same.

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3.10.2.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a deal on
a floating-rate loan:
Information

Description

Currency

Currency of the transaction.
If you specified the currency in the instrument setup, this is used as the default
currency in the transaction and cannot be modified.

Maturity Date

Date for the maturity of the contract.
If you use maturity date setup the date is calculated automatically from the selected
maturity period, otherwise you can enter the date manually.

Nominal Amount

Amount of the loan. This is equal to the principal (the amount on which the interest is
calculated).

Deal Price

Deal price of the transaction (expressed as a percentage of the nominal amount) used
to calculate the book value and the settlement amount.

3.10.2.2.2 Generated data
•

Book Value (clean price):
BV = A * p /100
where:
A = Nominal Amount
p = deal price

•

Book Value (dirty price):
BV = (A * p /100) - AI
where:
A = Nominal Amount
p = deal price
AI = Accrued Interest
These values alone are not sufficient to define the deal. To complete the creation of a
floating-rate loan, the cashflow structure of the deal also needs to be specified, either in the
instrument setup, or at deal entry.
See Appendix B Schedules on page 883.

3.10.2.2.3 Bullet repayment structure
For a floating-rate loan, a template which contains at least one schedule for floating-rate interest
cashflows and one schedule for repayment flows is required.

•

Input data
For each set of cashflows, the following information must be supplied:

–

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Interest flows
Information

Description

Frequency Method
and Period

The frequency method/period for the interest cashflows (for example, Years/1
generates one interest flow per year).

Interest Rate

The first rate of interest (for example, 5%), if known.

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Information

Description

Fixing parameters

Formulae used to evaluate the rate.
This is known as an "expression" in TRM. Typical expressions would be, for
example, "ir", referring to an ir rate market reference (yield curve) or "ir +
spread%". See Appendix D Expressions on page 917.
Yield curve to be used in the expression.
Period (for example, 3M or 6M) and the scenario used to get the rates when
fixing the cashflows.
Define if the fixing will be done in-advance or in-arrears and enter the offset in
days.

–

Repayment flows
Information

Description

Frequency Method
and Period

The frequency method/period for the repayment cashflow (for example, Bullet
means that the loan will be entirely repaid at maturity). It is also possible to
define amortizable or accreting principal cashflows.

Some other parameters in the schedule can be adjusted to modify the way the cashflows are
generated.
See Appendix B Schedules on page 883.

•

Generated data

–

Schedule
When a template is selected, one schedule is created for each item in the template. Some of
the values are automatically defaulted from the transaction parameters (see Appendix B
Schedules on page 883), while others can be modified at deal entry (see above).

–

Cashflows
For a floating-rate loan with repayment at maturity, the cashflows generated are as follows:

3.10.2.3 Processing
Floating-rate loans are processed in a similar way to fixed-rate loans, but with the following
additional process.

3.10.2.3.1 Interest fixing
For a floating-rate loan, the amount of each interest flow has to be determined before it is paid: this
process is known as fixing.

•

Execution

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Each interest cashflow of a floating-rate deal contains some parameters that define how its
amount is fixed.

–

The fixing period determined by a from/to date value pair indicates when the amount of the
flow has to be fixed; it can be before the interest starts accruing (in-advance fixing), or
before the payment of the interest (in-arrears fixing).

–

The fixing parameters (expression, rate, spread, and so on) that define how the fixing rate is
calculated.

–

An "expression value" which is informative and gives the current value of the expression.

Executing the fixing modifies the cashflow as follows:
Marks it as being fixed
Sets the fixing date
Stores the rate of the market reference used for fixing
Stores the effective interest rate (nominal rate) on the cashflow
Sets the amount of the cashflow
The fixing process can be performed in four ways in TRM: the process which is triggered is
exactly the same in the four cases, the only difference being the quantity of deals or cashflows
which are affected. The four ways of fixing are as follows:

–

Directly on the deal: the fixing only affects the deal

–

Directly on an individual cashflow in the Cashflow view: the fixing affects an individual
cashflow

–

On the instrument (in Instrument Editor): the fixing affects all the deals on this instrument

–

Using an automated activity (Fixing Transaction Cashflow): potentially all deals which have
to be fixed for a particular date may be affected.
See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

If the Fixing action is carried out directly on an individual cashflow using the second method, it is
possible to modify the fixing values. When the fixing quote is modified, this updates both the
nominal rate and the amount accordingly. Similarly, if the nominal rate is modified, the amount
is affected (but not the fixing quote). It is also possible to modify the amount independently
from the other fixing values. This may be necessary when rounding differences arise, for
example.

•

Cancellation
It is possible to cancel the fixing either manually, using the Undo Fixing action; or automatically,
using the Fixing Transaction Cashflow - Undo activity.
See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

3.10.3 Other loan structures
All the cashflow structures available for bonds are also available for loans (see 3.1 Bond on page
215). You can also find information about all system-defined cashflow structures available in TRM in
Appendix B Schedules on page 883.
Some of the structures that can be generated for a loan are described in this section.

3.10.3.1 Dual currency structure
•

Regular dual-currency:
The currency in which the instrument is issued (principal currency) differs from the currency in
which the principal is repaid (redemption currency). The currency of the interest flow can be
either the principal currency or the redemption currency.
The FX rate to apply can be known (determined on the date of issue) or fixed later (determined
a number of days before the payment date of the interest cashflow).

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•

Reverse dual-currency:
The principal currency and redemption currency are identical, but interest payments are in a
different currency.
The FX rate used for the calculation of interest is either known when the loan is agreed or fixed
later.

3.10.3.1.1 Instrument setup
Instrument setup for a dual-currency loan is similar to that of a standard loan (see 3.10 Loan on
page 326), except for the following:

•

Loan main characteristics
Information

Description

AI Method

The method used by the system to compute settlement accrued interests. For
dual-currency loans, there are two types of dual-currency methods:
•

Dual Currency Estimated

•

Dual Currency Last.

See 2.1.6.1 Accrued interest calculations on page 67 for more information.

•

Dual-currency attributes
This information defines the characteristics of the principal cashflow. Leave these fields blank if
you want to specify the details when you enter the deal.
Information

Description

Settlement
Currency

Currency in which the principal cashflow is settled.

Settlement FX
Rate

Rate used to calculate the settlement amount of the principal cashflow.

Need Fixing

Specify whether the FX rate needs to be fixed:
•

Select No when the FX rate is known

•

Select Yes, FX Rate when the FX rate is unknown.

The old value "Yes, Unmarked" is not used.
Fixing Offset

Number of days’ offset allowed, that is, the difference in days between the fixing date
and the due date (default = 0).

Fixing Max. Offset

Maximum number of days’ offset allowed.

See A.2.125 Dual Currency on page 771.

•

FX fixing
If the settlement FX rate is unknown when the deal is entered, then this feature needs to be
included in the instrument definition.
See A.2.174 FX Fixing on page 797.

3.10.3.1.2 Deal capture
•

Input data
Deals on dual-currency loans are captured in a similar way to those on a standard loan. To
complete the creation of a dual-currency loan transaction, the cashflow structure of the deal also
needs to be specified, either in the instrument setup, or at deal entry, by applying a schedule
template.
The following system templates are provided for dual-currency structures:

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–

Dual-Currency Known FX
This is a fixed bullet structure used for dual currency instruments when the FX rate is known
when the deal is entered.
For both interest and redemption schedules you can choose a different settlement currency
and specify the settlement FX rate.
See B.2.1.1.15 Dual Currency, Known FX Rate on page 893.

–

Dual-Currency Known FX Floating
This is a floating bullet structure used for dual currency instruments when the FX rate is
known when the deal is entered.
For both interest and redemption schedules you can choose a different settlement currency
and specify the settlement FX rate.
See B.2.1.1.16 Dual Currency, Known FX Rate, Floating on page 893.

–

Dual-Currency Unknown FX
This is a fixed bullet structure used for dual currency instruments when the settlement FX
rate is not known beforehand.
For both interest and principal schedules you can choose a different settlement currency.
See B.2.1.1.17 Dual Currency, Unknown FX Rate on page 893.
Note that this template covers fixed interest rates only. For floating rates, you also have to
use the Fixing Dates secondary template (see B.2.1.2.15 Fixing Dates on page 903).

You can choose one of these templates or any other template derived from them. Once the
template is applied to the transaction, the schedules are created and it is then possible to define
the settlement currency characteristics, as well as other characteristics such as, date basis,
payment convention, calendars, and so on.
See Appendix B Schedules on page 883.

•

Generated data

–

Cashflows
Settlement Currency = Settlement Currency (as defined in the schedule)
Settlement FX Rate = Settlement FX Rate (as defined in the schedule)
Settlement Amount = Amount * Settlement FX Rate

3.10.3.1.3 Processing
•

Early expiration
The early expiration of a dual currency loan is similar to that of a standard loan, except that you
can set the Settlement FX Rate and view the settlement amount. See 3.10.1.3 Processing on
page 332.

–

Execution
You perform the Early Expiration action in the Transaction Manager’s Transaction view on the
transaction that you want to early expire. You can enter the following information:

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Information

Description

Settlement Currency

(Read-only) Currency to use for settlement.

Settlement FX Rate

Rate used to calculate the settlement amount of the principal cashflow.

Settlement Accrued
Interest

Final amount to be settled.

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•

FX fixing
When the settlement FX rate of a dual-currency loan is not known beforehand, the FX rates need
to be fixed at the agreed fixing date.

–

Setup
Depending on the instrument setup, the fixing can be done in advance or in arrears. In both
cases there can be an offset of n days (before the beginning or end of the interest period).

–

Execution
The FX Fixing action performed in Transaction Manager’s Cashflow view on the cashflow
allows you to set the FX rate. The following values can be input:
Information

Description

Fixing Date

Day the cashflow is fixed.

Reference FX Rate

Fixing market quote.
This is defaulted by the system to the FX cross rate between the actual
currency and the currency on the fixing date and can be changed by the user.

The fixing process is performed directly on an individual cashflow in the Cashflow view. It is
possible to modify the fixing values.

–

Cancellation
It is possible to undo the FX fixing using the Undo FX Fixing action.

3.10.3.1.4 Position monitoring
For information about dual currency calculations, see 2.3.5 Dual currency on page 147.

3.10.3.2 Rainbow coupon structure
In these structures there is an option on each interest payment to choose the payment in a different
currency (a maximum of three currencies can be defined in TRM).

3.10.3.3 Callable structure
These structures are used to create callable/puttable loans. Call/Put can be simply optional or
triggered by a market event. It is also possible to have a Call/Put with barriers (in or out).

3.10.3.4 Currency transaction option
Options for repayment to occur in a different currency: this option can be simple, triggered or linked
with a barrier. This option can be applied to a principal repayment or a call option

3.10.3.5 Transaction conversion option
Deals with an embedded option to move to a different cashflow structure, for example, an option to
move from a fixed to a floating rate, or from an annual to a zero coupon structure. These
transaction conversions can also be linked to barriers or triggers.

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Chapter 4

Equities

In TRM, the term equity is used to cover the following instruments:

•

Common stock
Common stock is security that represents ownership in a company that has issued stock. The
stockholder has a right to receive dividends and the right to vote in the shareholders’ meeting.

•

Preferred stock
Preferred stock is security that represents ownership in a company that has issued stock.
Preferred stock typically has better rights to dividends than common stock, but less voting rights
(or even none at all).

•

Subscription rights
A subscription right gives the holder the right to buy the underlying security at a predetermined
price. Typically, the rights have a short lifetime: they are detached from stock at a specific date
and expire worthless if they are not used to purchase the underlying stock.

•

Mutual fund shares
A mutual fund share represents one unit of ownership in the assets of a mutual fund.

4.1 Equity
Equity instruments must be based on an instrument type derived from the class EQUITY.

4.1.1 Instrument setup
•

Equity main characteristics
The following basic information may be captured when defining the instrument. This information
is relevant to any kind of equity instrument.
Information

Description

Issuer and
Guarantor
parameters

Issuer and guarantor information for the equity instrument.

Currency

Currency in which the equity is traded.

Rounding
parameters

Method and precision used to round cashflow amounts.

See A.2.127 Equity on page 772.

•

Equity information
The outstanding number of shares and voting rights for the equity may change over time. It is
possible to define this information at instrument level.
See A.2.132 Equity Info on page 776.

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Quotation

•

You can specify quotation information for the equity at instrument level.
See A.2.274 Quoted on page 849.
Trading unit

•

Equities can be traded in multiples of a minimum bid size. It is possible to define this information
in the instrument setup.
See A.2.321 Trading Unit (Equity) on page 871.
For an equity instrument, it is also possible to set up:

•

Spot date calculation

•

Value date calculation

•

Delivery (custodian) information

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes.

See Appendix A Features on page 713.

4.1.2 Deal capture
4.1.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a
transaction with an equity instrument:
Information

Description

Value Date

Official date when money is transferred. This defaults to the spot date as defined for
the instrument.

Trading Units

Number of units bought or sold.
The Equity Trading Unit feature is used to define the minimum bid size of shares or
fund shares.
See A.2.321 Trading Unit (Equity) on page 871.

Deal Price

Price of one unit.

In addition, the following optional information can be captured:
Information

Description

Value Date Code

If the Value Date Setup feature is applied at instrument level, you can enter the value
date period you want to use to calculate the value date for the transaction, for
example, 3M (3 months).
This can be used to compute the value date for a forward purchase of equity.
Note: If you specify a value date period in the instrument setup, this is used as the
default in the transaction and cannot be modified: see A.2.339 Value Date
Setup on page 879.

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4.1.2.2 Generated data
•

Cashflows
For an equity instrument, the cashflows generated are as follows:
Value
date

Opening
date

Position
cashflow

Spot
days

Delivery
cashflow

Settlement
amount

4.1.3 Processing
When managing an equity portfolio, there are various corporate actions that need to be processed.
The processing in TRM of the most commonly used corporate actions is described in this section.

4.1.3.1 Cash dividend
In most cases, the holders of common stock, preferred stock, or mutual fund shares receive regular
cash dividends up to four times each year. In addition, they may receive special dividends.

•

Setup
When the information about the cash dividend is declared by the issuer of the security, the
instrument definition needs to be updated with the dividend information.
See A.2.128 Equity Cash Dividend on page 773.

•

Execution
On the ex-dividend date, the equity is quoted without the dividend and the market price drops
approximately by the amount of the dividend. The exact amount of the dividend is known at the
end of the previous business day. It is calculated from the position at the close of business prior
to the ex-dividend date. The activity Dividend that creates the dividend transaction(s) needs to
be performed at the beginning of the ex-dividend date (or at the end of the previous day).
The following information is needed to process the cash dividend:
Information

Description

Portfolio

The dividend is calculated for this portfolio and all of its subportfolios.

Minimum
Transaction State

The minimum transaction state that is taken into account when the position is
determined for the dividend calculation.

Note: See the TRM User Guide for information about this activity and how to set up activities in
general.

The execution creates the dividend transaction, which has an incoming cashflow on the dividend
payment date. From the ex-dividend date onwards, the market value of this transaction is
calculated separately from the equity position.
The execution processes each portfolio (and owner) separately: a dividend transaction is created
in each portfolio (and for each owner) where there is a position on the relevant equity on the day
preceding the ex-dividend date.

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•

Cancellation
In case the dividend transactions are incorrect it is possible to cancel them manually and rerun
the dividend activity.

4.1.3.2 Split and reverse split
When an equity instrument is split, the number of outstanding shares increases: each share is split
into a certain number of shares.
For example:
Before the split:
Buy 5,000 units of equity
where the price of each unit = 10 EUR (total book value = 50,000 EUR)
split 1 unit into 5 shares
After the split:
The position is 25,000 units of equity
where the price of each unit = 2 EUR (total book value = 50,000 EUR)
In a reverse split, the number of outstanding shares decreases with a certain ratio.
For example:
Before the split:
Buy 5,000 units of equity
where the price of each unit = 10 EUR (total book value = 50,000 EUR)
split 5 units into 1 share
After the split:
The position is 1,000 units of equity
where the price of each unit = 50 EUR (total book value = 50,000 EUR)

•

Setup
The data used to split an equity position is defined in the instrument setup. The following
information is required to process the split:
Information

Description

Date

Date on which the split was declared or the information was entered in the instrument
setup.

Split parameters

Date of the split, the split ratio, and the action required if an Odd Lot results from the
split.

See A.2.138 Equity Split on page 779.

•

Execution
If there are no Odd Lots or, if you do not want to create an Odd Lot adjustment transaction, you
can perform the split or reverse split simply by defining the split information using the Equity
Split feature in the instrument setup (see above).
Otherwise, if any Odd Lots do result from the split or reverse split (and you do want to create
the corresponding adjustment transactions), the Split activity must be used.

Note: See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

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Each portfolio is processed separately. Based on the existing position, a new position is created
using the following rules:
Old units = Number of units in the position at the moment of the split (that
is, at the end of the day before the split date)
New units = Old units * From/To Units, rounded using the rounding parameters
specified in the feature
Odd lot = Old units – Used units
Factor = Used units / Old units
If there is an Odd Lot, a Sell transaction is created to sell the Odd Lot for the specified
compensation price (as defined in the instrument definition):
Odd lot compensation = Odd lot compensation price * Odd lot
The existing position is adjusted so that the Odd Lot compensation amount (the resulting
number of units) is now considered as new units. The book value is adjusted by the factor.
If the factor = 1, there is no Odd Lot compensation and the book value is not adjusted.

•

Cancellation
If you need to cancel or correct the split or reverse split:

–

Correct the Equity Split parameters defined in the instrument setup

–

Cancel the incorrect Odd Lot transactions, if any

–

Rerun the Split activity, if you wish to create Odd Lot adjustment transactions.

4.1.3.3 Detachment
Detachment is a corporate action that takes place typically when a shareholder receives subscription
rights in place of equity. The number of subscription rights received by the shareholder is
proportional to the number of equity units held.
If subscription rights are detached from an equity, it is also possible to transfer part of the book
value from the equity to the subscription right (when the value of the equity and the value of the
right are specified).
For example:
Before the detachment:
Buy 5,000 units of equity
where the price of each unit = 10 EUR (total book value = 50,000 EUR)
Detachment of subscription rights: 1 right per 5 shares
Market price for 1 share = 8 EUR
Market price for subscription right = 2 EUR
After the detachment:
The book value that is transferred for the original position to the new one:
50,000 EUR * (1/5) * (2/8) = 2,500 EUR
Receipt of subscription rights incurs a cost (1 EUR), therefore the following
position cashflow is added to the generated detachment transaction:
New units * Price per unit = 5,000 * (1/5) * 1 = 1,000

Note: At a later date, subscription rights can also be used to buy equity (either the same as the

original equity or different equity) at a certain price (see 4.1.3.4 Conversion on page 351).

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•

Setup
When the information about the detachment is known, the instrument definition needs to be
updated.
Information

Description

Date

Date on which the detachment was declared or the information was entered in the
instrument setup.

Detachment
parameters

Date of the detachment and the action required if an Odd Lot results from the
detachment.

Value of the Right

Values required to determine how much of the book value is transferred from the
original equity to the new one.

Value of the
Equity

See A.2.130 Equity Detachment on page 774.

•

Execution
The Detachment activity is used to calculate what the shareholder gets per share held.

Note: See the TRM User Guide for general information on running activities, and also specific
information on the Detachment activity parameters.

Each portfolio is processed separately. Based on the existing position, a new position is created
using the following rules:
Old units = Number of units in the position at the moment of detachment
(in general, this is the position at the end of the previous day)
If, for example, there is a split on the same day as the detachment, you must define whether the
detachment is processed before or after the split.
New units = Units to receive * Round(Old units / Units to sell)
rounded using the rounding parameters specified for the detachment at
instrument level
Odd units are computed as follows:
Odd lot = Old units – Units to sell * Truncate(Old units / Units to sell)
Odd lot compensation = Odd lot compensation price * Odd lot
If there is an odd lot, the compensation amount is added as a profit/loss cashflow to the
detachment transaction.
Price to pay = Price to pay per unit * New units
The price to pay is added as settlement principal to the detachment transaction.
When subscription rights are detached from an equity, it is possible to determine the book value
amount that is transferred from the equity to the subscription right, using the following
calculation:
Book value amount * (Units to receive * Value of right)/(Units to sell * Value
of equity)

•

Cancellation
You can cancel the detachment action by cancelling the detachment transactions and also the
generated cashflows in the original transaction.

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4.1 Equity

4.1.3.4 Conversion
Subscription rights can be used to purchase new shares (either the same as the original equity or
different equity) at a certain price. This corporate action is known as Conversion. Conversion can be
used, for example, in a merger where shares held in one company are converted to shares in
another company.

•

Setup
When the information about the conversion is known, the instrument definition needs to be
updated.
Information

Description

Date

Date on which the conversion was declared or the information was entered in the
instrument setup.

Conversion
parameters

Date of the conversion, the conversion ratio, and the action required if an Odd Lot
results from the conversion.

See A.2.129 Equity Conversion on page 773.

•

Execution
The Conversion activity is used to convert shares or subscription rights into new equity. The
following information is needed to run the activity:
Information

Description

Portfolio

Conversion is processed for this portfolio and all of its subportfolios.

Minimum
Transaction State

Minimum transaction state that is taken into account when the position is determined
for the conversion.

Note: See the TRM User Guide for information about how to set up activities in general.
Each portfolio is processed separately. Based on the existing position, a new position is created
using the following rules:
Old units = Number of units in the position at the moment of conversion
New units = Units to receive * Round(Old units / Units to sell), rounded using
the rounding parameters specified for the detachment at instrument level
The new position is created with the correct number of units with regard to the rounding
conventions.
Price to pay = Price to pay per unit * New units
This amount is added as settlement principal to the conversion transaction.
Factor = Units to sell * Truncate(Old units / Units to sell) / Old units
This factor determines the part of the book value that is moved from the old position to the new
converted position.
The old position is closed completely if there is no odd lot (that is, a sell transaction is generated
with the whole number of units).
The position is closed partially in the case of an odd lot. The odd lot is sold at the compensation
price. The odd lot sell transaction has the following characteristics:
Odd lot units = Old units - Units to sell * Truncate(Old units / Units to sell)
Book value = Odd lot compensation = Odd lot selling price * Odd lot units

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Cancellation

•

You can cancel the conversion by cancelling the conversion transactions.

4.1.3.5 Return of capital
Return of Capital occurs when the company pays back part of the capital to the shareholders. This
corporate action differs from a cash dividend (see 4.1.3.1 Cash dividend on page 347), because the
book value of the shares is decreased by the amount of the capital returned.
Setup

•

When the information about the return of capital is known, the instrument definition needs to be
updated.
Information

Description

Date

Date on which the return of capital was declared or the information was entered in the
instrument setup.

Return of capital
parameters

Date of the return of capital, and information required to determine the capital to be
returned.

See A.2.137 Equity Return of Capital on page 778.
Execution

•

The Return of Capital activity is used to pay back the capital to the shareholders.
Running this activity decreases the book value by the amount of capital returned (the number of
units multiplied by capital per unit). The returned capital is shown as a principal cashflow.

Note: See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

Cancellation

•

You can cancel the return of capital action by cancelling the return of capital transactions and
also the generated cashflows in the original transaction.

4.1.4 Position monitoring
In this section, numerical examples demonstrate how the different figures are calculated for an
equity instrument.
If you need more theoretical information about the method used in these calculations, see Chapter 2
Market standards and calculations on page 33.
This example shows a share, with the following deal data:
Setup

•

Data

Symbol

Valuation Method
FX Exposure Offset

Example
Quoted, to Spot

h_fx

0.01

Symbol

Example

Transaction

•

Data
Opening Date
Trading Units

352

2004-02-02
n_m

10,000

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4 Equities
4.1 Equity

Data

Symbol

Example

Deal Price

P_b

3.00

Base Book FX Rate (EUR/USD)

S_b

1.2

Value Date

d_a

2004-02-04

Currency

USD

Portfolio Currency

EUR

Other important deal data is calculated by the system as follows:
Data

Symbol

Example

Formula

Book Value (Local)

V_b

30,000.00 = 10,000 * 3.00

= n_m * P_b

Book Value

V_p

25,000.00 = 30,000.00 / 1.2

= V_b / S_b

Unless otherwise stated, the figure date used in the calculations is 2004-03-01. On this date, the
market data is as follows:

•

•

Market data on 2004-03-01
Data

Symbol

Example

Figure date

d_f

2004-03-01

Market Price

P_f

3.20

FX Conversion Rate

S

1.260000

Valuation figures

The valuation method commonly used for an equity instrument is the Par method.
Data

Symbol

Example

Formula

Local Market Value

V_l

32,000.00 = 10,000 * 3.20

= n_m * P_f

Market Value

V

25,396.93 = 32,000.00 / 1.2600

= V_l / S

Clean Market Value

V_clean

32,000 = 10,000 * 3.20 / 1.2600

= n_m * P_f / S

Note that if the instrument is not defined as being valued To Spot, Market Value will be discounted
from spot to the figure date. However, Clean Market Value will not; therefore, the Clean Market
Value figure may be different from the Market Value figure.

•

Result figures

The setup of the instrument impacts the way result figures are computed.
Data

Symbol

Example

Formula

Total Profit (Local)

P_tl

2,000.00 = 32,000.00 – 30,000.00

= V_l – V_b

MtoM Profit (Local)

P_ml

2,000.00 = 32,000.00 – 30,000.00

= V_l – V_b

FX Profit

P_fx

-1,190.48 = 30,000.00*(1/1.260000 – 1/1.20000)

= V_b*(1/S - 1/S_b)

Total Profit

P_t

396.83 = 25,396.83 – 25,000.00

= V – V_p

MtoM Profit

P_m

1,587.30 = 2,000.00 / 1.260000

= P_ml / S

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Risk figures

•

Data

Symbol

Example

Formula

FX Exposure

E_fx

253.97 = 0.01 * 25,396.83

= h_fx * V

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Chapter 5

Security lending

5.1 Repurchase agreement
In a repurchase agreement (repo), one party sells a security to another party with the agreement to
repurchase the same security at a fixed future date and at an agreed price.
In essence, the seller of the security is borrowing the amount received from the sale and placing the
sold securities with the purchaser as collateral.
The difference between the sale price of the security and the cost of repurchase is, in effect, interest
charged to the borrower. The period of time between the sale and the repurchase is called the repo
period.
Physical transfer of the security from the custody of the borrower to the custody of the lender
usually takes place, but in the case of overnight repos, for example, there may be no transfer. If the
security does not physically change hands, the buyer of the security is exposed to a higher credit
risk.
Underlying a repo transaction is usually a fixed-rate government bond or discount paper. Collateral
delivered against the cash in a repo transaction can be in a single (single-collateral repo) or in
multiple (multi-collateral repo) underlying instruments. These collateral instruments must be
defined with the feature Collateral in order to be available as collateral, see 5.1.4 Collateral on page
365. TRM also allows you to use cash as collateral. To do so, you must define cash collateral account
instruments, see 5.1.7 Cash Collateral on page 376. You can use both collateral instruments and
cash collateral instruments for margin movement transactions.
Margin movements are required when the exposure exceeds the threshold defined in the collateral
agreement (Margin page). You must set up specific margin movement instruments to handle this
type of situation, see 5.1.6 Margin movement on page 370.
In some situations, you may need to substitute a collateral instrument for another during the
lifetime of a repo transaction. You must set up specific substitution instruments for this event, see
5.1.5 Substitution on page 366. To enable substitution, you need to set up the conditions for
substitution in the collateral agreement (Substitution page). See TRM User Guide for more
information about collateral agreements.
Repos are driven either by the need to lend or borrow cash, or the need to borrow a specific
security.

5.1.1 Repo (classic)
The following information is relevant to any kind of repo. If you want to setup a Buy/sell back repo
see 5.1.2 Buy/sell back and sell/buy back on page 362.

5.1.1.1 Instrument setup
Repo instruments must be based on an instrument type derived from the class REPO.

•

Repo main characteristics

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This information may be relevant to any kind of repo instrument.
Information
Currency

Description
Currency of the repo deal.
Leave this field blank if you want to specify the currency of the repo
transaction when you enter the deal.

Transaction Sign

Interest Type
Date Basis

Sign to be applied to the transaction: Reverse Repo (Buy/Lend) or Repo
(Sell/Borrow).
•

Select either Repo or Reverse Repo if you want this to be the default
direction of the transaction, that is, the direction cannot be modified at
deal entry.

•

Leave this field blank if you want to specify the direction of the repo deal at
deal entry.

Type of interest rate used to calculate the repo interest amount, for example,
Periodic Rate.
Date basis used to calculate the interest of the repo.
If this is not defined at instrument level, the date basis of the currency is used
unless you provide another date basis at deal entry.

Amount Rounding
parameters

Method used to round cashflow amounts of the repo.

Principal Cashflow Type

Type of repayment cashflow (for example, Principal or Expiration).

Interest Cashflow Type

Type of interest cashflows.

Collateral Calculation
Method

Calculation method defaulted to transaction column Collateral Calculation
Method of new transactions in repo instrument and applied when collateral
amount of a collateral entry in a repo transaction is manually updated.
•

Single: Select Single, if you want the system to keep settlement amount of
the collateral and recalculate collateral market price to match the new
collateral amount, This method can only be used in single collateral repo
transaction.

•

Multiple: Select Multiple, if you want the system to keep the collateral
market price of the collateral and recalculate settlement amount to match
the new collateral amount. This method allows you to enter multiple
collateral to a repo transaction.

Note: The Collateral Calculation Method always defaults to Multiple in
substitution and open margin transactions, but can be manually set to
Single.
Switches

•

Use Dirty Price: Switch on to define that the Collateral Price/Maturity
Collateral Price should be expressed as the dirty price. This information is
displayed at transaction level as Dirty Collateral Price.

•

Use Collateral Price Rounding: Switch on to define that Collateral Price and
Maturity Collateral Price are rounded using the rounding parameters of the
underlying collateral instrument. If this switch is not on, collateral prices
are always calculated exactly. If the feature Repo Rounding is used, the
rounding parameters are taken from the rounding setup of the collateral
instrument (see A.2.280 Repo Rounding on page 854). Otherwise, the
rounding parameters are taken from Trading Yield setup of the collateral
instrument (see A.2.323 Trading Yield on page 872).

See A.2.283 Repurchase Agreement on page 854.

•

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5.1 Repurchase agreement

It is possible to set up maturity information at instrument level.
Information

Description

Calendar parameters

Calendars used to calculate the maturity date.

Gap Set

Gap set used for supplying the available maturity periods.

Maturity Date Period

If defined, this maturity period is applied to each transaction.

See A.2.230 Maturity Date Setup on page 827.

•

Collateral agreement definition
It is possible to set up collateral agreement to be used in transactions at instrument level.
Information

Description

Agreement

The collateral agreement you want to use in the repo transactions.
•

If defined, this collateral agreement is defaulted to all new transactions.
The defaulted agreement can be changed to any other valid collateral
agreement in Transaction Manager.

•

If not defined, collateral agreement is defaulted according to collateral
agreement setup given in Client Editor for the owner of the transaction.

For more information about the setup of a collateral agreement at the
client-level, see TRM User Guide.

See A.2.95 Collateral Setup on page 756.

•

Collateral Quote defaulting
If feature Quote Default (Collateral) is selected for a repo instrument, the current market price
or yield is automatically defaulted according to the setup of the feature to fields collateral market
price or collateral market rate of a new collateral entry in a repo transaction as soon as a new
collateral instrument has been selected.
Information

Description

Scenario

Scenario to use to price the transactions.

Mode

Pricing mode:

Method

•

Select Automatic if you want to retrieve the quotes automatically in Transaction
Manager.

•

Select Manual if you want to retrieve the quotes manually in Transaction
Manager.

Defaulting method: Ask, Bid, Buy/Sell, or Mid.
If you select Buy/Sell: when the transaction sign is positive the Ask price is used,
and when the transaction sign is negative, the Bid price is used.

See A.2.270 Quote Default (Collateral) on page 847.

•

Repo Cash Delivery definition
This feature sets all non-delivery cashflows of a repo transaction with the attribute Not Payable
and creates a separate cash delivery flow corresponding to a delivery flow for each collateral
instrument. Concretely, the total settlement and maturity amounts on value date and maturity
date of the repo, respectively, are split by collateral instrument for settlement purposes. As cash
delivery flows have corresponding collateral instrument as leg instrument of the flow, these
flows can be identified by leg instrument in rules. This enables the setting of cash settlement
instructions correctly when they are dependent on collateral instruments. The splitting of
settlement amounts by collateral instrument also enables delivery versus payment (DvP)
settlements to be generated from multi-collateral repos.

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See A.2.277 Repo Cash Delivery on page 853.
It is also possible to set up:

•

Spot day and value date calculations

•

Manual charges

•

Cashflow and transaction charge rules

•

Branch codes.

See Appendix A Features on page 713.

5.1.1.2 Deal capture
Repo transactions can be entered in a cash-driven or collateral-driven manner depending on if the
transaction is initially agreed with the counterparty for a specific cash amount against any
acceptable collateral or for a specific amount of particular collateral.

5.1.1.2.1 Input data – cash amount
In addition to the standard deal parameters, the following information is required if you want to
trade cash versus general collateral.

•

Transaction view
Information
Currency

Description
Currency of the repo deal.
If the currency is not defined at instrument level, it can be specified separately
for each transaction.

Maturity Date

Date when the repo deal matures.

Maturity Code

•

If you enter a maturity code, the date is calculated automatically;
otherwise you can enter the date manually.

•

(Information only.) If the maturity definition parameters are defined at
instrument level, these are used by default.

Nominal Amount

Cash amount of the repo.

Deal Rate

Repo rate (expressed as a percentage) used to calculate the repo interest
(cash).

Date Basis

Date basis of the repo deal.
If the date basis is not defined at instrument level, it can be specified
separately for each transaction.

Collateral Agreement

Collateral Agreement of the repo deal.
If the agreement is not defined at instrument level, it defaults according to
collateral agreement definition given in Client Editor for the owner of the
transaction. You can change the default agreement to any other collateral
agreement as long as it is valid for the counterparty of the repo.
Collateral agreement specifies various conditions applied for the repo
including:
•

Collateral Valuation Currency

•

Collateral Requirement calculation

•

Cover Haircut of the repo

•

Total Collateral Haircut

•

Eligible collateral

•

Collateral Substitution

•

Margin calls and returns

See TRM User Guide for more information about the Collateral Agreement
Editor.

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•

Repo view
In this view, you can add collateral to the repo transaction by using the New Collateral action.
Information

Description

Collateral
Instrument

Instrument (bonds, discount papers, and additionally cash collateral account) to be
used as collateral. Only instruments with the Collateral feature (A.2.93 Collateral on
page 755) attached and not flagged as ineligible in Collateral Haircut definition of the
selected collateral agreement are available for selection.
For information about the collateral instrument setup, 5.1.4 Collateral on page 365.

Collateral Market
Price

Market price of the collateral instrument. This price can be defaulted by the system
when the feature Quote Default (Collateral) is used.
See A.2.270 Quote Default (Collateral) on page 847.

The system calculates the required amount of collateral automatically based on the above
transaction and repo attributes as well as the following:

–

Cover Haircut of the repo.

–

Total Collateral Haircut.

These are assigned automatically by the system according to the selected collateral agreement.
The calculated collateral amount or collateral units is rounded up to the closest deliverable
amount/units using minimum bid size or trading units definition of the collateral instrument.
If the multiple collateral are delivered against cash, the Collateral Calculation Method must be
set to Multiple at the transaction level and the collateral amount or collateral units of the first
collateral must be manually adjusted down to the correct amount/units before adding a new
collateral in Repo view by using the New Collateral action.
If the Collateral Calculation Method is set to Single before adjusting down collateral amount, the
system recalculates collateral market price to match settlement amount of the collateral and the
new collateral amount, instead of recalculating the settlement amount. Adding new collateral
after that will not be possible because the transaction is already fully collateralized.

Note: Manually changing the collateral calculation method of the transaction at any time will
always affect the calculations of the last collateral of the transaction.

When a collateral instrument is selected, the eligibility of the selected instrument is validated
against the selected collateral agreement.

5.1.1.2.2 Input data - collateral amount
If you want to trade a specific amount of a security against cash, then the nominal amount of the
transaction is not given. Unlike a cash-driven scenario where you only have to enter the collateral
instrument and collateral market price, in a collateral-driven scenario, you must also give collateral
instrument, collateral market price and collateral amount. Based on this information, the system
calculates automatically correct nominal amount for the transaction., using collateral price rounding
if the repo instrument is set up with switch Use Collateral Price Rounding.
As long as nominal amount of the transaction has not been manually given, the system continues to
treat the transaction as a collateral-driven one and updates the nominal amount according to
collateral attributes that you provided.

5.1.1.3 Processing
This section describes the actions that can be done throughout the life of a repo transaction.

5.1.1.3.1 Roll over
You can defer the maturity of a repo transaction to a later date. This process is called a rollover.

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•

Setup
The feature Allow Roll Over (repo) enables repo transactions to be rolled over. Repo transactions
can be rolled over in a similar manner to short-term loans.

•

See A.2.13 Allow Roll Over (repo) on page 719.

•

Execution
Rollover of a repo is always collateral-driven in that any partial rollovers are identified by
adjusting down the collateral amount of one or several collaterals of the maturing repo.
Rollover transactions are created by executing the Roll Over action from an outstanding repo deal
in Transaction Manager or Collateral Valuation Board. Rollover is available if the remaining
collateral amount of at least one of the collateral instruments is greater than zero. This action
can be triggered from the following places:

–

Transaction Manager - Transaction view (for all collaterals of the transaction)

–

Transaction Manager - Repo view (for a specific collateral)

–

Collateral Valuation Board - Collateral Position view (for all collaterals of the transaction). See
TRM User Guide for more information.

Rollover transactions are created by executing the Roll Over action from an outstanding repo deal
in Transaction Manager or Collateral Valuation Board. Rollover is available if the remaining
collateral amount of at least one of the collateral instruments is greater than zero. This action
can be triggered from either of the following places:

–

Transaction Manager - Transaction view (for all collaterals of the transaction)

–

Transaction Manager - Repo view (for a specific collateral)

–

Collateral Valuation Board - Collateral Position view (for all collaterals of the transaction)

Required input for the rollover is given in the Roll Over dialog but can be modified or completed in
Repo view of Transaction Manager in the new row created by the action.
When the action is selected from the right-click action, the system opens one of two dialogs
depending on whether single or multiple maturing collateral instruments are affected by the
rollover. Note, that all previous collateral substitutions are taken into account when the system
identifies collateral for the roll-over transaction. This means that the roll-over collateral is not
necessarily the same as the original collateral of the repo being rolled over.
If the action is executed from Transaction view of Transaction Manager and multiple collateral
instruments with remaining collateral amount greater than zero are found, you must capture the
following information:
Information

Description

Opening Date

Opening date of the rollover transaction.
Defaulted to the current date or if given before selecting the action, as
fixing/action date of the underlying transaction.

Value Date

(Information only.) Value date of the rollover transaction.
Defaulted to the opening date adjusted with spot days of the repo instrument.

Roll over Method

(Mandatory) Method used for the rollover.
Defaulted according to the select default method at instrument-level, but can
be modified to any of the other methods if these are not identified as
excluded.

Gap

Gap used to calculate new maturity date from value date of the rollover.
If the maturity gap is identified in the maturing repo, the same gap is
defaulted to the rollover as well, but can be modified to any other gap.

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Information

Description

Maturity Date

Maturity Date of the rollover.
The maturity date is calculated by the system based on value date and
selected the maturity gap, but can be modified to any other valid date.

Deal Rate

Repo rate of the rollover.
Defaulted to the deal rate of the maturing repo, but can be modified to any
other rate.

Re-Price Collateral

If set the collateral of the repo transaction is re-priced using the market price
at the time of the rollover to calculate the cash amount of the rollover. The
difference between the maturing cash amount of the repo and new cash
amount of the rollover is settled as part of the maturity settlement of the
maturing repo and included in the nominal amount of the rollover.
This is defaulted according to corresponding setup in the repo instrument but
can be manually set/cleared in the dialog.

If only one collateral instrument with a remaining collateral amount greater than zero is found,
the dialog contains the following additional fields:
Information

Description

Collateral Instrument

(Information only.) Collateral instrument of the maturing collateral.

Collateral Amount

Collateral amount of the maturing collateral.
Defaulted to the remaining collateral amount, but can be modified to any
amount that does not exceed the remaining amount.

Collateral Units

Units of the maturing collateral if the collateral instrument is set up with
trading units.

Collateral Market Rate

Current market yield of the collateral instrument, if Re-Price Collateral is used.

Collateral Market Price

Current market price of the collateral instrument, if Re-Price Collateral is used.

All deliveries of rolled-over collateral (as well as settlements of maturing principal) are always
deferred to the maturity date of the rollover. The various rollover methods available in the dialog
reflect different treatments of maturing interest in the rollover. Each method can be used with or
without Re-Price Collateral, resulting in an additional cash settlement that reflects the difference
between original and current value of the rolled-over collateral, increasing or decreasing the
nominal amount of the rollover transaction accordingly. The following methods are supported:
Method

Description

Settle Interest

The interest of the maturing repo transaction is paid at the initial maturity
date.
The nominal amount of the rolled over transaction is equal to the principal
cashflow of the initial transaction according to the collateral amount of the
rollover (i.e. if half of the maturing collateral is rolled over, the nominal
amount is half of the principal) adjusted up or down when Re-Price Collateral is
used.

Delay Interest

The interest of the maturing repo transaction is deferred to the new maturity
date of the rollover.
The nominal amount of the rolled over transaction is equal to the principal
cashflow of the initial transaction according to the collateral amount of the
rollover adjusted up or down when Re-Price Collateral is used.

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Method

Description

Compound Interest

The interest of the maturing repo transaction is deferred to the new maturity
date of the rollover, and the new interest of the rollover transaction is
calculated based on the total of the nominal amount and deferred interest.
The nominal amount of the rolled over transaction is equal to the principal
cashflow of the initial transaction according to the collateral amount of the
rollover adjusted up or down when Re-Price Collateral is used.

Capitalize Interest

The interest of the maturing repo transaction is capitalized to the principal of
the rollover transaction, and the new interest of the rollover transaction is
calculated from the nominal amount including capitalized interest.
The nominal amount of the rolled over transaction is equal equal to the total of
principal and interest cashflows of the initial transaction according to the
collateral amount of the rollover adjusted up or down when Re-Price Collateral is
used.

Accepting the dialog creates a new rollover transaction, if necessary, you can finalize this
rollover transaction in the Repo view of Transaction Manager.
If the action was executed from Transaction view of Transaction Manager for more than one
maturing collateral instruments, you can modify the defaulted collateral amount or units of each
collateral to a smaller value in the event of a partial rollover, or delete one or several of the
maturing collaterals to restrict the rollover to a subset of collaterals. If Re-Price Collateral was
used, you can also adjust the defaulted collateral market prices.

•

Cancellation
You can undo the roll-over by canceling the roll-over transaction.

5.1.2 Buy/sell back and sell/buy back
Sell/buy backs and buy/sell backs are similar to classic repos and reverse repos respectively. With
sell/buy backs and buy/sell backs, however, the coupon that is payable during the repo term and
received by the buyer of the bond is not immediately transferred to the seller, as in a classic repo or
reverse repo, but paid back at the end of the repo term, compounded by the repo rate.
5.1.1 Repo (classic) on page 355.

5.1.2.1 Instrument setup
A buy/sell back (and sell/buy back) instrument is set up in the same way as a normal repo
instrument (see 5.1.1 Repo (classic) on page 355) with the following additional attributes:

•

Repo main characteristics
Information

Description

Switches

•

Reinvest Coupon: Switch on for a buy/sell back where the coupon is received by the
buyer of the bond and only paid back at the end of the repo.

This information is displayed in the Reinvest Coupon column in Transaction Manager’s
Transaction view.

See A.2.283 Repurchase Agreement on page 854.

5.1.2.2 Deal capture
•

Input data
Buy/sell back (and sell/buy back) deals are captured in a similar way to collateral-driven repo
deals (see 5.1.1.2 Deal capture on page 358). The following additional fields may also be used at
deal entry.

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–

Transaction view
Information

Description

Reinvestment Rate

Rate used to reinvest the coupon.
By default, this is the same as the repo rate (i.e Deal Rate of the transaction)
but can be set manually to a different rate.

5.1.3 Floating Repo
A floating repo is like a classic repo except that the single interest payment (which is payable at repo
maturity) is not agreed up front as with a normal repo but is fixed in arrears at the end of the repo
period. In all other aspects, the transaction is like a normal classic repo.

5.1.3.1 Instrument setup
The setup for a floating-repo instrument is, for the most part, identical to that of a normal fixed-rate
repo instrument. The differences are described below.
Floating-repo instruments must be based on an instrument type derived from the class
REPO-FLOATING.

•

Main characteristics
In addition to the standard information that applies to any repo instrument (provided in the Repo
page), you can define the floating characteristics of the instrument in the Floating Repo page.
Information

Description

Interest Method

Interest calculation method that controls which expression is used in the
floating interest cashflow of the transaction. The following methods are
available:
•

Average: The expression 'average' is used to support the calculation of the
interest rate as an average of daily observations during the interest period.

•

Average (Business Days): The expression 'average_q' is used to support
the calculation of the interest rate as an average of daily observations
during the interest period using quotations on business days only.

•

Compound: The expression 'compound' is used to support the calculation
of the interest rate as a compund rate using daily observations during the
interest period.

•

In Arrears: The expression 'ir+spread' is used to support the calculation of
the interest rate using a single observation at the end of the interest
period.

Fixing Rate

IR Quote reference used when fixing the cashflow.

Fixing Period

Tenor from which the quotation is retrieved when fixing the interest rate of the
transaction, for example, O/N or 1M.

Fixing Subscenario

Rate subscenario from which the interest rate is retrieved.

Fixing Offset

Number of business days before the interest date.
Fixing of interest occurs on this date. If the fixing offset is set to anything
other than 0 when average/compound interest methods are used, the
quotation of the fixing date is used for all dates between the fixing date and
the interest date.

Fixing Calendar

Calendar used for fixing.

See A.2.284 Repurchase Agreement (Floating) on page 856.

•

Repo cash delivery (floating) definition

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The feature Repo Cash Delivery (Floating), like the feature Repo Cash Delivery for fixed-rate
repos, sets all non-delivery cashflows of a repo transaction to Not Payable and creates a separate
cash delivery flow corresponding to a delivery flow for each collateral instrument. The difference
between the two features is that in floating-rate repos, cash delivery flows are only created for
the value date of the repo when the transaction is captured. Corresponding flows for the
maturity date are created by the Fixing action executed on the fixing date of the interest
cashflow.
See A.2.278 Repo Cash Delivery (Floating) on page 853.

•

Repo valuation (floating) definition
The normal valuation setup options used in floating loans are available in floating-repo
instruments too. In particular, it is important to select the correct risk profile after selecting the
feature Valuation Setup (Floating). For information on risk profiles see 2.3.4.8 Risk profiles on
page 124.
See A.2.338 Valuation Setup (Floating) on page 879.

5.1.3.2 Deal capture
Floating repo transactions are entered in the same way as fixed-rate repos with the few exceptions
described below.

5.1.3.2.1 Input data
In addition to the standard deal parameters and repo specific parameters described earlier (see
5.1.2.1 Instrument setup on page 362), the following information is required if you want to trade a
floating-rate repo.

•

Transaction view
Information

Description

Deal Rate

The Deal Rate of a floating-rate repo is the spread over or under the reference
given as basis points.
For example, 2.50 is interpreted as a spread of 0.025%. The value given in
this field is propagated to the Spread field of the interest cashflow. This field is
mandatory.

Fixing Rate

IR Quote reference used when fixing the cashflow.
This field is automatically populated if the Fixing Rate is given at instrument
level. If not, any valid IR Quote with usage Fixing can be given for the
transaction.
This field is mandatory.

Fixing Period

Tenor from which the quotation is retrieved when fixing the interest rate of the
transaction, for example, O/N or 1M.
This field is automatically populated if the Fixing Period is given at instrument
level. Otherwise, any valid tenor in the identified Fixing Rate can be given for
the transaction. This field is mandatory.

Fixing Subscenario

Rate subscenario from which the interest rate is retrieved.
This field is automatically populated if the Fixing Subscenario is given at
instrument level. Otherwise, any valid subscenario can be given for the
transaction. If nothing is given, the system uses the default subscenario.

Fixing Offset

Number of business days before the interest date.
This field is automatically populated if the Fixing Offset is given at instrument
level. Otherwise, any number of business days can be given in the field. If
nothing is given, 0 is used by the system and the Fixing To date of the floating
interest cashflow is always set to the Maturity Date of the transaction.

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Information

Description

Fixing Calendar

Calendar used for fixing.
This field is automatically populated if Fixing Calendar is given at the instrument
level. Otherwise, any valid calendar can be given for the transaction. If
nothing is given, the calendar of the currency of the transaction is used when
setting the fixing date for the floating interest cashflow.

5.1.3.3 Processing
This section describes the different actions that can be done throughout the life of a floating-rate
repo transaction as opposed to a fixed-rate repo transaction.

5.1.3.3.1 Interest fixing
Like for a floating-rate loan, the amount of each interest flow in a floating repo transaction has to be
determined before it is paid: this process is known as fixing. Fixing is done in exactly the same way
as for a floating loan transaction.
When fixing is executed for a floating repo transaction with an instrument with feature Repo Cash
Delivery (Floating), the system also creates Cash Delivery flows required for maturity date settlement.
This cannot be done before fixing because the final cash settlement amount on the maturity date is
not known.
See 3.10.2.3.1 Interest fixing on page 339 for more information.

5.1.3.3.2 Roll over
Floating repo transactions can be rolled over in the same way as fixed-rate repos but with two minor
differences:
1. The Rollover action is only available for a floating repo transaction after it has been fixed. This is
because the final interest payment at the maturity of the original floating-repo transaction must
be known before the rollover can be successfully processed.
2. In the same way as in the capture of a new floating repo transaction, the Deal Rate of the rollover
given in the Rollover action dialog is interpreted as a spread over or under the fixing reference as
basis points and passed to the Spread field of the floating interest cashflow of the new rollover
transaction.
See 5.1.1.3.1 Roll over on page 359 for more information.

5.1.4 Collateral
Some instrument setup affecting repo transactions is made directly in the collateral instruments
instead of the repo instrument. You can define the following instruments as collateral instruments
available for repo transactions:

•

Bonds: 3.1 Bond on page 215.

•

Discount papers: 3.9 Discount paper on page 316.

•

Floating Rate Notes (FRNs): 3.1.2 Floating rate note on page 228.

To use these instruments as collateral, you must ensure that they are properly set up with feature
Collateral, see A.2.93 Collateral on page 755.
Additionally, you can define the following instruments to support using cash as margin collateral in
repo operations:

•

Cash collateral account: 5.1.7 Cash Collateral on page 376.

5.1.4.1 Instrument setup
•

Main characteristics

–

Trading Units definition

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Smallest possible denomination of the security that can be delivered under a (Repo)
transaction in the market can be identified in Trading Unit setup of the collateral instrument.
Information

Description

Trading Units

If the instrument is traded in units, the size of one unit is given here (for
example, 10,000.00).
Units definition should only be used if the instrument is structured in
units. This setup should not be made only to indicate the smallest
deliverable denomination since trading units definition makes all cashflow
calculations (for example, interest amounts) to be first made for one unit
of instrument and then multiplied by the number of units of the
transaction, instead of calculating the amounts for the full nominal
amount of the transaction directly.

Minimum Bid Size

If the instrument is traded and delivered in nominal amount instead of
units, the smallest deliverable denomination can be given as Minimum Bid
Size (for example, 10,000.00).
Minimum Bid Size has no impact on cashflow calculations, only on
rounding of nominal amount (transactions traded directly in the
instrument) and collateral amount (repo transactions using the instrument
as collateral).
Note that only one of the definitions can be given for any given instrument
(either Trading Units or Minimum Bid Size).

Refer to the relevant primary feature.

•

Collateral definition
This feature identifies the instrument as a valid collateral to be used in repo transactions.
See A.2.93 Collateral on page 755.

•

Repo rounding feature
This feature allows you to define the pricing precision to be used in repo transactions for the
collateral instrument. If defined, this setup overrides the rounding parameters of the instrument
specified with the Trading Yield feature (unless Use Bond Rounding has been set in the repo
instrument) when collateral price and collateral maturity price are calculated in repo
transactions.
Information

Description

Price rounding
parameters

Rounding used for collateral price.

Maturity price rounding
parameters

Rounding used for maturity collateral price.

This can be specified at deal entry in the Repo view.

This can be specified at deal entry in the Repo view.

See A.2.280 Repo Rounding on page 854.

5.1.5 Substitution
Collateral substitution takes place when existing collateral that is held or given against a repo
exposure is partially or fully substituted against new collateral.
The return of the existing collateral and receipt of the new collateral can be settled free or versus a
cash payment. If delivery versus payment is used, the cash amount to be settled against the
delivery of securities can be either the initial amount of cash that was originally settled against the
delivery of existing collateral or the value of original collateral at the time of substitution. In both
cases, the same amount of cash is used in the delivery of both collateral instruments. The net cash
effect is zero but both deliveries take place as DvP (Delivery versus Payment).

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The value of original collateral to be substituted is used to calculate required amount of new
collateral. Either initial value of the substituted collateral in the repo transaction or the current value
of it at the time of substitution can be used as a basis for this calculation. The method used is
specified at collateral agreement level by identifying the substitution method to be used in the
agreement. If no method has been identified in a collateral agreement, substitutions are not allowed
for any repos in it.
The substitution is modeled with an independent action transaction created from the original repo.
The substitution transaction is not created in the original repo instrument but a separate substitution
instrument is used instead.

5.1.5.1 Instrument setup
Substitution instruments must be based on an instrument type derived from the class
SUBSTITUTION.

•

Main characteristics
Substitution features use the primary feature Substitution (see A.2.306 Substitution on page
865). Substitution instruments do not require any specific set up.

•

Collateral Quote defaulting
This feature can also be used in a substitution instrument to make the system automatically
default current market price or yield according to the setup of the feature for both old (if
substitution method Current Value is used) and new collateral in a substitution transaction.
See A.2.270 Quote Default (Collateral) on page 847.

•

Repo Cash Delivery definition
The feature Repo Cash Delivery (Substitution) must be used in substitution instruments when
delivery-versus-payment settlements are required on the value date of the substitution.
Typically, a substitution instrument with this feature is used if the repo instrument of the
transaction from which the substitution transaction is created uses feature Repo Cash Delivery.
This feature creates a separate Cash Delivery flow corresponding to a delivery flow in each
collateral instrument on the value date of the substitution. As in a repo, the total settlement
amount on the value date of the substitution is split by the collateral instrument for settlement
purposes.
See A.2.277 Repo Cash Delivery on page 853.

It is also possible to set up:

•

Spot day calculations

•

Manual charges

•

Cashflow and transaction charge rules

•

Branch codes.

See Appendix A Features on page 713.

5.1.5.2 Deal capture
5.1.5.2.1 Input data
Substitution transactions are always created by executing a Substitution action from an outstanding
repo or earlier substitution deal. This action can be triggered from one of the following places:

•

Transaction view of Transaction Manager (for all collaterals of the transaction).

•

Repo view of Transaction Manager (for a specific collateral).

•

Collateral view of Collateral Valuation Board (for a specific collateral).

When the action is triggered from Transaction view of Transaction Manager, any number of existing
collateral holdings can be substituted in the same substitution action from a multi-collateral repo. In

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the other two views, this action is executed from a specific collateral holding and only that collateral
is substituted. In all cases, old collateral can be substituted for new collateral in one or several
collateral instruments.

5.1.5.3 Processing
This section describes the actions that can be done throughout the life of a repo transaction.

5.1.5.3.1 Substitution
Substitution action is available if the remaining collateral amount of at least one of the collateral
instruments is greater than zero and if the collateral agreement of the transaction allows
substitutions. Required input data for the substitution is given in the action dialog and in the new
transaction created by the action in the Repo view of Transaction Manager.

•

Setup
The collateral agreement defines whether the Substitution action is enabled (Collateral Agreement
Editor - Substitution page).
See the TRM User Guide for more information about collateral agreements.

•

Execution
When the Substitution action is selected from the right-click menu, the system opens one of two
dialogs depending on whether single or multiple old collateral instruments are affected by the
substitution.
If the action is executed from Transaction view of Transaction Manager and multiple collateral
instruments with remaining collateral amount greater than zero are found, you must provide the
following information.
Information

Description

Opening Date

Opening Date of the substitution transaction.
This is defaulted as current date or, if given before selecting the action, as
fixing/action date of the underlying transaction.

Value Date

Value Date of the substitution transaction.
This is defaulted as opening date adjusted with spot days of the substitution
instrument identified in the collateral agreement of the underlying transaction.

Substitution Method

Method used to calculate the value of substituted collateral.
This is defaulted as the method identified in the Collateral Agreement of the
underlying transaction as one of the following:
•

Original Collateral Value
Original value of old collateral in the underlying transaction is used to
calculate required amount of new collateral

•

Current Collateral Value
Current value of old collateral calculated by using the latest available
collateral market price is used to calculate required amount of new
collateral.

If only one collateral instrument with the remaining collateral amount greater than zero is found,
the dialog contains the following additional fields.
Information

Description

Substitution Collateral

(Information only.) The collateral instrument of the old collateral.

Amount

Amount of old collateral.
This is defaulted to the full remaining collateral amount but can be modified to
any smaller amount.

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Information

Description

Units

Units of old collateral if collateral instrument has been set up with trading
units.

Market Rate

This field is used to identify current market yield of the collateral instrument if
the substitution method Current Collateral Value is used.

Market Price

This field is used to identify current market price of the collateral instrument if
the substitution method Current Collateral Value is used.

Accepting the dialog creates a new substitution transaction which must be completed by adding
the new collateral delivered against the substituted collateral in Repo view of Transaction
Manager.

–

If the action is executed from Collateral Valuation Board, a Transaction Manager application
in which the substitution transaction is created is opened automatically.

–

If the action is executed from Transaction view of Transaction Manager for more than one old
collateral instrument, you can modify defaulted collateral amount/units of each collateral to a
smaller value in case of a partial substitution, or delete one or several of the old collaterals to
restrict the substitution to a subset of collaterals. If the substitution method Current Collateral
Value is used, you can also adjust defaulted collateral market prices of old collaterals. After
this, you can add the first new collateral using the New Collateral action. When the first new
collateral is added, the old collateral is frozen and can no longer be modified.

–

If the action was executed for a single old collateral instrument, the system freezes the old
collateral and creates the first new collateral automatically.

After the first new collateral has been manually or automatically created, you can finalize the
transaction by giving the details of new collateral delivered against the substituted collateral as
follows:
Information

Description

Collateral Instrument

Instrument (bonds, discount papers, and additionally cash collateral account)
to be used as collateral. Only instruments with the Collateral feature (A.2.93
Collateral on page 755) attached and not flagged as ineligible in collateral
haircut definition of the selected collateral agreement are available for
selection.
For information about the collateral instrument setup, 5.1.4 Collateral on page
365.

Collateral Market Price

Market price of the collateral instrument. This price can be defaulted by the
system when the feature Quote Default (Collateral) is used.
See A.2.269 Quote Default (Collateral) on page 673.

Collateral Amount

Amount of the collateral.

Collateral Units

Number of units of the collateral if collateral instrument has been set up with
Trading Units.

When new collateral is added to a substitution transaction, it behaves like a cash-driven repo
transaction. The system sets the nominal amount of the transaction as the value of old collateral
and automatically calculates the required collateral amount/units of new collateral based on
collateral market price as soon as the collateral instrument has been selected.

Note: The Collateral Calculation Method always defaults to Multiple in substitution transactions,

but it can be manually set to Single to affect calculations resulting from a manual
adjustment of collateral amount in the last new collateral of the substitution transaction in
the same manner as in a cash-driven repo transaction.

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5.1.6 Margin movement
A margin movement transaction (a margin call) is required when exposure exceeds the threshold
defined in a collateral agreement and an additional deposit of collateral is required.

Note: Managing collateral is described in the TRM User Guide.

5.1.6.1 Instrument setup
Margin movement instruments must be based on an instrument type derived from the class
MARGIN-MOVEMENT.

•

Main characteristics
Margin movement instruments do not require any specific set up. They are simply recognized by
the following feature in the Margin Movement instrument class:

–
•

The primary feature Margin-Movement (see A.2.229 Margin Movement on page 827).

Collateral Quote defaulting
If feature Quote Default (Collateral) is selected for a margin instrument, current market price or
yield is automatically defaulted according to the setup of the feature to fields collateral market
price or collateral market rate of a new collateral entry in a margin transaction as soon as a new
collateral instrument has been selected.
See A.2.270 Quote Default (Collateral) on page 847.

•

Collateral Agreement definition
It is possible to set up collateral agreement to be used in transactions at instrument level.
Information

Description

Agreement

If defined, this collateral agreement is defaulted to all new transactions. The
defaulted agreement can be changed to any other valid collateral agreement
in Transaction Manager.
If not defined, collateral agreement is defaulted according to collateral
agreement setup given in Client Editor for the owner of the transaction.

See A.2.95 Collateral Setup on page 756.
It is also possible to set up:

•

Spot day calculations

•

Manual charges

•

Cashflow and transaction charge rules

•

Branch codes.

See Appendix A Features on page 713.

5.1.6.2 Deal capture
Margin movements can be made for an indefinite maturity against overall exposure of a
counterparty under a specific collateral agreement (Open Margin) or for the remaining maturity of a
specific repo transaction against the exposure of that particular repo (Margin).

5.1.6.2.1 Input data - Open Margin
Open Margin transactions are independent new transactions that can be captured in Transaction
Manager or through the Open Margin Movement action in Collateral Position view of Collateral Valuation
Board.

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Capturing an open margin transaction directly in Transaction Manager is very similar to capturing a
new repo transaction. Margin movements are normally made to deliver a specific value of collateral
required to bring the total value of collateral in balance with the value of underlying exposure it is
securing. Consequently, transactions are typically entered in a cash-driven manner where the target
value of margin collateral is given as nominal amount of the transaction before identifying the
collateral. It is also possible to enter an open margin transaction in a collateral-driven manner.
In addition to the standard deal parameters, the following information is required, if you want to
capture a margin call directly in Transaction Manager.

•

Transaction view
Information

Description

Nominal Amount

Value of the margin collateral.
If the nominal amount is not given, the system automatically calculates it
based on collateral amounts and collateral market prices of the selected
collateral instruments.

Collateral Agreement

Collateral agreement of the margin call.
If the agreement is not defined at the instrument level, it is defaulted
according to collateral agreement definition given in Client Editor for the
Owner of the transaction. You can change the default agreement to any other
valid collateral agreement for the counterparty of the repo.
Collateral agreement specifies various conditions applied for the margin call
transaction including:

•

•

Currency

•

Total Collateral Haircut

•

Eligible collateral.

Repo view
In this view, you can add collateral to the open margin transaction by click New Collateral from the
right-click menu.
Information

Description

Collateral
Instrument

Instrument (bonds, discount papers, and additionally cash collateral account) to be
used as collateral. Only instruments with the Collateral feature (A.2.93 Collateral on
page 755) attached and not flagged as ineligible in Collateral Haircut definition of the
selected collateral agreement are available for selection.
For information about the collateral instrument setup, 5.1.4 Collateral on page 365.

Collateral Market
Price

Market price of the collateral instrument. This price can be defaulted by the system
when the feature Quote Default (Collateral) is used.
See A.2.270 Quote Default (Collateral) on page 847.

Collateral Amount

Amount of collateral
If the nominal amount was given in the transaction, the system calculates the
required amount of the collateral automatically based on the above transaction and
repo attributes, as well as valuation haircut of the collateral instrument assigned
automatically by the system according to the setup of the selected collateral
agreement.
If multiple margin collateral is delivered against a target value identified in nominal
amount of transaction, the collateral amount of the first collateral must be manually
adjusted down to the correct amount before adding a new collateral in Repo view by
clicking New Collateral in the right-click menu.

Collateral Units

Units of collateral if the collateral instrument is set up with Trading Units.

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Note: As in substitutions, the Collateral Calculation Method always defaults to Multiple, but can be
manually set to Single to affect calculations resulting from a manual adjustment of
collateral amount in the last new collateral of the margin transaction in the same manner
as in a cash-driven repo transaction.

5.1.6.2.2 Generated data
•

•

•

Transaction Type = Margin or Open Margin:

–

If a specific maturity date is specified (maturity date of the underlying repo transaction),
Transaction Type = Margin.

–

If the maturity date is not specified at deal entry, Transaction Type = Open Margin.

Collateral Amount

–

If the amount is input at deal entry, the collateral amount (nominal amount) is calculated
from the collateral instrument/market price and valuation haircut.

–

The calculation of the collateral amount also takes into account the contract size of the
collateral.

Collateral Amount Rounding

–

If margin is received, the collateral amount is rounded up.

–

If margin is given, the collateral amount is rounded down.

5.1.6.3 Processing
5.1.6.3.1 Open Margin Movement
•

Execution
If an open margin transaction is created using Open Margin Movement action from Collateral Position
view of Collateral Valuation Board, a dialog with following fields is opened:
Information
Opening Date

Description
Opening date of the open margin transaction.
Defaulted to the current date but can be modified to any other valid date.

Value Date

Value date of the open margin transaction.
Defaulted to the opening date adjusted with spot days of the margin
instrument identified in the collateral agreement of the collateral position but
can be modified to any other valid date.

Portfolio

Portfolio of the open margin transaction.
Defaulted to the portfolio of the collateral position but can be modified to any
other valid portfolio.

Counterparty

Counterparty of the open margin transaction.
Defaulted to the counterparty of the collateral position and cannot be
changed.

Collateral Agreement

Collateral agreement of the open margin transaction.
Defaulted to the collateral agreement of the collateral position and cannot be
changed.

Sign

Transaction sign of the open margin transaction.
Default according to the action in the column Collateral Action of the collateral
position and cannot be changed.

Currency

(Information only.) Currency of the open margin transaction.
Defaulted to the currency of the collateral position.

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Information

Description

Value

Target value of the margin collateral.
Defaulted based on cover difference of the collateral position and can be
modified to any other value larger than minimum movement value of the
collateral agreement of the collateral position.

When the dialog is accepted, a Transaction Manager application is opened and a new open
margin transaction with the first new collateral is automatically created in it. You can then
finalize the transaction by giving the details of margin collateral normally in Repo view of
Transaction Manager.
Since open margin transactions are for an indefinite period of time, return of the margin
collateral does not happen automatically, you must create a separate margin return transaction
must be created when you want the margin collateral to be returned. Also, all future cashflows
of fixed income securities, including both coupons and principal repayments, are created in the
open margin transactions to support settlements of these flows both against the issuer or
clearing client of the security and against the counterparty of margin transaction.

•

Cancellation
You can undo this action by canceling the open margin movement transaction.

5.1.6.3.2 Margin Movement
Margin transactions are always created by using the Margin Movement action from an outstanding
repo transaction either in Transaction Manager or in Collateral Position view of Collateral Valuation
Board.

•

Execution
If the action is selected directly from an existing repo transaction in Transaction Manager, the
action dialog contains the following fields and default values:
Information

Description

Opening Date

Opening date of the margin transaction.
Defaulted to the current date or, if given before selecting the action, as
fixing/action date of the underlying transaction but can be modified to any
other valid date

Value Date

Value date of the margin transaction.
Defaulted to the opening date adjusted with spot days of the margin
instrument identified in the collateral agreement of the underlying transaction
but can be modified to any other valid date

Sign

Transaction sign of the margin transaction.
Defaulted to +1 (i.e. collateral received from margin call).

Currency

Currency of the margin transaction.
Defaulted to the currency of the collateral agreement of the underlying
transaction and cannot be changed.

Value

Target value of the margin collateral.
Defaulted to the minimum movement value of the collateral agreement of the
underlying transaction but can be modified to any higher value.

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If the action is selected from Collateral Position view (grouped by Collateral Number) of Collateral
Valuation Board, the action dialog is slightly different:
Information

Description

Opening Date

Opening date of the margin transaction.
Defaulted to the current date but can be modified to any other valid date

Value Date

Value Date of the margin transaction.
Defaulted to the opening date adjusted with spot days of the margin
instrument identified in the collateral agreement of the collateral position but
can be modified to any other valid date.

Collateral Number

(Information only.) Transaction number of the repo transaction underlying the
collateral position.
This is defaulted as collateral number of the collateral position.

Sign

(Information only.) Transaction sign of the margin transaction.
Default according to the action in the column Collateral Action of the collateral
position.

Currency

(Information only.) Currency of the margin transaction.
Defaulted to the currency of the collateral agreement of the collateral
position.

Value

Target value of the margin collateral.
This is defaulted based on cover difference of the collateral position and can
be modified to any other value larger than minimum movement value of the
collateral agreement of the collateral position.

Note: If the action was executed from Collateral Valuation Board, a Transaction Manager
application in which the margin call transaction is created is opened automatically.

In both cases, a new margin transaction with the first new collateral is automatically created.
You can then finalize the transaction by giving the details of margin collateral normally in Repo
view of Transaction Manager.
Since margin transactions are for the specific remaining maturity of the underlying repo
transaction, return of the margin collateral happens automatically on the maturity date of the
underlying repo. Also, coupons and principal repayment cashflows of fixed income securities are
only created if they are due for payment before the maturity of the underlying repo transaction.

•

Cancellation
You can undo this action by canceling the margin movement transaction.

5.1.6.3.3 Margin Return
A separate margin return (of an earlier margin call) transaction is required when margin collateral
must be returned in an unscheduled manner. This is always true when returning margin collateral
delivered in an earlier open margin transaction and when the collateral received in a margin
transaction must be returned before the scheduled return on the maturity date of the underlying
repo transaction.
Margin return transactions can only be created using a margin return action from Collateral view of
Collateral Valuation Board for a margin collateral holding in a specific collateral instrument. The logic
for Margin Return is exactly the same as for Open Margin Return.

•

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When an Open Margin Return or Margin Return action is selected in the Collateral view of Collateral
Valuation Board, a dialog with following fields is opened:
Information

Description

Opening Date

Opening date of the margin return transaction.
Defaulted to the current date but can be modified to any other valid date

Value Date

Value date of the margin return transaction.
Defaulted to the opening date adjusted with spot days of the margin
instrument identified in the Collateral Agreement of the underlying margin
transaction(s) but can be modified to any other valid date

Portfolio

Portfolio of the margin return transaction.
Defaulted to the portfolio of the underlying margin transaction(s) and cannot
be changed.

Counterparty

Counterparty of the margin return transaction.
Defaulted to the counterparty of the underlying margin transaction(s) and
cannot be changed.

Collateral Agreement

Collateral agreement of the margin return transaction.
Defaulted to the collateral agreement of the underlying margin transaction(s)
and cannot be changed.

Sign

Transaction Sign of the margin return transaction.
Defaulted to the opposite of the sign of the underlying margin transaction(s)
and cannot be changed.

Currency

Currency of the margin return transaction.
Defaulted to the currency of the collateral agreement of the underlying margin
transaction(s) and cannot be changed.

Collateral Currency

Currency of the margin collateral instrument.
Defaulted to the currency of the collateral instrument of the underlying margin
transaction(s) and cannot be changed.

FX Rate

FX Rate used to convert value of collateral instrument from collateral currency
to Currency of the collateral agreement.
Defaulted to the current FX spot rate between collateral currency and currency
but can be modified to any other rate when collateral currency and currency
are not the same.

Instrument

Collateral instrument being returned.
Defaulted to the collateral instrument of the underlying margin transaction(s)
and cannot be changed.

Collateral Amount

Amount of collateral to return.
Calculated by the system as the smallest deliverable of the collateral amount
with adequate collateral value to match total collateral value to return, but can
be modified to any other deliverable amount less than total collateral amount
of the underlying margin transaction(s).

Collateral Units

Units of collateral to return when collateral instrument has been set up with
trading units.

Collateral Market Price

Current market price of collateral instrument.

Collateral Market Rate

Current market yield of collateral instrument.

Cover Value

Cover value of the identified collateral amount of the collateral instrument.
Calculated by the system using collateral amount, collateral market price and
valuation haircuts as defined in the collateral agreement. This value can be
modified to any other value, in which case the new collateral amount is
calculated accordingly.

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Information

Description

Total Cover Value To
Return

(Information only.) Total cover value required to be returned to correct
over-collateralization of the collateral position.
Defaulted to the cover difference of collateral position.

Cover Difference

The difference between cover value and total cover value to return. This value
is informative only and can be used to check whether cover value of selected
collateral to be returned is sufficient. A negative value indicates that more
collateral must be returned to correct over-collateralization of the collateral
position.

When the dialog is accepted, a Transaction Manager application is opened, all underlying margin
or open margin transactions affected by the margin return are identified and a new margin
return transaction is created, returning the given amount of collateral and closing the current
margin or open margin transaction. The new transaction is completed with the data given in the
dialog and can be applied and accepted forward in the flow directly.

•

Cancellation
You can undo this action by canceling the margin return transaction.

5.1.7 Cash Collateral
Cash can also be used as collateral for an underlying exposure in a collateral agreement. Cash
collateral is delivered in a similar manner to security collateral in margin movement transactions
(margin calls).
Cash collateral is managed in the system as balances with ability to accrue interest. The general
characteristics of cash collateral account transactions are the same as those of call Account
transactions.
See 8.2 Call account on page 446.

5.1.7.1 Instrument setup
Cash collateral instruments must be based on an instrument type derived from the class
CASH-COLLATERAL-ACCOUNT.

•

Main characteristics
The following basic information may be captured when defining a cash collateral account
instrument.
Information

Description

Currency

Currency of the cash collateral account.

Balance

Minimum and maximum balance allowed on the cash collateral account.

information
Notice period information

•

Required notice period for cash movements.

Interest accrual parameters
For cash collateral accounts, you can specify the interest rates used, and the method and
frequency that interest is accrued on the cash collateral account.

•

Interest realization parameters
You can also specify how the accrued interest is realized on the cash collateral account.

See A.2.90 Cash Collateral Account on page 752.
It is also possible to set up:

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•

Spot day calculations

•

Collateral

•

Manual charges

•

Cashflow and transaction charge rules

•

Branch codes.

See Appendix A Features on page 713.

5.1.7.2 Deal capture
Cash collateral account transactions are made for an indefinite maturity either against overall
exposure of a counterparty under a specific collateral agreement (Open Cash Collateral) or against
the exposure of a particular repo operation (Cash Collateral).
In order to be able to use cash collateral in a collateral agreement, at least one cash collateral
instrument must be identified as eligible collateral in the agreement.

5.1.7.2.1 Input data – Open Cash Collateral
New Open Cash Collateral (Account) transactions as well as new movements in existing transactions
can be captured and managed in Cash Collateral applications in a similar manner to call accounts.
New transactions and movements can also be created using actions from the Collateral Position view
in Collateral Valuation Board.
Capturing an Open Margin transaction directly in a Cash Collateral Account application is almost
identical to capturing a call account transaction. The only difference is that a cash collateral
transaction must always be attached to a collateral agreement. Open Cash Collateral transactions
are not linked to an existing collateral number, but always attached to a collateral agreement.
In addition to the standard deal parameters, the following information is required if you want to
capture a new cash collateral account in a Cash Collateral Account application.

•

•

Transaction view
Information

Description

Movement / Initial
Balance

Initial cash movement (inflow or outflow) on the cash collateral account.

Collateral Agreement

Collateral Agreement of the cash collateral account.

This amount can be zero if you want to open a cash collateral account without
any initial movement of cash.

Movement view
In this view, you can add a cash collateral movement to an existing transaction using the New
Movement action.
Information

Description

Opening Date

Opening date of the new movement.

Value Date

Value date of the new movement.
This is set automatically by the system based on opening date and notice
period setup of the instrument but can be manually changed to a different
date.

Amount

Amount of the new movement.

5.1.7.2.2 Input data – Cash Collateral
New Cash Collateral Account transactions targeting specific repos as well as new movements in
them are always captured using actions either from the repo transaction in Transaction Manager
or in the Collateral Valuation Board.

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If the Cash Collateral action is selected directly from an existing repo transaction in Transaction
Manager, the action dialog contains the following fields and default values:
Information

Description

Opening Date

Opening date of the cash collateral transaction or movement.
Defaulted to the current date or, if given before selecting the action, as
fixing/action date of the underlying transaction but can be modified to any
other valid date.

Value Date

Value Date of the cash collateral transaction or movement.
Defaulted to the opening date adjusted with spot days of the selected cash
collateral instrument but can be modified to any other valid date.

Margin Instrument

Instrument used for the cash collateral transaction or movement.
Manually select one of the eligible cash collateral instruments in the collateral
agreement of the underlying repo transaction.

Sign

Transaction sign of the margin transaction.
Defaulted to +1 (i.e. cash collateral given from margin call).

Currency

Currency of the margin transaction.
Defaulted to the currency of the collateral agreement of the underlying repo
transaction and cannot be changed.

Amount

Amount of the cash collateral movement.
Defaulted to the minimum movement value of the collateral agreement of the
underlying repo transaction but can be modified to any higher value.

5.1.7.3 Processing
5.1.7.3.1 Open Cash Collateral
•

Execution
A cash Collateral transaction or movement can be created through the Open Cash Collateral action
from Collateral Position view of Collateral Valuation Board. The following dialog is displayed:
Information
Opening Date

Description
Opening date of the cash collateral transaction or movement.
Defaulted to the current date but can be modified to any other valid date.

Value Date

Value date of the cash collateral transaction or movement.
Defaulted to the opening date adjusted with spot days of the selected cash
collateral instrument but can be modified to any other valid date.

Portfolio

Portfolio of the cash collateral transaction or movement.
Defaulted to the portfolio of the collateral position but can be modified to any
other valid portfolio.

Counterparty

Counterparty of the cash collateral transaction or movement.
Defaulted to the counterparty of the collateral position and cannot be
changed.

Collateral Agreement

Collateral agreement of the cash collateral transaction or movement.
This is defaulted as the collateral agreement of the collateral position and
cannot be changed.

Margin Instrument

Instrument used for the cash collateral transaction or movement.
This must be manually selected as one of the eligible cash collateral
instruments in the collateral agreement.

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Information

Description

Sign

Sign of the cash collateral transaction or movement.
Default according to the action in the column Collateral Action of the collateral
position and cannot be changed.

Currency

(Information only.) Currency of the cash collateral transaction or movement.
Defaulted to the currency of the collateral position.

Amount

Amount of the cash collateral movement.
Defaulted according to the cover difference of the collateral position and can
be modified to any other value larger than minimum movement value of the
collateral agreement of the collateral position.

When the dialog is accepted, a Cash Collateral Account application opens, usually Cash Collateral
Account Trading (default setup).
If the system cannot find an existing cash collateral transaction that matches the following
values with those given in the dialog, a new cash collateral transaction with a first movement is
automatically created:

–

Portfolio

–

Counterparty

–

Collateral Agreement

–

Margin Instrument

–

Currency.

If an existing transaction is found, a new movement is added to the identified cash collateral
transaction.
There is no separate return of the cash collateral. Instead, both positive and negative
movements of cash can be made in the same cash collateral transaction using the same
functionality.

•

Cancellation
To undo this action cancel the new movement, or if a new account transaction was created,
cancel the whole transaction.

5.1.7.3.2 Cash Collateral
•

Execution
If the Cash Collateral action is selected from Collateral Position view (grouped by Collateral Number)
of Collateral Valuation Board, the dialog is the same as the Open Cash Collateral dialog with the
following additions:
Information

Description

Return Date

Scheduled return date of the cash collateral.
Defaulted to the maturity date of the underlying repo transaction and cannot
be changed. The field is informative only and indicates the date as of which
the underlying exposures is scheduled to expire.

Collateral Number

Transaction number of the repo transaction underlying the collateral position.
Defaulted to the collateral number of the collateral position and cannot be
changed.

When the dialog is accepted in Transaction Manager or in Collateral Valuation Board, a Cash
Collateral Account application opens, usually Cash Collateral Account Trading (default setup).

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If the system cannot find an existing cash collateral transaction that matches the following
values with those given in the dialog, a new cash collateral transaction with a first movement is
automatically created.

–

Portfolio

–

Counterparty

–

Collateral Agreement

–

Margin Instrument

–

Currency

–

Collateral Number.

If an existing transaction is found, a new movement is added to the identified cash collateral
transaction.
There is no automatic return of the cash collateral on the maturity date of the underlying repo
transaction, therefore you must create a separate cash collateral movement in the Cash
Collateral Account application when the cash is returned.
Cancellation

•

To undo this action cancel the new movement, or if a new account transaction was created,
cancel the whole transaction.

5.2 Security loan
A security loan is a transaction in which a given interest-bearing or equity security is lent against a
financial compensation. The loan is agreed for an open-ended transaction.
Security loans impact only custody movements and balances. The actual security positions for
purposes of valuation and accounting, for example, are not impacted. Coupons and dividends are
also calculated without considering the security loan transactions.

5.2.1 Instrument setup
Security loan instruments must be based on an instrument type derived from the class
SECURITY-LOAN. The ALLOW-SECURITY-LOAN feature (see A.2.19 Allow Security Loan on page
721) specifies if the instrument can be loaned.

5.2.2 Deal capture
5.2.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a
securities loan:
Information

Description

Secondary Instrument

The security being lent (bond or equity).

Nominal Amount or
Trading Unit

nominal amount (bond) or trading unit (equity) to be lent out.

Nominal Spot/Rate

Lending fee.

Currency

Currency of instrument.

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5.2.3 Processing
This section describes the actions that can be taken throughout the life of a security loan.

5.2.3.1 Entering security loan fees
A security loan fee can be entered at any time by selecting the Security Loan Fee action.

•

Execution
The following information is required:

•

Information

Description

Direction

Fee direction (In or Out).

Amount

Fee amount.

Opening Date

Fee opening date.

Value Date

Fee value date.

Payment Date

Fee payment date.

From When Date

Date from which fee payment is based.

Cancellation
An Undo Security Loan Fee action is available for undoing (deleting) selected fees.

5.2.3.2 Cutting a security loan transaction
The security loan can be cut (matured) by selecting the Security Loan Cut action.

•

Execution
The following information is required:

•

Information

Description

Opening Date

Date of execution, used as opening date.

Value Date

Closing date of the transaction.

Fee Direction

In or Out.

Fee Amount

Amount.

Fee Opening Date

Fee opening date.

Fee Value Date

Fee value date.

Fee Payment Date

Fee payment date.

Fee From When Date

Date from which fee payment is based.

Cancellation
An Undo Security Loan Cut action is available to undo (delete) a captured cut.

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Chapter 6

Forex

6.1 FX spot and FX forward
In the foreign exchange market, buyers and sellers conduct foreign exchange (FX) transactions.
A currency spot or forward transaction is a deal where one currency is exchanged for another (a
base currency and a quote currency). If the value date is the spot date, then the transaction is
called a spot deal. If the value date is further in the future, the transaction is a forward.
Non-deliverable forwards (NDFs) are FX forward deals that can have a net settlement.
Spot rates are quoted as one unit of the base currency against a number of units of the quote
currency. In international financial markets, the US dollar is used as the base currency in most
quotes.
A direct quote is a foreign exchange rate quoted as the domestic currency per unit of the foreign
currency. For example, in the US, a direct quote for Japanese yen would be USD/JPY. Conversely, in
Japan, a direct quote for US dollars would be JPY/USD.
An indirect quote is a foreign exchange rate quoted as the foreign currency per unit of the domestic
currency. For example, in the US, an indirect quote for Japanese yen would be JPY/USD. Conversely,
in Japan, an indirect quote for US dollars would be USD/JPY.
In TRM, FX spot and forward transactions belong to the instrument class FX.

6.1.1 Instrument setup
FX spot/forward instruments are based on an instrument type derived from the class FX.

•

Rate defaulting
You can specify that you expect the system to default the rates from the market at deal entry.
See A.2.272 Quote Default (FX) on page 848.

•

Currency information
You can specify the currencies of the FX transaction either in the instrument setup or at deal
entry.
See A.2.192 FX Setup on page 806.

•

Date information
It is possible to set up value date information at instrument level.
Information

Description

Calendar
parameters

Calendars used to calculate the value date.

Gap Set

Gap set used for supplying the available value periods.

Value Date Period

If defined, this value period is applied to each transaction.

For an FX instrument, it is also possible to set up:

•

Spot date calculation

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Note that it is recommended that you do not specify the spot days in the instrument setup as
these are taken by default from the spot days of the two currencies at deal entry.

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes

•

FX Margin Result.

See Appendix A Features on page 713.
The attributes required for the different types of FX instrument are described in the following
sections.

6.1.1.1 FX forward
FX forward instruments are set up in a similar way to FX spot instruments. To calculate forward
points from currency pairs interest rates, you can specify additional parameters such as Absolute IR
Difference.
See A.2.175 FX Forward on page 797.

6.1.1.2 Non-deliverable forward (NDF)
NDFs are FX forward deals that can have a net settlement. NDFs are set up in a similar way to FX
forward instruments. NDFs should use the primary feature Non Deliverable Forward FX Instrument.
See A.2.248 Non Deliverable Forward FX Instrument on page 837.

6.1.1.3 FX cross deal
An FX spot/forward deal where neither currency is the portfolio base currency is called a cross deal.
FX cross deals are set up in a similar way to FX spot/forward instruments, with the following
additional parameters:

•

FX cross rate calculation
You need to define how the FX rates (Base Spot FX and Base FX Rate) are calculated.
See A.2.171 FX Cross Method on page 796.

6.1.2 Market information
6.1.2.1 Currencies
Some additional parameters need to be defined for the currencies which are relevant to your FX
transactions: see the TRM User Guide.

6.1.2.2 Quotations and market information
Quotations for currencies can be viewed and modified in Rate Monitor. It is possible to define market
information feeds for each currency (for example, from Reuters): see the TRM User Guide.

6.1.3 Deal capture
6.1.3.1 Input data
•

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6.1 FX spot and FX forward

In addition to the standard deal parameters, the following information is required to enter an FX
spot transaction:
Information

Description

Base Currency

Base currency of the transaction.

(Currency)
Quote Currency

Quote currency of the transaction.

(Currency 2nd)
FX Base Amount

Amount of the FX transaction in the base currency.

FX Quote Amount

Amount of the FX transaction in the quote currency.

Deal Rate

Final FX rate of the transaction =

Nominal / Spot Rate + FX Forward Points (+ Margins if applicable)

•

FX forward (input forward points)
In addition to the standard deal parameters, the following information is required to enter an FX
forward transaction where the forward points are input manually:
Information

Description

Base Currency

Base currency of the transaction.

(Currency)
Quote Currency

Quote currency of the transaction.

(Currency 2nd)
Value Date

Official date when money is transferred.

FX Base Amount

Amount of the FX transaction in the base currency.

FX Quote Amount

Amount of the FX transaction in the quote currency.

Nominal/Spot
Rate

Final FX spot rate.

FX Forward Points

Forward points for the transaction.

Deal Rate

Final FX rate of the transaction =

Nominal / Spot Rate + FX Forward Points (+ Margins if applicable)

•

FX forward (calculated forward points)
In addition to the standard deal parameters, the following information is required to enter an FX
forward transaction where the forward points are calculated from Base Currency Interest % and
Quote Currency Interest %:
Information

Description

Base Currency

Base currency of the transaction.

(Currency)
Quote Currency

Quote currency of the transaction.

(Currency 2nd)
Value Date

Official date when money is transferred.

FX Base Amount

Amount of the FX transaction in the base currency.

FX Quote Amount

Amount of the FX transaction in the quote currency.

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Information

Description

Nominal/Spot
Rate

Final FX spot rate.

Base CCY Interest
%

Interest rate of the base currency for the period from the opening date to the value
date.

Quote CCY
Interest %

Interest rate of the quote currency for the period from the opening date to the value
date.

6.1.3.2 Generated data
•

Cashflows
The figure below illustrates the cashflows which are established in TRM for an FX spot
transaction.

The figure below illustrates the cashflows which are established in TRM for an FX forward
transaction:

The figure below illustrates the cashflows which are established in TRM for a non-deliverable
forward transaction:

The following section describes the cashflows when the feature FX Margin Result is used. FX
Margin Result creates one cashflow of type Margin with following characteristics:
Currency = quote currency
Active From = Opening date of the transaction
Value Date; Payment Date; From When; Until When; Active To = Value date of the
transaction
Fixing Rate; Fixing Quote = Spot Margin + Forward Margin
Amount = transaction quote amount - quote amount we would have had without any
margin

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6.1.4 Processing
This section describes the actions that can be done throughout the life of an FX transaction.

6.1.4.1 Early expiration
You can force FX transactions to mature earlier than their value date. This process is referred to as
early expiration.

•

Execution
The following information is needed to process the early expiration:
Information

Description

Early Expiration
Date

Date when the early expiration is executed.

Value Date

Date when the early expiration is settled. This cannot be later than the maturity date
of the initial transaction.

Amount to Expire

Amount to be early-expired. This defaults to the amount left and is expressed in the
same currency (base or quote) as the input amount of the initial transaction. You can
enter any amount between 0 and the remaining amount of the initial transaction.

Currency

The currency in which the above amount is expressed, can be base or quote currency
depending on the initial transaction. (Read-only.)

Forward Points

Forward points of the early expiration transaction. This defaults to the number of
forward points between the early expiration date and the maturity date of the initial
transaction.

Deal Rate

Deal rate for the early expiration transaction.

By default, this is today’s date unless a Fixing/Action Date is specified at transaction
level.

Deal Rate = Original Deal Rate - Forward Points
Original Deal Rate

The deal rate of the initial transaction. (Read-only.)

Quote Amount

The corresponding amount of the transaction.

Quote Currency

Shows the currency of the deal. The currency can be quote or base depending on
default Currency.

The execution generates an early expiration transaction with the following attributes:
If the original input amount was FX Base Amount:
FX base amount = amount to expire
If the original input amount was FX Quote Amount:
FX quote amount = amount to expire
Deal Rate = early expiration deal rate
Opening date = date when the early expiration is done
Value date = date when the early expiration is settled
Kind = Early Expiration
The remaining attributes are inherited from the initial transaction.

•

Cancellation
You can undo the early expiration by canceling the early expiration transaction.

•

Redo
You can redo the action on the generated transaction.

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6.1.4.2 Early expiration of NDFs
You can force netted non-deliverable forwards to mature earlier than their value date.

•

Execution
The following information is needed to process the early expiration of netted NDFs:
Information

Description

Early Expiration Date

Date when the early expiration is executed. By default, this is today's date
unless a Fixing/Action Date is specified at transaction level.

Value Date

Date when the early expiration is settled. This cannot be later than the
maturity date of the initial transaction.

Base Currency

Base currency of the transaction (information).

Base Amount Left

Amount left in base currency (information).

Base Amount to Expire

Defaults to the base amount left. (Modifiable if the initial deal was entered in
base currency.) You can enter any amount between 0 and the amount left.

Quote Currency

Quote currency of the transaction (information).

Quote Amount Left

Amount left in quote currency (information).

Quote Amount to Expire

Defaults to the base amount left. (Modifiable if the initial deal was entered in
base currency.) You can enter any amount between 0 and the amount left.

Original Deal Rate

The forward rate on the original NDF (information).

FX Forward Rate

The forward market rate at the date of Early Expiration. You can enter a
different rate agreed with the counterparty.

Netting Currency

The currency in which the netting is calculated, either base or quote. (This is
copied from the original deal and depends on the netting method specified on
the instrument.)

Forward Netting Amount

Amount corresponding to the difference between the initial deal rate and the
current forward rate (information).

Discount Rate

This is the rate to be used to discount the Forward Netting Amount to calculate
the netting amount. (Modifiable)

Netting Amount

Amount to be settled, calculated as previously explained.

The following fields are only visible if the initial NDF can be settled in a different currency to the
netting currency.
Information

Description

Settlement Currency

Currency to use for settlement (information)

Settlement FX Rate

Cross rate between netting currency and settlement currency at settlement
date (can be modified)

Settlement Amount

Final amount to be settled

Early expiring a netted NDF results in the following:

–

All cashflows are closed at the original transaction’s maturity

–

A single netting cashflow is created at the early expiration date, where Amount = FX netting
at maturity discounted to the early expiration date.
The netting amount is calculated using the date basis and rate type defined for the
interpolation method of the currency’s default curve.

•
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6.1 FX spot and FX forward

You can redo the action on the generated transaction.

6.1.4.3 Roll over
You can defer the maturity of an FX transaction to a later date. This process is referred to as
roll-over.
See A.2.11 Allow Roll Over (FX) on page 717.

•

Execution
If the Spot Rate for the roll-over equals the Original Deal Rate, the following information is
needed to process the roll over:
Information

Description

Roll Over Date

Date when the roll over is done. The opening date of the roll over transaction.

Value Date

Value date of the roll over transaction. This corresponds to the maturity date of the
initial transaction.

Maturity Code

Gap to add to the value date to calculate the maturity date.

Maturity Date

New maturity date of the FX deal. This must be later than the maturity date of the
initial transaction.
This defaults to the maturity code of the initial transaction.

Amount Left

Remaining amount of the initial transaction. (Read-only.)

Amount

Amount to roll over defaults to the amount left and is expressed in the same currency
(base or quote) as the input amount of the initial transaction. You can enter any
amount between 0 and the remaining amount of the initial transaction.

Currency

Shows the currency of the amount to roll over. The amount is expressed in either base
or quote currency depending on the initial transaction. (Read-only.)

The execution generates a roll over transaction with the following attributes:
If the original input amount was FX Base Amount:
FX Base amount = amount to roll over
If the original input amount was FX Quote Amount:
FX Quote amount = amount to roll over
Deal Rate = roll over deal rate
Opening Date = date when the roll over is done
Maturity Date = new maturity date
Kind = Roll Over
The remaining attributes are inherited from the initial transaction.
If the Spot Rate for the roll-over is different from the Original Deal Rate, the following additional
information is needed to process the roll over and settle the subsequent difference:
Information

Description

Settle Differential

By default, this switch is off: the Spot Rate for the roll over is equal to the Original
Deal Rate.
Switch on if the Spot Rate for the roll-over is different from the Original Deal Rate.
If this switch is on: the Spot Rate (see below) defaults to the spot rate of the market
but can be modified. The roll over generates a netting cashflow to handle the
settlement of the difference.

Original Deal Rate

The deal rate of the initial transaction. (Read-only.)

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Information

Description

Spot Rate

Exchange spot rate of the roll over. This defaults to the Original Deal Rate.
If Settle Differential is activated (see above), this field becomes available. The Spot
Rate defaults to the spot rate of the market but can be modified.
Note: Roll Over Date, Value Date, Maturity Code, Maturity Date, and Settle
Differential are adjusted automatically.

Base CCY Interest
%

Interest rate of the base currency for the period from the original settlement date to
the new settlement date.

Quote CCY
Interest %

Interest rate of the quote currency for the period from the original settlement date to
the new settlement date.

Forward Points

Forward points of the roll over transaction. This defaults to the number of forward
points from the roll over date to the maturity date.
Note: Roll Over Date, Value Date, Maturity Code, and Maturity Date are adjusted
automatically.

Deal Rate

Deal rate for the roll over.
•

If the Spot Rate for the roll-over is equal to the Original Deal Rate:

•

If the Spot Rate for the roll-over is different from the Original Deal Rate:

Deal Rate = Original Deal Rate + Forward Points
Deal Rate = Spot Rate + Forward Points
Quote Amount

The corresponding amount of the roll over transaction. (Read-only.)

Quote Currency

Shows the currency of the deal. The currency can be quote or base depending on
default Currency.(Read-only.)

Clear Packaging

Clears all packages from the roll over transaction.

The execution generates a roll over transaction as before with an additional cashflow as follows:
A netting cashflow is created to handle the settlement of the difference
Value Date = Roll over value date
Currency = Roll over currency 2
Amount = Base Amount * Original Deal Rate - (-Base Amount * Spot Rate)

•

Cancellation
You can undo the roll over by canceling the roll over transaction.

•

Redo
You can redo the action on the generated transaction.

6.1.4.4 Roll over with margins
You can specify margins in case you roll over FX transactions.
A.2.12 Allow Roll Over (FX - Margin Result) on page 718

•

Execution
If the Spot Rate for the roll-over margin equals the Original Deal Rate, the following information
is needed to process the roll over:

390

Information

Description

Roll Over Date

Date when the roll over is done. The opening date of the roll over transaction.

Value Date

Date of the roll over transaction. Corresponds to the maturity date of the initial
transaction.

Maturity Code

Gap to add to the value date to calculate the maturity date.

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6 Forex
6.1 FX spot and FX forward

Information

Description

Maturity Date

Maturity date of the roll over transaction.

Amount Left

Remaining amount of the initial transaction. (Read-only.)

Amount

The amount you want to roll over, which can be any amount between 0 and the
remaining amount of the initial transaction. Defaults to the amount left and is
expressed in the same currency (base or quote) as the input amount of the initial
transaction.

Currency

Shows the currency of the transaction. The amount is expressed in either base or
quote currency depending on the initial transaction. (Read-only.)

The execution generates a roll over transaction with the following attributes:
If the original input amount was FX Base Amount:
FX Base amount = amount to roll over
If the original input amount was FX Quote Amount:
FX Quote amount = amount to roll over
Deal Rate = roll over deal rate
Opening Date = date when the roll over is done
Maturity Date = new maturity date
Kind = Roll Over Margin
The remaining attributes are inherited from the initial transaction.
If the Spot Rate for the roll-over margin is different from the Original Deal Rate, the following
additional information is needed to process the roll over and settle the subsequent difference:
Information

Description

Settle Differential

Switch on if the Spot Rate for the roll-over is different from the Original Deal Rate.
By default, this switch is off.

Original Deal Rate

The deal rate of the initial transaction. (Read-only.)

Spot Rate

The spot rate of the roll over transaction. If Settle Differential is activated, this field
becomes available.
Spot Rate defaults to the spot rate of the market but this value can be modified.
Note: Roll Over Date, Value Date, Maturity Code, Maturity Date, and Settle
Differential are adjusted automatically.

Spot Margin

Margin to apply to the near leg of the roll over transaction. If Settle Differential is
enabled, Spot Margin defaults to the price.
Note: Settle Differential is adjusted automatically.

Final Spot Rate

(Read-only.)
Spot rate including margins. If Settle Differential is activated, then

Spot Rate + (Sign * Spot Margin / 10000)
Forward Points

Forward points of the roll over transaction. This defaults to the number of forward
points from the roll over date to the maturity date.
Note: Roll Over Date, Value Date, Maturity Code, and Maturity Date are adjusted
automatically.

Forward Margin

Margin applied on the far leg of the roll over transaction.

Deal Rate

Deal rate for the roll over.

Deal Rate = Spot Rate + Forward Points
Quote Amount

The corresponding amount of the roll over transaction. (Read-only.)

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Information

Description

Quote Currency

Shows the currency of the deal. The currency can be quote or base depending on
default Currency.(Read-only.)

The execution generates a roll over transaction as before with an additional cashflow as follows:
A netting cashflow is created to handle the settlement of the difference
Value Date = Roll over value date
Currency = Roll over currency 2
Amount = Base Amount * Original Deal Rate - (-Base Amount * Spot Rate)

•

Redo
You can redo the action on the generated transaction.

6.1.4.5 Netting
Non-deliverable forwards (NDFs) are FX forward deals that can have a net settlement. Instead of
exchanging principal amounts, the counterparties agree on the value date and the contractual spot
rate. The difference between the actual spot rate and the contractual rate, multiplied by the nominal
amount of the deal, is paid.
See A.2.248 Non Deliverable Forward FX Instrument on page 837.

•

Setup
The fixing parameters for the netting of non-deliverable forwards can be defined either at
instrument level or at transaction level. Where the fixing parameters are defined depends on
how narrow or open the instrument definition needs to be.
The following information is required to set up netting for an NDF:
Information

Description

Fixing Offset

Number of days’ offset allowed, that is, the difference in days between the fixing date
and the due date (default = 0).

Fixing
Subscenario

Subscenario from which the FX spot rate is retrieved.

Calendar

Calendar to use when calculating the fixing date.

Netting Method

Home Currency:
When this method is used the netting currency is set to either base or quote, if one of
those is equal to the portfolio currency; otherwise, it defaults to the base currency.

•

Execution
The following information is needed to process the netting:
Information

Description

Netting Date

Date when netting is executed.

Netting Currency

Currency used to compute netting amount, either base or quote depending on
instrument setup (read-only).
Note: You can change the netting currency in the FX Netting Currency field in the
Transaction view.

392

Other Currency

Shows the other currency involved (read-only).

Original Deal Rate

The forward rate on the original NDF (read-only).

FX Rate

The current FX rate.

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6 Forex
6.1 FX spot and FX forward

Information

Description

Netting Amount

Amount to be settled calculated in netting currency.

The following fields are only visible if the initial NDF can be settled in a different currency to the
netting currency.
Information

Description

Settlement Currency

Currency to use for settlement (read-only).

Settlement FX Rate

Cross rate between netting currency and settlement currency at settlement
date (can be modified).

Settlement Amount

Final amount to be settled.

The execution sets the amount of the netting cashflow to the calculated net settlement amount
(P/L).

•

Cancellation
You can undo the netting of cash settlements for an FX transaction.

6.1.4.6 Currency pair shift
It is possible to split a position from one underlying currency pair into two new positions, each of
which contains one of the currencies with a third currency (usually, the portfolio currency). This
process is called an FX Pair Shift.

•

Setup
The FX Pair Shift action is available on an FX transaction if the Allow FX Currency Pair Shift
feature is included in the instrument definition: see A.2.7 Allow FX Currency Pair Shift on page
716.

•

Execution
See the TRM User Guide for information about this action.

6.1.5 Position monitoring
There are two basic methods for valuation of FX instruments: Theoretical or Quoted:

•

In the Theoretical method, each cashflow is discounted to the spot date using the cashflow
currency interest rate, converted to the portfolio currency using the spot rate, then discounted
from spot date to valuation date using the portfolio currency interest rate.
See 6.1.5.2 Calculations - Theoretical valuation method on page 394.

•

In the Quoted method, the cashflow is valuated using the forward FX rate between the cashflow
currency and the valuation currency, and discounted using the valuation currency interest rate.
See 6.1.5.3 Calculations - Quoted valuation method on page 402.

Theoretical corresponds to the zero-coupon method and quoted to the par method.

6.1.5.1 Setup
By default, the figures are calculated using the Theoretical valuation method. This is the default
behavior, but it can be overridden using Base Valuation Setup.
See A.2.50 Base Valuation Setup on page 734.
If you need more information about the methods used in these calculations, see Chapter 2 Market
standards and calculations on page 33.

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6.1.5.2 Calculations - Theoretical valuation method
In this section, numerical examples demonstrate how the figures are calculated for the example FX
forward deal using the Theoretical valuation method.
This example shows an FX forward Buy 1,000,000 USD/EUR 3M, with the following deal data.
Setup data

•

Data

Symbol

Example

Instrument Date Basis

B

Act/360

Point Factor

p_fact

0.0001 (from currency)

FX Forward Points

p_fx

From Market

Valuation Method

Theoretical

Valuation Date

Figure Date

Risk Date

Figure Date

Risk Yield Type

Continuous

Portfolio data

•

Data

Symbol

Example

FX Exposure Offset

e_fx

0.01

Formula

Transaction data

•

Data

Symbol

Example

Opening Date

dt_o

2004-06-24

Spot Date

dt_s

2004-06-28

Value Date

dt_v

2004-09-28

Nominal Amount

A

1,000,000

FX Spot Rate

S_0

1.187100

FX Forward Points

p_fx

-0.1560000

Currency

USD

Currency 2nd

EUR

Portfolio Currency

EUR

Base CCY Interest %

r_0.b

1.100000%

Quote CCY Interest %

r_0.q

1.616348%

Date basis

B

360

= (F_0 - S_0) * 100

= (S_0 / F_0 / D.b - 1) / t_p

Calculated transaction data

•

Data

Symbol

Example

Formula

Deal Rate

F_0

1.185540 = 1.1871 + (-15.6) * 0.0001

= S_0 + p_fx * p_fact

FX Quote Amount

A.q

-843,497.48 = -1,000,000 / 1.18554

= -A / F_0

Period

t_p

0.2555556 = (2004/09/28 – 2004/06/28) / 360

= (dt_v – dt_s) / B

394

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6.1 FX spot and FX forward

•

•

•

•

Calculated transaction data - Base CCY
Data

Symbol

Example

Formula

Discount Factor

D.b

0.99719677 = 1/(1+0.011*0.2555556)

=1 / (1 + r_0.b * t_p)

Result Value (Local)

V_bl.b

997,196.77 = 1,000,000 * 0.99719677

= A * D.b

Result Value

V_b.b

840,027.60 = 997,196.77 / 1.1871

= V_bl.b / S_0

Base CCY Yield %

1.104512%

= POWER(D, -1 / t_p) -1

Implied Interest

1.100000% = (1.185540 / 1.187100 /
0.99588633 - 1) / 0.255556

= (F_0 / S_0 / D.q - 1) / t_p

Calculated transaction data - Quote CCY
Data

Symbol

Example

Formula

Discount Factor

D.q

0.99588633 = 1 / (1 + 0.01616348 *
0.2555556)

= 1 / (1 + r_0.q * t_p)

Result Value (Local)

V_bl.q

-840,027.60

= -V_b.b

Result Value

V_b.q

-840,027.60

= V_bl.q

Quote CCY Yield %

1.626098%

= POWER (D.q, -1 / t_p) -1

Implied Interest

1.616348% = (1.187100 / 1.185540 /
0.99719677 – 1) / 0.2555556

=(S_0 / F_0 / D.b - 1) / t_p

Market data on Figure Date
Data

Symbol

Example

Figure date

dt_f

2004-08-16

Days to Spot

d_fs

2

Discount Rate

r_d

3.048771%

FX Conversion Rate

S

1.200000

FX Forward

F

1.325000

Base CCY Interest Rate

r_f.b

1.067917%

Quote CCY Interest Rate

r_f.q

3.197691%

Calculated market data on Figure Date
Data

Symbol

Days to Maturity

•

Example

Formula

43 = 2004/09/28 -2004/08/16

= dt_v - dt_f

Time to Spot

t_s

0.00555556 = 2 / 360

= d_fs / B

Time to Maturity

t_m

0.11944444 = (2004/09/28 -2004/08/16) / 360

= (dt_v - dt_f) / B

Discount Factor Spot

D_s

0.999830638

= EXP (-t_s * r_d)

The market data specific to the base currency on the figure date
Data

Symbol

Example

Market Value Discount Factor

D_V.b

0.998615345

Formula

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6.1 FX spot and FX forward

Data

Symbol

Example

Formula

Present Value Discount Factor

D_P.b

0.998615345 = 0.999830638 *
0.998784501

= D_s * D_f.b

Discount Factor Spot Forward

D_f.b

0.99878450

= EXP(-(t_m - t_s) * r_f.b)

The market data specific to the quote currency on the figure date

•

Data

Symbol

Example

Formula

Market Value Discount Factor

D_V.q

0.996196063

Present Value Discount Factor

D_P.q

0.996196062 = 0.999830638 *
0.996364809

= D_s * D_f.q

Discount Factor Spot Forward

D_f.q

0.996364809

= EXP (-r_f.q * (t_m - t_s))

6.1.5.2.1 Valuation figures
The valuation method used for this deal is the Theoretical method.
Base currency figures

•

Data

Symbol

Example

Formula

Local Market Value

Local_Market_Value

998,615.35 = 1,000,000 *
0.998615345

= A * D_V.b

Market Value

V

832,179.45 = 998,615.35 /
1.2000

= Local_Market_Value / S

Quote currency figures

•

Data

Symbol

Example

Formula

Local Market Value

V_l_q

-840,288.87 = -843,497.48 *
0.996196063

= A.q * D_V.q

Market Value

V.q

-840,288.87

= V_l_q

6.1.5.2.2 Result figures
Base currency figures

•

Data

Symbol

Example

Formula

Total Profit (Local)

Total_Profit_Local

1,418.58 = 998,615.35 –
997,196.77

= Local_Market_Value V_bl.b

Total Profit

Total_Profit.b

-7,848.15 = 832,179.45 –
840,027.60

= V - V_b.b

Quote currency figures

•

Data

Symbol

Example

Formula

Total Profit

Total_Profit.q

-261.26 = -840,288.87 –
(-840,027.60)

= V.q - V_b.q

396

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6 Forex
6.1 FX spot and FX forward

Profit Method = FX Forward
•

•

Base currency figures
Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit_Local.b

1,587.73 = 1,000,000 *
0.998784501 – 997,196.77

= A * D_f.b - V_bl.b

Accrued Interest
(Local)

Accrued_Interest_Local.b

=0

Accrued Profit (Local)

P_al

=0

Other Profit (Local)

Other_Profit_Local.b

-169.16 = 1,418.58 1,587.73 – 0 - 0

= Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b –
P_al

FX Profit

FX_Profit

-9,021.23 = 1,000,000 *
(1/1.2 – 1/1.1871) *
0.9961960626

= A * (1 / S - 1 / S_0) *
D_V.q

MtoM Profit

MtoM_Profit.b

1,323.11 = 1,587.73 / 1.2

= MtoM_Profit_Local.b / S

Other Profit

Other_Profit_b

-150.03 = -7,848.15 1,323.11 – (-9,021.23)

= Total_Profit.b MtoM_Profit.b - FX_Profit

Clean Market Value

CMV_b

832,179.45

=V

Quote currency figures
Data

Symbol

Example

Formula

Accrued Interest
(Local)

Accrued_Interest.q

=0

Accrued Profit (Local)

P_al

=0

MtoM Profit

MtoM_Profit.q

-403.60 = -843,497.48
* 0.996364809 –
(-840,027.60)

= A.q * D_f.q - V_b.q

Other Profit

Other_Profit_q

142.34 = -261.26 –
(-403.60) – 0

= Total_Profit.q - MtoM_Profit.q
- Accrued_Interest.q

Clean Market Value

CMV_q

-840,288.87

= V.q

Profit Method = FX IR Difference
•

Base currency figures
Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit_Local.b

2,288.57 = 1,000,000 *
0.998784501 – 997,196.77
- (-700.84)

= A * D_f.b - V_bl.b Accrued_Interest_Local.b

Accrued Interest
(Local)

Accrued_Interest_Local.b

-700.84 = 997,196.77 *
(-0.516348) * (2004/08/16
- 2004/06/28) / 360

= V_bl.b * (-dr) * (dt_f dt_s) / B

Other Profit (Local)

Other_Profit_Local.b

-169.16 = 1,418.58 –
2,288.57 – (-700.84)

=Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b

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6.1 FX spot and FX forward

Data

Symbol

Example

Formula

FX Profit

FX_Profit

-9,021.23 = 1,000,000 *
(1/1.2 – 1/1.1871) *
0.996196063

= A * (1 / S - 1 / S_0) *
D_V.q

MtoM Profit

MtoM_Profit.b

1,913.49 = (1,000,000 *
0.998784501 - 997,196.77)
/ 1.2 - (-590.38)

= (A * D_f.b - V_bl.b) / S Accrued_Interest.b

Accrued Interest

Accrued_Interest.b

-590.38 = -840,027.60 *
0.516348 * (2004/08/16 2004/06/08) / 360

= (V_bl.q) * dr * (dt_f dt_s) / B

Other Profit

Other_Profit.b

-150.03 = -7,848.15 1,913.49 – (-590.38) –
(-9,021.23)

= Total_Profit.b MtoM_Profit.b Accrued_Interest.b FX_Profit

Clean Market Value

CMV_b

832,769.83 = 832,179.45 (-590.38)

= V - Accrued_Interest.b

Quote currency figures

•

Data

Symbol

Example

Formula

Accrued Interest
(Local)

Accrued_Interest_Local.b

MtoM Profit

MtoM_Profit.q

-403.60 = -843,497.48 *
0.996364809 – (-840,027.60)

= A.q * D_f.q - V_b.q

Other Profit (Local)

Other_Profit.q

142.34 = -261.26 – (-403.60)
–0

= Total_Profit.q MtoM_Profit.q Accrued_Interest.q

Clean Market Value

CMV_q

-840,288.87

= V.q

=0

Profit Method = FX Interest
Base currency figures

•

Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit_Local.b

1,587.73 = 1,000,000 *
0.998784501 –
997,196.77

= A * D_f.b - V_bl.b

Accrued Interest
(Local)

Accrued_Interest_Local.b

Other Profit (Local)

Other_Profit_Local.b

-169.16 = 1,418.58 –
1,587.73

= Total_Profit_Local.b MtoM_Profit_Local.b

FX Profit

FX_Profit

-9,055.68 = 1,000,000 *
(1 / 1.2000 – 1 /
1.187100)

= A * (1 / S - 1 / S_0)

MtoM Profit

MtoM_Profit.b

1,323.11 = 1,587.73 /
1.2000

= MtoM_Profit_Local.b / S

Accrued Interest

Accrued_Interest.b

0

= Accrued_Interest_Local.b / S

Other Profit

Other_Profit.b

-115.58 = -7,848.15 –
1,323.11 – (-9,055.68)

= Total_Profit.b MtoM_Profit.b - FX_Profit

Clean Market Value

CMV_b

832,179.45 =
832,179.45 - 0

= V - Accrued_Interest.b

398

=0

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6 Forex
6.1 FX spot and FX forward

•

Quote currency figures
Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit_Local.q

186.78 = -843,497.48 *
0.996364809 – (-840,027.60)
– (-590.38)

= A.q * D_f.q - V_b.q Accrued_Interest.q

Accrued Interest
(Local)

Accrued_Interest.q

-590.38 = -840,027.60
*0.00516348) * (2004/08/16 2004/06/28) / 360

= V_bl.q * dr * (dt_f - dt_s) / B

Other Profit (Local)

Other_Profit.q

142.34 = -261.26 – 186.78 –
(-590.38)

= Total_Profit.q MtoM_Profit_Local.q Accrued_Interest.q

Clean Market Value

CMV_q

-839,698.49 = -840,288.87 (-590.38)

= V.q - Accrued_Interest.q

Profit Method = FX IR DIfference No Discount
•

•

Base currency figures
Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit_Local.b

2,288.57 = 1,000,000 *
0.998784501 997,196.77 - (-700.84)

= A * D_f.b - V_bl.b Accrued_Interest_Local.b

Accrued Interest
(Local)

Accrued_Interest_Local.b

-700.84 = 997,196.77 *
(-0.516348) *
(2004/08/16 2004/06/28) / 360

= V_bl.b * (-dr) * (dt_f - dt_s)
/B

Other Profit (Local)

Other_Profit_Local.b

-169.16 = 1,418.58 2,288.57 - (-700.84)

= Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b

FX Profit

FX_Profit

-9,055.68 = 1,000,000 *
(1/1.2 - 1/1.187100)

= A * (1 / S - 1 / S_0)

MtoM Profit

MtoM_Profit.b

1,913.49 = (1,000,000 *
0.998784501 997,196.77) / 1.2 (-590.38)

= (A * D_f.b - V_bl.b) / S Accrued_Interest.b

Accrued Interest

Accrued_Interest.b

-590.38 = (-840,027.60) *
0.516348 * (2004/08/16 2004/06/28) / 360

= (V_bl.q) * dr * (dt_f - dt_s) /
B

Other Profit

Other_Profit.b

-115.58 = -7,848.15 1,913.49 - (-590.38) (-9,055.68)

= Total_Profit.b - MtoM_Profit.b
- Accrued_Interest.b - FX_Profit

Clean Market Value

CMV_b

832,769.83 = 832,179.45
- (-590.38)

= V - Accrued_Interest.b

Quote currency figures
Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit.q

-403.60 = -843,497.48 *
0.996364809 (-840,027.60)

= A.q * D_f.q - V_b.q

Accrued Interest
(Local)

Accrued_Interest.q

=0

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6 Forex
6.1 FX spot and FX forward

Data

Symbol

Example

Formula

Other Profit (Local)

Other_Profit.q

142.34 = -261.26 (-403.60) - 0

= Total_Profit.q - MtoM_Profit.q
- Accrued_Interest.q

Clean Market Value

CMV_q

-840,288.87

= V.q

Profit Method = FX Implied Interest
Base currency figures

•

Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit_Local.b

94.71 = 1,000,000 *
0.998784501 –
997,196.77 – 1,493.03

= A * D_f.b - V_bl.b Accrued_Interest_Local.b

Accrued Interest
(Local)

Accrued_Interest_Local.b

1,493.03 = 997,196.77 *
0.01100 * (2004/08/16 –
2004/06/28) / 360

= V_bl.b * r_0.b * (dt_f - dt_s)
/B

Other Profit (Local)

Other_Profit_Local.b

-169.16 = 1,418.58 –
94.71 -1,493.03

= Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b

FX Profit

FX_Profit

-9,030.30 = 997,196.77 *
(1 / 1.2000 – 1 /
1.187100)

= V_bl.b * (1 / S – 1 / S_0)

MtoM Profit

MtoM_Profit.b

78.92 = 94.71 / 1.2000

= MtoM_Profit_Local.b / S

Accrued Interest

Accured_Interest.b

1,244.19 = 1,493.03 /
1.2000

= Accrued_Interest_Local.b / S

Other Profit

Other_Profit.b

-140.96 = -7,848.15 –
78.92 - 1,244.19 –
(-9,030.30)

= Total_Profit.b - MtoM_Profit.b
- Accrued_Interest.b - FX_Profit

Clean Market Value

CMV_b

830,935.27 = 832,179.45
-1,244.19

= V - Accrued_Interest.b

Quote currency figures

•

Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit.q

1,444.49 = -843,497.48
*0.996364809 – (-840,027.60) –
(-1,848.09)

= A.q * D_f.q - V_b.q Accrued_Interest.q

Accrued Interest
(Local)

Accrued_Interest.q

-1,848.08 = -840,027.60 *
0.01616348 * (2004/08/16
-2004/06/28) / B

= V_bl.q * r_0.q * (dt_f - dt_s)
/B

Other Profit (Local)

Other_Profit.q

142.34 = -261.26 – 1,444.49 –
(-1,848.09)

= Total_Profit.q - MtoM_Profit.q
- Accrued_Interest.q

Clean Market Value

CMV_q

-838,440.78 = -840,288.87 (-1,848.08)

= V.q - Accrued_Interest.q

400

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6 Forex
6.1 FX spot and FX forward

Profit Method = FX Implied Yield
•

•

Base currency figures
Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit_Local.b

95.69 = 1,000,000 *
0.998784501 –
997,196.77 - 1,492.05

= A * D_f.b - V_bl.b Accrued_Interest_Local.b

Accrued Interest
(Local)

Accrued_Interest_Local.b

1,492.05 =
1,000,000*(POWER(1+0.0
1104512, -0.11944444) –
POWER(1+0.01104512,
-0.2555556))

=A*
(POWER(1+Base_CCY_Yield, t_m) POWER(1+Base_CCY_Yield,
-t_p))

Other Profit (Local)

Other_Profit_Local.b

-169.16 = 1,418.58 –
95.69 – 1,492.05

= Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b

FX Profit

FX_Profit

-9,030.30 = 997,196.77 *
(1 / 1.2000 – 1 /
1.187100)

= V_bl.b * (1 / S – 1 / S_0)

MtoM Profit

MtoM_Profit.b

79.74 = 95.69 / 1.2000

= MtoM_Profit_Local.b / S

Accrued Interest

Accrued_Interest.b

1,243.37 = 1,492.05 /
1.2000

= Accrued_Interest_Local.b / S

Other Profit

Other_Profit.b

-140.96 = -7,848.15 –
79.74 - 1,243.37 –
(-9,030.30)

= Total_Profit.b - MtoM_Profit.b
- Accrued_Interest.b FX_Profit

Clean Market Value

CMV_b

830,936.08 = 832,179.45
- 1,243.37

= V - Accrued_Interest.b

Quote currency figures
Data

Symbol

Example

Formula

MtoM Profit (Local)

MtoM_Profit.q

1,442.71 = -843,497.48 *
0.996364809 – (-840,027.60)

= A.q * D_f.q - V_b.q Accrued_Interest.q

Accrued Interest
(Local)

Accrued_Interest.q

-1,846.30 = -843,497.48 *
(POWER(1+0.01626098, 0.11944444) – POWER(1 +
0.01626098, - 0.2555556)

= A.q * (POWER(1 +
Quote_CCY_Yield, - t_m) POWER(1 + Quote_CCY_Yield,
-t_p))

Other Profit (Local)

Other_Profit.q

142.34 = -261.26 – 1,442.71 –
(-1,846.30)

=Total_Profit.q - MtoM_Profit.q
- Accrued_Interest.q

Clean Market Value

CMV_q

-838,442.56 = -840,288.87 (-1,846.30)

= V.q - Accrued_Interest.q

6.1.5.2.3 Risk figures
The risk method used for this FX forward deal is the Theoretical method.

•

Base currency figures
Data

Symbol

Example

Formula

IR Exposure 1bp

E_ip

-9.94 = 1,000,000 *
(-(0.11944444-0.00555556) *
0.01067917-t_s*D_f.b*D_s)/1.0*0.0001

= A * (-(t_m-t_s) * D_f.b * D_s
- t_s *D_f.b* D_s) / S * 0.0001

FX Exposure

E_fx

8,321.79 = 0.01 * 832,179.45

= e_fx * V

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6 Forex
6.1 FX spot and FX forward

Data

Symbol

Example

Formula

Effective Duration

U_eff

0.1194444 = -9.94 / 832,179.45 / 0.0001

= -E_ip / V / 0.0001

Quote currency figures

•

Data

Symbol

Example

Formula

IR Exposure 1bp

E_ipq

10.04 = -843,497.48 *
(-(0.11944444-0.00555556) *
0.996364809*0.999830638-t_s*D_f.q*D_s)
* 0.0001

= A.q * (-(t_m-t_s) * D_f.q *
D_s - t_s * D_f.q * D_s) *
0.0001

FX Exposure

E_fx

Effective Duration

U_eff

=0
0.1194444 = 10.04 / (-840,288.87) / 0.0001

= -E_ipq / V.q / 0.0001

6.1.5.3 Calculations - Quoted valuation method
In this section, numerical examples demonstrate how the different figures are calculated for the
example FX forward deal using the Quoted valuation method.
This example shows an FX forward Buy 1,000,000 USD/EUR 3M, with the following deal data.

Transaction data
Data

Symbol

Opening Date

Example
2009-04-04

Spot Date

dt_s

2009-04-07

Nominal Amount

A_q

1,000,000

Deal Rate

F_0

1.350000

FX Spot Rate

S_0

1.400000

Base Spot FX Rate (Quote
CCY)

S_0_q

1.400000

Base Spot FX Rate (Base CCY)

S_0_b

1.000000

Base FX Rate (Quote CCY)

F_0_q

1.350000

Base FX Rate (Base CCY)

F_0_b

1.000000

Base CCY Interest %

r_0.b

2.000000%

Maturity Date

dt_m

2010-04-07

Date Basis (Base CCY)

B_b

360

Date Basis (Quote CCY)

B_q

360

Data

Symbol

Example

Formula

Base Amount

A_b

-740,740.74

=-A_q /F_0

IR Difference

d_r

3.727042%

=r_0.q*t_p_q / t_p_b -r_0.b

Period

t_p

1.0138889

=(dt_m-dt_s)/B_b

Period (Quote CCY)

t_p_q

1.0138889

=(dt_m-dt_s)/B_q

Calculated transaction data

402

© Wall Street Systems IPH AB - Confidential

6 Forex
6.1 FX spot and FX forward

Data

Symbol

Example

Formula

Base CCY Yield

y_0.b

5.724808%

=POWER(D_0_q, -1/t_p) - 1

Quote CCY Yield

y_0.q

1.999724%

=POWER(D_0_b,-1/t_p_q)-1

Discount Factor

Base CCY: D_0_b

0.98012524

=1/(1+r_0_b * t_p_b)

Quote CCY: D_0_q

0.94512077

=1/(1+r_0_q*t_p_q)

Book/Reference Value

Base CCY: V_b_b

-700,089.46

=A_b * D_0_q

Quote CCY: V_b_q

980,125.24

=A_q * D_0_b

Data

Symbol

Example

Formula

Figure date

dt_f

2009-06-15

Base CCY: D_V_b

0.971428368804

Market data on Figure Date

Market Value Discount Factor

Quote CCY: D_V_q
Discount Factor Spot

Base CCY: D_s_b

0.999862792158

Quote CCY: D_s_q
FX Spot Rate

FX Rate

Time to maturity

Base CCY: S_b

1.000000000

Quote CCY: S_q

1.2936

Base CCY: F_b

1.000000000

Quote CCY: F_q

1.2963

Base CCY: t_m_b

0.822222

=(dt_m- dt_f)/B_b

Quote CCY: t_m_q

0.822222

=(dt_m - dt_f)/B_q

6.1.5.3.1 Valuation figures
The valuation method used for this deal is the Quoted method.
Data
Market Value

Result Value

Symbol

Example

Formula

Base CCY: V_b

-719,576.57

=A_b * D_V_b / F_b

Quote CCY: V_q

749,385.46

=A_q *D_V_q / F_q

Base CCY: V_p_b

-719,576.57

= A_b * D_V_b / F_0_b

Quote CCY: V_p_q

719,576.57

= A_q * D_V_q / F_0_q

6.1.5.3.2 Result figures
Data

Symbol

Example

Formula

Total Profit per CCY

Base CCY: P_t_b

0.00

= V_b - V_p_b

Quote CCY: P_t_q

29,808.89

= V_q - V_p_q

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6 Forex
6.1 FX spot and FX forward

Profit Method = FX Forward
Data
FX Profit

MtoM Profit

Other Profit

Symbol

Example

Formula

Base CCY: P_fx_b

0.00

=A_b * (1 / S_b-1 / S_0_b) * D_V_b

Quote CCY: P_fx_q

57,072.17

= A_q * (1 / S_q-1 / S_0_q) * D_V_q

Base CCY: P_mtom_b

.00

=_b/D_s_b - V_p_b/D_s_b - P_fx_b

Quote CCY: P_mtom_q

-27,259.19

=V_q/D_s_q - V_p_q/D_s_q - P_fx_q

Base CCY:

0.00

= P_t_b - P_fx_b - P_mtom_b

Quote CCY:

-4.09

= P_t_q - P_fx_q - P_mtom_q

Profit Method = FX/IR Difference
Data

Symbol

Example

Formula

Accrued Interest

Base CCY: Ai_b

.000000

=A_b*(1/S_0_b-1/F_0_b)*(t_p_b-t_m_b)/t_p_b

Quote CCY: Ai_q

-5,001.09

=A_q*(1/S_0_q-1/F_0_q) * (t_p_q t_m_q)/t_p_q

Base CCY:

.00

=P_fx_b

Quote CCY:

57,072.17

=P_fx_q

Base CCY: P_mtom_b_2

.00

=V_b/D_s_b - V_p_b / D_s_b - P_fx_b - Ai_b

Quote CCY: P_mtom_q_2

-22,258.10

=V_q/D_s_q - V_p_q/D_s_q - P_fx_q - Ai_q

Base CCY:

.00

=P_t_b - P_fx_b - P_mtom_b_2 - Ai_b

Quote CCY:

-4.09

=P_t_q - P_fx_q - P_mtom_q_2 - Ai_q

FX Profit

MtoM Profit

Other Profit

Profit Method = FX/IR Difference No Discounting
Data

Symbol

Example

Formula

Accrued Interest

Base CCY:

.00

=Ai_b

Quote CCY:

-5,001.09

=Ai_q

Base CCY: P_fx_b_2

.00

=A_b*(1/S_b-1/S_0_b )

Quote CCY: P_fx_q_2

58,750.77

=A_q*(1/S_q-1/S_0_q)

Base CCY: P_mtom_b_3

.00

= V_b/D_s_b - V_p_b / D_s_b - P_fx_b_2 Ai_b

Quote CCY: P_mtom_q_3

-23,937.79

=V_q / D_s_q - V_p_q / D_s_q - P_fx_q_2 Ai_q

Base CCY: missing

.00

= P_t_b - P_fx_b_2 - P_mtom_b_3 - Ai_b

Quote CCY: missing

-4.09

=P_t_q - P_fx_q_2 - P_mtom_q_3 - Ai_q

FX Profit

MtoM Profit

Other Profit

404

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6 Forex
6.1 FX spot and FX forward

Profit Method = FX Interest
Data
Accrued Interest

FX Profit

MtoM Profit

Other Profit

Symbol

Example

Formula

Base CCY: Ai_b_3

-5,001.09

=A_b*(1 - F_0/S_0) * (t_p_b - t_m_b)/t_p_b

Quote CCY:

.00

=0

Base CCY:

.00

=0

Quote CCY:

58,750.77

=P_fx_q_2

Base CCY: P_mtom_b_4

5,001.09

=V_b / D_s_b - V_p_b / D_s_b - P_fx_b_2 Ai_b_3

Quote CCY: P_mtom_q_4

-28,937.79

=V_q / D_s_q - V_p_q / D_s_q - P_fx_q_2

Base CCY:

.00

=P_t_b - P_fx_b_2 - P_mtom_b_4 - Ai_b_3

Quote CCY:

-4.09

=P_t_q - P_fx_q_2 - P_mtom_q_4

Profit Method = FX Implied Interest
Data
Accrued Interest

FX Profit

MtoM Profit

Other Profit

Symbol

Example

Formula

Base CCY: Ai_b_2

-7,684.76

=A_b*r_0_q * (dt_f-dt_s)/B_q *D_0_q / S_b

Quote CCY: Ai_q_2

2,904.41

=A_q*r_0_b * (dt_f-dt_s)/B_b *D_0_b / S_q

Base CCY: P_fx_b_3

.00

=0

Quote CCY: P_fx_q_3

57,583.12

=V_b_q * (1/S_q-1/S_0_q)

Base CCY: P_mtom_b_5

7,684.76

=V_b / D_s_b - V_p_b / D_s_b - P_fx_b_3 Ai_b_2

Quote CCY: P_mtom_q_5 -30,674.55

=V_q / D_s_q - V_p_q / D_s_q - P_fx_q_3 Ai_q_2

Base CCY:

.00

=P_t_b - P_fx_b_3 - P_mtom_b_5- Ai_b_2

Quote CCY:

-4.09

=P_t_q - P_fx_q_3 - P_mtom_q_5- Ai_q_2

Profit Method = FX Implied Yield
Data

Symbol

Example

Formula

Accrued Interest

Base CCY: Ai_b_4

-7,509.92

=A_b * (POWER(1+y_0.b,-t_m_b)
-POWER(1+y_0.b,-t_p ))/S_b

Quote CCY: Ai_q_4

2,880.82

=A_q * (POWER(1+y_0.q,-t_m_q)
-POWER(1+y_0.q,-t_p ))/S_q

Base CCY:

.00

=0

Quote CCY:

57,583.12

=P_fx_q_3

Base CCY: P_mtom_b_6

7,509.92

=V_b / D_s_b - V_p_b / D_s_b - P_fx_b_3 Ai_b_4

FX Profit

MtoM Profit

Other Profit

Quote CCY: P_mtom_q_6 -30,650.96

=V_q / D_s_q - V_p_q / D_s_q - P_fx_q_3 Ai_q_4

Base CCY:

.00

=P_t_b - P_fx_b_3 - P_mtom_b_6- Ai_b_4

Quote CCY:

-4.09

=P_t_q - P_fx_q_3 - P_mtom_q_6- Ai_q_4

6.1.5.3.3 Risk figures
The risk method used for this FX forward deal is the Theoretical method: see 6.1.5.2.3 Risk figures
on page 401.

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6 Forex
6.2 Average FX rate forward

6.2 Average FX rate forward
An average rate forward gives the buyer the ability to create a hedge rate for a future exposure by
locking in forward points and a spot rate today. At some point in the future, there is an averaging
period of spot observations to determine an average rate which, when compared to the hedge rate,
will set the payout. Unlike options, this hedge tool is a forward contract and has no premium cost
associated with it.
If the receivable currency is weaker during the averaging period compared to the hedge rate, the
forward seller will make a payment to the forward buyer. Conversely, if the receivable currency
appreciates during the averaging period, the forward buyer must make a payment to the forward
seller. These structures are cash-settled.

6.2.1 Instrument setup
Average FX rate forwards are based on an instrument type derived from the class FX.

•

Main characteristics
Average FX rate forwards are set up in a similar way to non-deliverable FX forwards, except that
you can configure the type of average rate forward in terms of observation dates and weights:
Information

Description

Observation Method

Choices are: Irregular and Business Days.
•

If you select Business Days, observation dates are defined for all business
days (regarding the fixing currency at transaction level) between the spot
date and the value date - the fixing offset (specified in the Netting page).

•

If you select Irregular, you can define the observation dates and weights at
deal entry in the views Observation Date and Observation Schedule in
Transaction Manager.

Choices are: Irregular Weights and Equally Weighted (default).

Weighting Method

Note: Only editable when the observation method is Irregular.
Average Rounding Method
Average Rounding

Rounding method and precision to be used for the average.

See A.2.41 Average FX Rate Forward on page 728.

6.2.2 Deal capture
6.2.2.1 Input data
In addition to the standard deal parameters, the following mandatory information is required to
enter an average FX rate forward transaction. See 6.1.3.1 Input data on page 384.

•

Transaction view

Note: This information defaults to the information defined at the instrument level.

406

Information

Description

Observation
Method

Choices are: Irregular and Business Days.
•

If you select Business Days, observation dates are defined for all business days
(regarding the fixing currency at transaction level) between the spot date and the
value date - the fixing offset (specified in the Netting page).

•

If you select Irregular, you can define the observation dates and weights at deal
entry in the views Observation Date and Observation Schedule in Transaction Manager.

© Wall Street Systems IPH AB - Confidential

6 Forex
6.2 Average FX rate forward

Information

Description

Weighting
Method

Choices are: Equally Weighted (default) and Irregular Weights.
If you select Irregular Weights, you will need to enter the weights manually at the
transaction level in the Observation Date view.
Note: Only editable when the observation method is Irregular.

Average
Rounding Method
Average
Rounding

Rounding method and precision to be used for the average.

The Fixing Calendar field can be edited at the transaction level to enable the user to specify the
calendar to be used to generate the observation dates. The Fixing Subscenario field can be
edited to specify the subscenario to be used for FX rates observations.
When the observation method is set to Business Days, the observation dates are defined by the
business days (according to the fixing calendar specified at the transaction level) between spot
date and value date – fixing offset (specified at the instrument level in the Netting page)
If you selected to use the Irregular method, you need to provide the relevant information in order
to generate the observation dates.

•

Observation Schedule view
Information

Description

Start Date

Defaults to the spot date of the transaction.

End Date

Defaults to the transaction value value - the fixing offset.

Method

Combined with the specified frequency defines how often the cashflows will be
generated. (Used with Frequency.)
•

Days, Business Days, Weeks, Months or Years: One flow every specified
frequency days or business days or weeks or months or years. For
example, if you select year and you specify a frequency of 1, you will have
one flow every year; a frequency of 2, one flow every two years, and so
on.

•

Times/Year: The specified frequency determines how many times per year.
For example, if you specify a frequency of 1, the cashflows will be
generated once per year; if you specify 2, the cashflows will be generated
twice per year.

•

Last of Month: One flow the last day of every specified frequency month.

•

Months (sticky): The same as Last of Month, if the end date falls at month
end, otherwise like Months.

•

ISDA Dates (Q): 15 March, 15 June, 15 Sept. and 15 Dec.

•

IMM Dates (M): One flow every 3rd Wednesday of every specified frequency
month

•

Manual: Select if you want to be able to enter the dates directly in the
Observation Date view. When this method is selected, the dates will no
longer be generated from the transaction, and the following fields are
cleared and are no longer editable.

Frequency

Number of time units (to be used with Method).

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6 Forex
6.2 Average FX rate forward

Information

Description

Convention

Convention used to adjust the observation dates:
•

Backward - previous business day

•

Following - next business day

•

Modified Backward - previous business day except if not in the same month
(next in this case)

•

Modified Following - next business day except if not in the same month

•

None - no adjustment.

(previous in this case)

Holiday Calendar

Additional calendar to supplement the calendar specified in the Fixing Calendar
column (at the transaction level).

Roll from Start

Yes or No:
When set to Yes, dates are calculated from Start Date rather than from the End

Date.
Long Stub

Yes or No:
To change the first coupon period to a long first coupon. By default, it is a
short first coupon when the period is broken.
For example, selecting Yes in the Roll from Start field causes a long last coupon.

Fixed Roll Date

•

Specific date to be used in the schedule each year, without reference to the
year: for example, 15 March annually.

Observation Date
Information

Description

Observation Date

If you selected to enter the observation dates manually (Manual method in the
Observation Schedule view), enter the dates, otherwise the dates generated
from the inputs in the observation schedule are displayed.

Weight

Enter the weight if you selected the Irregular Weights method.

6.2.2.2 Generated data
The generated cashflows are the same as for non-deliverable forwards, i.e. two pseudo FX
settlement flows and one netting flow.

6.2.3 Processing
This section describes the actions that can be done throughout the life of an average FX rate forward
transaction. These actions are similar to those that can be done on non-deliverable forwards except
for the differences explained further on.

6.2.3.1 Early expiration
This action remains unchanged to FX non-deliverable forwards, except that the defaulted FX
Forward Rate is replaced by the average of the already observed FX Rate and Forward FX rate based
on the early expiration date:

•

Execution
Right-click the transaction and select Early Expiration. As well as the usual information for an early
expiration on a standard FX non-deliverable forward, the following information is required:

408

Information

Description

Avg FX Observed Rate

Average value of already observed Fx rates.

© Wall Street Systems IPH AB - Confidential

6 Forex
6.3 Open Window FX Forward (FX Time Option)

Information

Description

Avg FX Forecasted Rate

Average value of the forecast value of FX Rate (observations in the future
according to the early expiration date).

Avg FX Forward Rate

Average value of the observed and forecast FX rates.

See 6.1.4.2 Early expiration of NDFs on page 388.

6.2.3.2 Netting
The netting action is similar to the netting action of a non-deliverable forward FX instrument, except
that the FX Rate is replaced by the Average FX Rate.

•

Execution
Right-click the netting cashflow and select Execute Netting. As well as the usual information for a
netting action on a standard FX non-deliverable forward, the following information is needed:
Information

Description

Avg FX Rate

Defaults to the average value of past observation dates.

Netting Amount

Computed and rounded according to the values defined at the instrument and
transaction levels.

As usual, the execution of this action sets the amount of the netting cashflow, and stores the
netting price in the Nominal Rate field at the cashflow level.
See 6.1.4.5 Netting on page 392.

6.2.4 Position monitoring
6.2.4.1 Setup
You need to use the specific valuation feature Average FX Rate Valuation to support specific Quoted
valuation needed for this instrument. See A.2.42 Average FX Rate Valuation on page 728.

6.2.4.2 Calculations
With this valuation feature Average FX Rate Valuation, the average rate forward is taken instead of
forward FX rate when computing market value. Indeed, the cashflow is converted using the forward
rate between cashflow currency and valuation currency before being discounted with valuation
currency interest rate. The average rate is computed with the already observed FX rates and
forecasted FX rates for the future dates regarding the valuation. This average FX rate is visible in
Figure FX Rate.
The Theoretical valuation is the same as for FX non-deliverable forward instruments. See 6.1.5
Position monitoring on page 393.

6.3 Open Window FX Forward (FX Time Option)
An open window FX forward differs from a regular FX Forward in that the owner of the contract can
choose the date (from within a defined time window) when the forward cashflows are exchanged.
This means that the transaction is specified in terms of a maturity window rather than a single
maturity date. The owner of the contract must also be specified.

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6.3.1 Instrument setup
Open Window FX Forward instruments are based on an instrument type derived from the class
FX-TIME-OPTION.
Main characteristics

•

The main characteristics of an Open Window FX Forward instrument are defined using the
primary feature FX Time Option.

–

Date information
It is possible to define the periods for which the start and end of the exercise window are
derived.

–

Information

Description

Value Date Period

Period from which start of exercise window is derived.

Maturity Date Period

Period from which end of exercise window is derived.

Time option owner
It is possible to define the owner (counterparty or portfolio owner).
Information

Description

Base Currency

Base and quote currencies for the instrument.

Quote Currency

Leave these fields blank if you want to specify the currencies when you enter the
deal.

Transaction Sign

Owner

Sign to be applied to the transaction: Any (default), Buy/Lend, or Sell/Borrow:
•

Select Any or leave this field blank if you want to specify the direction of the
transaction when you enter the deal.

•

Select either Buy/Lend or Sell/Borrow if you want this to be the direction of the
transactions, that is, the direction cannot be modified at deal entry.

Owner of the contract. Select Counterparty or Portfolio Owner.
Leave this field blank if you want to specify the owner when you enter the deal.
Note: This is used with Optimal maturity method when you are using the valuation
approach FX Time Option Valuation.

See A.2.198 FX Time Option on page 810.

6.3.2 Deal capture
In addition to the standard deal parameters, the following information is required to enter an open
window FX forward transaction:
Information

Description

Value Date

Start of the exercise period

Maturity Date

End of the exercise period.

Time option
owner

The person who chooses the exercise day of the transaction (Portfolio Owner or
Counterparty).
If the owner is not defined at instrument level, it can be specified at the transaction level.
Note: This is used with Optimal maturity method when you are using the valuation
approach FX Time Option Valuation Method.

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6.3.3 Processing
This section describes the actions that can be done throughout the life of an FX transaction.

6.3.3.1 Exercise
Within the window period, it is possible to exercise the transaction. That is, to determine the
payment dates of the cashflows.

•

Execution
The following information is needed to process the early expiration:
Information

Description

Early Expiration
Date

Date when the exercise is done.

Value Date

Date when the early expiration is settled. This cannot be later than the maturity date
of the initial transaction.

Amount Left

Remaining amount of the initial transaction. (Read-only.)

Amount to Expire

Amount to be exercised. This defaults to the amount left and is expressed in the same
currency (base or quote) as the input amount of the initial transaction. You can enter
any amount between 0 and the remaining amount of the initial transaction.

Currency

The currency in which the above amount is expressed, can be base or quote currency
depending on the initial transaction. (Read-only.)

Deal Rate

Agreed forward rate for the exercised transaction.

Quote Amount

The corresponding amount of the transaction.

Quote Currency

Shows the currency of the deal. The currency can be quote or base depending on
default Currency.

By default, this is today’s date unless a Fixing/Action Date is specified at transaction
level.

6.3.4 Position monitoring
6.3.4.1 Setup
Time option valuation is chosen with the feature FX-TIME-OPTION-METHOD.
Information

Description

Maturity Method

Choose from Earliest, Latest, Optimal

Valuation Modes

Choose from Benchmark, Default, Theoretical.

6.3.4.2 Calculations
This section describes the valuation and provides numerical examples to illustrate the calculations of
Open Window FX Forward (FX Time Option) deals.

6.3.4.2.1 Valuation
FX Time Option instruments use a special valuation feature FX Time Option Valuation (A.2.199 FX
Time Option Valuation on page 811). This valuation method simply creates a virtual payment date
for the forward cashflows, and then uses the standard fixed method for key figures. That is, the
calculation of an Open Window FX Forward (FX Time Option) deal is similar to that of a regular FX
Forward (6.1 FX spot and FX forward on page 383), except that we need to assume a payment date
(from within a defined time window). To do this, the user chooses a maturity method from the
available methods:

•

Earliest: Calculate open transactions with maturity at the start of the window.

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Latest: Calculate open transactions with maturity at the end of the window.

•

For Earliest or Latest method, the payment date is directly copied from the window.
Optimal: Calculate open transactions with maturity at either start (earliest) or end (latest) of the
window, so that the value for the owner is maximized. Refer to the following section for a
detailed description of the calculation.

•

Optimal method calculation
For the Optimal method, the following logic is used to determine whether the start or end date of the
window should be chosen as the virtual payment date to obtain the best value for the time option
owner. (To set up the owner refer to 6.3.1 Instrument setup on page 410.)
Let Ab and Aq be the (absolute) amounts of the bought and sold currencies, respectively, and Sb
and Sq the corresponding spot exchange rates against the portfolio currency.
Let

D1b , D2b , D1q , D2q

be the discount factors for the two currencies (superscript q or b) for the start

and the end of the window (subscript 1 or 2).
Then, if we own the right to choose the exercise date (Owner set to Portfolio Owner), the closer date
is chosen if
Equation 6-1

S b Ab D1b − S q Aq D1q > S b Ab D 2b − S q Aq D 2q
Otherwise, the end date of the window is chosen.
If the counterparty owns the right to choose (Owner set to Counterparty), then the decision logic is
reversed.
If Quoted valuation method is used, the closer date is chosen if
Equation 6-2 Quoted valuation method

Fb1 Ab D1p − Fq1 As D1p > Fb2 Ab D 2p − Fq2 As D 2p
where now all discount factors are in portfolio currency, and

Fi

j

are forward FX rates between the

cashflow and portfolio currencies.
If the currency pair’s figure spot date is within the window period, the start date used in the
valuation is the spot date corresponding to the figure date.
Result calculations are similar to those of an FX forward maturing on the virtual payment date.
However, accrued interest is always calculated for the maturity period, regardless of the virtual
payment date.

6.3.4.3 Numerical examples
The numerical examples in this section demonstrate how the different figures are calculated for the
example Open Window FX forward deal using the Theoretical valuation method.
This example shows an FX forward Buy 1,000,000 USD/EUR 3M, with the following deal data:
Setup

•

Data
Valuation Method

412

Symbol

Example
Theoretical

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6.3 Open Window FX Forward (FX Time Option)

•

•

Transaction data
Data

Symbol

Example

Opening Date

dt_o

2007-11-09

Spot Date

dt_s

2007-11-13

Nominal Amount

A

1,000,000

Deal Rate

F_0

2.050000

FX Spot Rate

S_0

2.010000

Base FX Spot Rate

S_B.b

1.430000 (base)

Base FX Spot Rate

S_B.q

1.405594 (quote)

Base FX Rate

F_B.*

1.434600

Base CCY Interest %

r_0.b

5.000000%

Value Date

dt_v

2008-06-16

Maturity Date

dt_m

2008-12-15

Date Basis (Base CCY)

B

360

Date Basis (Quote CCY)

B.q

365

Symbol

Example

Formula

1,000,000.00

=A

Calculated transaction data
Data
Amount (Base CCY)

•

Amount (Quote CCY)

A.q

-487,804.88

= -A / F_0

FX Forward Points

p_fx

400

=10000*(F_0-S_0)

IR Difference

dr

-1.862483%

= (S_0 / F_0 / D.b - 1) / t_p-r_0.b

Quote CCY Interest %

r_0.q

End Period

t_p

1.1055556

=(dt_m-dt_s)/B

Other important calculated transaction data
Data

Symbol

Example

Formula

Discount Factor

D.b

0.94761779

=1/(1+r_0.b*t_p)

1,000,000.00

=A

Base Value (Base CCY)

•

Base Value (Quote CCY)

BaseValue.q

-497,512.44

=-A / S_0

Result Value (Base CCY)

ResultValue.b

662,669.79

=ResultValueLocal.b /S_B.b

Result Value (Quote CCY)

ResultValue.q

-662,669.59

=ResultValueLocal.q * S_B.q

Local Result Value (Base CCY)

ResultValueLocal.b

947,617.79

= A * D.b

Local Result Value (Quote CCY)

ResultValueLocal.q

-471,451.64

=-ResultValueLocal.b / S_0

Data

Symbol

Example

Figure Date

dt_f

12/12/2007

Market Data on Figure Date

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Data

Symbol

Example

FX Spot Rate (Base CCY)

F_S.b

1.4844

FX Spot Rate (Quote CCY)

F_S.q

1.390697

Calculated Market Data on Figure Date

•

Data

Symbol

Example

Formula

FX Convert (Base CCY)

S

0.673673

= 1 / F_S.b

FX Convert (Quote CCY)

S.q

1.390697

=F_S.q

MV Discount Factor Start (Base
CCY)

D_V.s.b

0.961217301872

MV Discount Factor Start (Quote
CCY)

D_V.s.q

0.970243996748

MV Discount Factor End (Base
CCY)

D_V.e.b

0.925429031747

MV Discount Factor End (Quote
CCY)

D_V.e.q

0.942867984024

Discount Factor Spot (Base CCY)

D_s

0.99975004706

Discount Factor Spot (Quote
CCY)

D_s.q

0.99975004706

6.3.4.3.1 Window start
Key Figures on Figure Date
Data

Symbol

Example

Formula

Local Market Value (Base CCY)

LocalMarketV
alue.s.b

961,217.30

=A*D_V.s.b

Local Market Value (Quote CCY)

LocalMarketV
alue.s.q

-473,289.75

=A.q*D_V.s.q

Market Value (Base CCY)

V.s.b

647,546.01

=LocalMarketValue.s.b * S

Market Value (Quote CCY)

V.s.q

-639,631.06

=LocalMarketValue.s.q * S.q

Result Figures - Method FX Forward
Data

Symbol

Example

Formula

Local Total Profit (Base CCY)

TotalProfitLo
cal.s.b

13,599.51

=LocalMarketValue.s.b ResultValueLocal.b

Local Total Profit (Quote CCY)

TotalProfitLo
cal.s.q

-1,838.12

= LocalMarketValue.s.q ResultValueLocal.q

Total Profit (Base CCY)

TotalProfit.s.
b

-15,123.77

= V.s.b - ResultValue.b

Total Profit (Quote CCY)

TotalProfit.s.
q

4,466.95

=V.s.q - ResultValue.q

Local MtoM Profit (Base CCY)

MtoMProfitLo
cal.s.b

13,839.83

= A * D_V.s.b/D_s ResultValueLocal.b

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Data

Symbol

Example

Formula

Local MtoM Profit (Quote CCY)

MtoMProfitLo
cal.s.q

-2,663.78

= A.q * D_V.s.q/D_s.q ResultValueLocal.q AccruedInterestLocal.s.q

Local Accrued Interest (Quote CCY)

AccruedInter
estLocal.s.q

707.33

= ResultValueLocal.q * dr * (dt_f dt_s) / B

Local Other Profit (Base CCY)

Other_Profit
_Local.b

-240.32

=TotalProfitLocal.s.b-MtoMProfitLoca
l.s.b

118.33

=TotalProfitLocal.s.q MtoMProfitLocal.s.q AccruedInterestLocal.s.q

Local Other Profit (Quote CCY)

FX Profit (Base CCY)

FXProfit.s.b

-25,627.83

= A * (1/F_S.b-1/S_B.b)

FX Profit (Quote CCY)

FXProfit.s.q

7,411.44

= BaseValue.q * (F_S.q-S_B.q)

MtoM Profit (Base CCY)

MtoMProfit.s.
b

9,323.52

= MtoMProfitLocal.s.b / F_S.b

MtoM Profit (Quote CCY)

MtoMProfit.s.
q

-3,704.51

=MtoMProfitLocal.s.q * F_S.q

Accrued Interest (Quote CCY)

AccruedInter
est.s.q

983.69

=AccruedInterestLocal.s.q * S.q

Other Profit (Base CCY)

Other_Profit
_h

1,180.55

= TotalProfit.s.b - MtoMProfit.s.b FXProfit.s.b

-223.67

= TotalProfit.s.q - FXProfit.s.q
-MtoMProfit.s.q -AccruedInterest.s.q

Other Profit (Quote CCY)

6.3.4.3.2 Window end
Key Figures on Figure Date
Data

Symbol

Example

Formula

Local Market Value (Base CCY)

LocalMarket
Value.e.b

925,429.03

=A*D_V.e.b

Local Market Value (Quote CCY)

LocalMarket
Value.e.q

-459,935.60

=A.q*D_V.e.q

Market Value (Base CCY)

V.e.b

623,436.43

=LocalMarketValue.e.b * S

Market Value (Quote CCY)

V.e.q

-639,631.06

=LocalMarketValue.e.q * S.q

Data

Symbol

Example

Formula

Local Total Profit (Base CCY)

TotalProfitLo
cal.e.b

-22,188.76

=LocalMarketValue.e.b ResultValueLocal.b

Local Total Profit (Quote CCY)

TotalProfitLo
cal.e.q

11,516.04

= LocalMarketValue.e.q ResultValueLocal.q

Total Profit (Base CCY)

TotalProfit.e.
b

-39,233.36

= V.e.b - ResultValue.b

Total Profit (Quote CCY)

TotalProfit.e.
q

23,038.53

=V.e.q - ResultValue.q

Result Figures - Method FX Forward

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6.4 FX swap

Data

Symbol

Example

Formula

Local MtoM Profit (Base CCY)

MtoMProfitLo
cal.e.b

-21,957.39

= A * D_V.e.b/D_s ResultValueLocal.b

Local MtoM Profit (Quote CCY)

MtoMProfitLo
cal.e.q

10,693.71

= A.q * D_V.e.q /D_s.qResultValueLocal.q AccruedInterestLocal.e.q

Local Accrued Interest (Quote CCY)

AccruedInter
estLocal.e.q

707.33

= ResultValueLocal.q * dr * (dt_f dt_s) / B

Local Other Profit (Base CCY)

-231.37

=TotalProfitLocal.e.b MtoMProfitLocal.e.b

Local Other Profit (Quote CCY)

114.99

=TotalProfitLocal.e.q MtoMProfitLocal.e.q AccruedInterestLocal.e.q

FX Profit (Base CCY)

FXProfit.e.b

-25,627.83

= A * (1/F_S.b-1/S_B.b)

FX Profit (Quote CCY)

FXProfit.e.q

7,411.44

=BaseValue.q * (F_S.q-S_B.q)

MtoM Profit (Base CCY)

MtoMProfit.e
.b

-14,792.10

=MtoMProfitLocal.e.b / F_S.b

MtoM Profit (Quote CCY)

MtoMProfit.e
.q

14,871.71

=MtoMProfitLocal.e.q * F_S.q

Accrued Interest (Quote CCY)

AccruedInter
est.e.q

983.69

= AccruedInterestLocal.e.q * F_S.q

Other Profit (Base CCY)

OtherProfit.e
.b

1,186.57

=TotalProfit.e.b - FXProfit.e.b MtoMProfit.e.b

Other Profit (Quote CCY)

OtherProfit.e
.q

-228.31

=TotalProfit.e.q - MtoMProfit.e.q AccruedInterest.e.q - FXProfit.e.q

6.4 FX swap
A currency swap transaction in the inter-bank market is the simultaneous purchase and sale of a
given amount of foreign exchange for two different value dates. Both purchase and sale are with the
same counterparty. A common type of swap is spot against forward. The dealer buys a currency as
a spot market transaction and simultaneously sells the same amount back to the same counterparty
as a forward transaction. Since this is executed as a single transaction with the same counterparty,
TRM has a separate trade entry for FX swap transactions.
In TRM, FX swaps belong to the instrument class FX-SWAP.

6.4.1 Instrument setup
FX swaps are based on an instrument type derived from the class FX-SWAP. They are set up in a
similar way to FX spot/forward instruments.

•

FX Swap main characteristics
For an FX swap, you may want to set up maturity date and value date information. The maturity
of the contract is calculated using the periods specified for both the maturity date and the value
date. For example, to define a 3M/6M forward FX swap, you need to specify 3M for both periods.

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For maturity and value date information:
Information

Description

Gap Set

Gap set used for supplying the value date periods; these in turn are used to define
exact dates.

Value Date Period

Value date period used to calculate the value date for the instrument at deal entry.
If this is specified at the instrument level, it is used as default in the transaction
and cannot be modified.

Maturity Date Period

Maturity period used to calculate the maturity date for an instrument at deal entry,
for example, 6M or 1Y.
If you specify the maturity date period in the instrument setup, this is used as the
default in the transaction and cannot be modified.

Spot Days

Number of business days between opening and value dates. Defaults to currency
spot days when left blank.
Note: It is recommended not to specify the spot days in the instrument setup as
these are taken by default from the spot days of the two currencies at deal
entry.

Calendar

Calendar and Holiday Calendar used to calculate the value date.

Holiday Calendar

If you enter both a Calendar and a Holiday Calendar, the value date calculation
takes both calendars into account.
Note: When you define the Calendar or Holiday Calendar in one date setup, the
Calendar fields in all date setup pages applied to the instrument default to
the same values.

Spot Time

Cut-off time for operations.

Spot Time Zone

For global operations, a cut-off time has to be defined: deals before that time have
the number of spot days calculated from that day; deals after that time have the
spot days calculated from the following day. Define a time (Spot Time) within a
selected time zone (Spot Time Zone).
The market convention is 5 p.m. New York time.

A.2.193 FX Swap on page 807.

•

Currency information
You can specify the currencies of the FX swap either in the instrument setup or at deal entry.
See A.2.192 FX Setup on page 806.

•

Forward points calculation
You can specify whether forward points are taken from the market or calculated. If you do not
define a method for obtaining or calculating forward points, the FX spot rate is taken from the
market and the forward points need to be input manually.
See A.2.175 FX Forward on page 797.

•

FX cross rate calculation
For an FX swap where neither currency is the portfolio base currency, you need to define how
the FX rates (Base Spot FX and Base FX Rate) are calculated.
See A.2.171 FX Cross Method on page 796.

For an FX swap, it is also possible to set up:

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes

•

Competitive Rates (FX Swap)

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•

FX Swap Margin.

See Appendix A Features on page 713.

6.4.2 Market information
6.4.2.1 Currencies
Some additional parameters need to be defined for the currencies which are relevant to your FX
transactions: see the TRM User Guide.

6.4.2.2 Quotations and market information
Quotations for currencies can be viewed and modified in Rate Monitor. It is possible to define market
information feeds for each currency (for example, from Reuters): see the TRM User Guide.

6.4.3 Deal capture
6.4.3.1 Input data
In addition to the standard deal parameters, the following information is needed to enter an FX swap
transaction:

•

FX swap (input forward points)
In addition to the standard deal parameters, the following information is required to enter an FX
swap transaction where the forward points are input manually:
Information

Description

Base Currency
(Currency)

Base currency of the transaction.

Quote Currency
(Currency 2nd)

Quote currency of the transaction.

Value Date

Date of the near leg (spot transaction).

Maturity Date

Date of the far leg (forward transaction) and maturity of the contract.

FX Base Spot
Amount

Amount of the near leg (spot transaction) in the base currency.

FX Quote Spot
Amount

Amount of the near leg (spot transaction) in the quote currency.

Nominal/Spot
Rate

Exchange rate of the near leg (spot transaction).

FX Forward Points

Forward points for the transaction.

Deal Rate

Exchange rate of the far leg =

Nominal / Spot Rate + FX Forward Points (+ Margins if applicable)

•

Uneven FX swap
In addition to the standard deal parameters, the following information is required to enter an
uneven FX swap transaction, where the input amount of the near leg is different from the input
amount of the far leg:

418

Information

Description

Base Currency
(Currency)

Base currency of the transaction.

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6.4 FX swap

Information

Description

Quote Currency
(Currency 2nd)

Quote currency of the transaction.

Value Date

Date of the near leg (spot transaction).

Maturity Date

Date of the far leg (forward transaction) and maturity of the contract.

FX Base Spot
Amount

Amount of the near leg (spot transaction) in the base currency.

FX Quote Spot
Amount

Amount of the near leg (spot transaction) in the quote currency.

FX Base Amount

Amount of the far leg (forward transaction) in the base currency.

FX Quote Amount

Amount of the far leg (forward transaction) in the quote currency.

Nominal/Spot
Rate

Exchange Rate of the near leg (spot transaction)

FX Forward Points

Forward points for the transaction.

Deal Rate

Exchange rate of the far leg =

Nominal / Spot Rate + FX Forward Points (+ Margins if applicable)

•

FX swap (with interest rate)
In addition to the standard deal parameters, the following information is required to enter an FX
swap transaction with interest rate where the forward points are input manually:
Information

Description

Base Currency
(Currency)

Base currency of the transaction.

Quote Currency
(Currency 2nd)

Quote currency of the transaction.

Value Date

Date of the near leg (spot transaction).

Maturity Date

Date of the far leg (forward transaction) and maturity of the contract.

FX Base Spot
Amount

Amount of the near leg (spot transaction) in the base currency.

FX Quote Spot
Amount

Amount of the near leg (spot transaction) in the quote currency.

Nominal/Spot
Rate

Exchange Rate of the near leg (spot transaction)

FX Finance Rate

Implied borrowing rate for an FX swap transaction.

FX Forward Points

Forward points for the transaction.

Deal Rate

Exchange rate of the far leg =

Nominal / Spot Rate + FX Forward Points (+ Margins if applicable)

6.4.3.2 Generated data
•

Cashflows

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The figure below illustrates the cashflows which are established in TRM for an FX swap
transaction.

The figure below illustrates the cashflows which are established in TRM for a forward FX swap
transaction.

6.4.4 Processing
This section describes the actions that can be done throughout the life of an FX swap.

6.4.4.1 Early expiration
You can force the forward leg of an FX swap to mature earlier using the action Early Expiration.

•

Execution
The following information is needed to process the early expiration:
Information

Description

Early Expiration
Date

Date when the early expiration is executed. By default, this is today’s date unless a
Fixing/Action Date is specified at transaction level.
Opening Date must be after the near leg of the initial FX swap.

Value Date

Date when the early expiration is settled. This cannot be later than the maturity date
of the initial transaction.

Amount

Amount to be early-expired. This defaults to the amount left and is expressed in the
same currency (base or quote) as the input amount of the initial transaction. You can
enter any amount between 0 and the remaining amount of the initial transaction.

Deal Rate

Deal rate for the early expiration transaction.
Deal Rate = Original Spot Rate - Forward Points

Forward Points

Forward points of the early expiration transaction. This defaults to the number of
forward points between the early expiration date and the maturity date of the initial
transaction.

The execution generates an early expiration transaction with the following attributes:

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If the original input amount was Base Amount:
FX Base amount = amount to expire
If the original input amount was Quote Amount:
FX Quote amount = amount to expire
Deal Rate = early expiration deal rate
Opening date = date when the early expiration is done
Value date = date when the early expiration is settled
Kind = Early Expiration
The remaining attributes are inherited from the initial transaction.

•

Cancellation
You can undo the early expiration by canceling the early expiration transaction.

6.4.4.2 Roll over
You can defer the maturity of the forward leg of an FX swap to a later date. This process is referred
to as roll-over.
See A.2.11 Allow Roll Over (FX) on page 717.

•

Execution
If the Spot Rate for the roll-over equals the Original Deal Rate, the following information is
needed to process the roll over:
Information

Description

Roll Over Date

Date when the roll over is done.

Maturity Date

New maturity date of the FX deal. This must be later than the maturity date of the
initial transaction.

Amount

Amount to roll over defaults to the amount left and is expressed in the same currency
(base or quote) as the input amount of the initial transaction. You can enter any
amount between 0 and the remaining amount of the initial transaction.

Forward Points

Forward points of the roll over transaction. This defaults to the number of forward
points from the roll over date to the maturity date.

Deal Rate

Deal rate for the roll over.
Deal Rate = Original Spot Rate + Forward Points

The execution generates a roll over transaction with the following attributes:
If the original input amount was FX Base Amount:
FX Base amount = amount to roll over
If the original input amount was FX Quote Amount:
FX Quote amount = amount to roll over
Deal Rate = roll over deal rate
Opening Date = date when the roll over is done
Maturity Date = new maturity date
Kind = Roll Over
The remaining attributes are inherited from the initial transaction.

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If the Spot Rate for the roll-over is different from the Original Deal Rate, the following additional
information is needed to process the roll over and settle the subsequent difference:
Information

Description

Settle Differential

Switch on if the Spot Rate for the roll-over is different from the Original Deal Rate.
By default, this switch is off.

Spot Rate

If Settle Differential is activated, this field becomes available.
Spot Rate defaults to the spot rate of the market but this value can be modified.
The Forward Points and Deal rate are adjusted automatically.

Base CCY Interest
%

Interest rate of the base currency for the period from the original settlement date to
the new settlement date.

Quote CCY
Interest %

Interest rate of the quote currency for the period from the original settlement date to
the new settlement date.

Deal Rate

Deal rate for the roll over.
Deal Rate = Spot Rate + Forward Points

The execution generates a roll over transaction as before with an additional cashflow as follows:
A netting cashflow is created to handle the settlement of the difference
Value Date = Roll over value date
Currency = Roll over currency 2
Amount = Base Amount * Original Deal Rate - (-Base Amount * Spot Rate)

•

Cancellation
You can undo the roll over by canceling the roll over transaction.

6.4.4.3 Currency pair shift
It is possible to split a position from one underlying currency pair into two new positions, each of
which contains one of the currencies with a third currency (usually, the portfolio currency). This
process is called an FX Pair Shift.

•

Setup
The FX Pair Shift action is available on an FX swap transaction if the Allow FX Currency Pair Shift
feature is included in the instrument definition: see A.2.7 Allow FX Currency Pair Shift on page
716.

•

Execution
See the TRM User Guide for information about this action.

6.4.5 Position monitoring
Figures for FX swaps are calculated in the same way as the figures for FX forwards: see 6.1.5
Position monitoring on page 393.

6.5 Cost-of-funding FX swap
Cost-of-funding FX swaps are a special case of FX swap, where the nominal amount for the far leg is
based on the nominal amount of the near leg and an interest rate component.
This instrument enables you to set up defaulting for the interest rate/spread value. Then, at deal
entry, the base amount of the far leg will be defaulted to the base amount of the near leg with the
interest computed between the value date and the maturity date of the FX swap.

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This interest is computed based on the interest rate and the spread value according to date basis of
the base currency. FX quote amounts are defaulted as usual from base amounts by using FX
rate/forward points.

6.5.1 Instrument setup
The set up is the same as for a standard FX swap except that you need to attach the trading feature
FX Swap Cost-of-Funding.

•

cost-of-funding characteristics
Information

Description

Active from/to

Set active from and to dates if you want the defaulting to be used only for a given
period.

Currency

Currency you want to specify.

C-o-F Curve

The default curve from which the interest rate will be defaulted.
Note: Only IR quotes (i.e. curve with fixing/interest calculation usage) defined with
the Bootstrap Yield Curve feature are available.

C-o-F Spread Curve

The default spread curve from which the spread will be defaulted.

Scenario

The default scenario from which the values will be retrieved.

Method

Defaulting method: Ask, Bid, Bid/Ask (Spread Against), Bid/Ask (Spread in Favor), or Mid.
•

If you select Bid/Ask (Spread Against): if you are buying the base currency of the
quoted currency pair, the Ask price is used; if you are selling the base currency
of the quoted currency pair, the Bid price is used.

•

If you select Bid/Ask (Spread in Favor): if you are buying the base currency of the
quoted currency pair, the Bid price is used; if you are selling the base currency
of the quoted currency pair, the Ask price is used.

See A.2.194 FX Swap Cost-of-Funding on page 807.

6.5.2 Deal capture
6.5.2.1 Input data
In addition to the standard FX swap deal parameters, the following information is needed to enter a
cost-of-funding FX swap:

Hint:

You will need to display the following columns in the Transaction view: C-o-F Curve, C-o-F
Rate, C-o-F Spread %, C-o-F Spread Curve, C-o-F Subscenario, and C-o-F Tenor.

Label

Value

C-o-F curve

ID of the curve to be used to default the cost-of-funding
rate.

Editable

Mandatory

Y

N

Defaults to the curve specified at instrument level for the
base currency, otherwise, it is empty.
C-o-F Subscenario

Subscenario to be used to compute the cost-of-funding
rate. By default, it is empty.

Y

N

C-o-F Tenor

Fixing period to be used to retrieve the cost-of-funding
rate. By default, it is empty.

Y

N

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Label

Value

Editable

C-o-F Rate

Defaults to the rate defined at the curve level for the
specific tenor, otherwise, defaults to the interpolated rate
between the transaction value date and the maturity date
according to the date basis and rate type set up at the
curve level.

Mandatory

Y

Y

Note: For a forward-forward FX swap, the forward FX rate
computed between the value and maturity dates.
C-o-F Spread Curve

Defaults to the spread curve defined at instrument level,
otherwise, it is left empty.

Y

N

C-o-F Spread %

If the C-o-F Spread Curve is populated then the displayed
value for the tenor is equal to the maturity date,
otherwise, it is left empty.

Y

N

FX Finance Rate(*)

Computed from C-o-F Rate and C-o-F Spread:

N

Y

N

Y

FX Finance Rate = C-o-F Rate + C-o-F Spread
Quote Currency Yield

Yield computed from quote amounts of the FX swap as
follows:

QuoteCurrencyYield =
(FXQuoteAmount-FXQuoteSpotAmount)* B /
MaturityDate - ValueDate * 1 /
FXQuoteSpotAmount
where
•

B is the date basis defined at the currency level for the
quote currency (Currency Editor - Journal page).

6.5.3 Processing
The actions you can perform on a cost-of-funding swap are the same as for a standard FX swap, see
6.4.4 Processing on page 420.

6.5.4 Position monitoring
Figures for cost-of-funding swaps are calculated in the same way as for FX swaps: see 6.4.5 Position
monitoring on page 422.

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Index

7.1 Index types
TRM supports the following index types:

•

Simple index
A simple index does not contain information on composition; it is a simple instrument to which a
price can be input. It can be used as an underlying for derivatives, and the price is used for
valuation and payoff calculations. It is also used in performance measurement for return
comparison.

•

Composite index
A composite index is an index defined in the product as a basket of several equities, discount
papers, or bonds, for example, CAC-40. If you do not want to manage the composition in TRM,
the composite index is treated as a simple index.

•

Derived index
A derived index is an index derived from several simple indexes. They can be composites, but
are treated as simple: their internal composition is not considered. A derived index can be
re-balanced. It can be used in performance measurement whenever internal performance
(allocation) is not needed

•

Performance index
A performance index is a special type of composite index, used to compute the payback of a
specific issue. TRM implements the following two index performance formulae to compute the
index value.

–

Performance averaging index

This is calculated as follows:
N

1--Index i
N∑
i=1
------------------------------ –1
1
--P

P

∑ Indexj
j=1

where:
1
Index i = ----------------------NbComp

NbComp

∑

w k Comp i, k

k=1

P = number of observation dates for the denominator
N = number of observation dates for the numerator
NbComp = number of components of the index
Wk = weight of kst component of the index

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Compi,k = value of the kst component at time i

–

Performance Totaling Index

This is calculated as follows:
N

Index j – Index j – 1

-⎞ ⎞
∑ Max ⎛⎝ Floor ;Min ⎛⎝ Cap ;--------------------------------------------⎠⎠
Index j – 1

j=1

where:
1
Index i = ----------------------NbComp

NbComp

∑

W k Comp i, k

k=1

N = number of observation dates for the numerator
Floor = predefined constant floor value
Cap = predefined constant cap value
NbComp = number of components of the index
Wk = weight of kst component of the index
Compi,k = value of the kst component at time i

7.2 Instrument setup
Index instruments must be set up in the following order:

7.2.1 Simple Index
Index instruments are based on an instrument type derived from the class INDEX.

•

Main characteristics (Quoted page):
This information enables you to either enter the quotation manually in Rate Monitor, or to
retrieve it automatically in real-time.
Information

Description

Price Type
information

Index.

Quote Handling

Index.

Currency

Currency of the index.

Note: Real-time market information is set up for the instrument in the Market Info page.
See A.2.203 Index on page 813.
It is also possible to set up:

•

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7.2.2 Composite Index
Composite Index instruments are based on an instrument type derived from the class INDEX.

•

Main characteristics
Features INDEX-COMPOSITE (primary) and QUOTED must be used.
See A.2.205 Index Composite on page 814.
This feature allows you to define the information in the instrument setup tabs as described in the
following sections.

7.2.2.1 Structure
Defines the principal characteristics of the index.
Information

Description

Currency

Reference currency for the index, used as the basis of index calculations.

Composition Type

Defines the component types used in this index: DEBT-SECURITY (bond, quoted
Discount Paper), EQUITY, and COMPOSITE (other composite index).

Weight Cap

The max % of the market value a single component can attain.

Calculation Method

Defines how Composite Indexes are calculated. The following methods can be used
to take the outflows (coupons, dividends and bond accrued interest) into account:
•

Clean Price: Used mainly for bonds. Only takes into account price return, not
accrued interest or cashflows. Unlike the other methods, this method discards
the accrued interest from the calculations of bond indices.

•

Hold Cash On Security: Cashflows are held under security until the index is
revised, but not reinvested. In which case, the field amount contains the
amount of the cashflow, and is populated when the cashflow is detached from
the security (in security currency). The amounts between two rebalancings are
added to the security amount (price * units) and eventually, accrued interest
before being converted to index currency.

•

Hold Cash On Index: Cashflows are held under index until the index is revised, but
not reinvested. In which case, the field amount contains the amount of the
cashflow converted to the index currency, and is populated when cashflow is
detached from the security. The amounts between two rebalancings are added
to the market value of the index.

•

Reinvest Cash On Security: The amount of the cashflow is reinvested on the
security from which it is detached. TRM calculates a factor to simulate
reinvestment of the cash in the security itself (stored in the Rebalance page).

•

Reinvest Cash On Index: The amount of the cashflow is reinvested in the index.
TRM calculates a factor which is applied to the whole index (stored in the
Rebase page).

Rounding Precision

Rounding precision to be applied in calculations.

Rounding Method

Rounding method to be applied in calculations.

Input Method

Defines how weightings are input (see 7.2.2.3 Composition on page 429). Available
methods are:
•

Units/Nominal: the absolute units for the component

•

Market Value: the market value of the component in index currency

•

Weight %: the % of the total market value of the component

•

Outstanding: number of times the outstanding units/nominal (typically 1).
Available for Bond and Equity

•

Free Float: same as above but with the units available for trading. Available only
for Equity.

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7.2.2.2 Base
Periodically models the revisions of the index including the initial definition
Information

Description

From

Date of the revision

To

Read-only. Date up to which this revision is valid.

Index Value

•

For the initial base the default is 100. This can be changed if you want to start
the index with another value. For example, to manage the CAC-40 today, you
would use the CAC-40’s current value.

•

For revision bases this is defaulted to the last known frozen base (from the
previous day). It can be changed (if incorrect in the database for example) but
should normally not be changed: it will be used as the base for index
calculations for every date until the next revision.

Market Value

The total market value of the index in the index currency. It is automatically set
with Calculate (see Actions). It can also be forced, and then Calculate will adjust
composition to match it.

Last Market Value

Read-only.

Attributes

•

Error: calculation of the base is impossible (incorrect base/component attributes
and/or inputs/market value)

•

Keep Market Value: affects Calculate button behavior (see below); always on

•

Modified: composition has been modified for this base and calculation must be

when input method is Weight %.
done before saving

Actions
•

Copy composition from template
Initializes an index from one or more template indexes, available only for the initial base. The
template must be selected for this action to be visible. A factor can be used to scale template
composition. The action can be executed several times to combine several templates.

•

Duplicate previous composition
Duplicates composition which can be manually revised: when using outstanding and free float
methods this does automatic revision without requiring manual intervention (it re-fetches new
market information at revision time). Only on revision bases (when you have more than one
base).

•

Update composition attributes
Automatically sets or resets the Keep Input flag for all the components of the base, so component
flags need not be set or reset manually (see 7.2.2.3 Composition on page 429).

•

Calculate...
This button is used to recalculate the specified base when Components are added, removed, or
modified. The calculation makes sure that the setup of the base is consistent: that the sum of all
the components amount matches the market value of the base and, if input method is weight %,
that the inputs sum to 100%.
The calculation is affected by the Keep Market Value switch of the base and the Keep Inputs flags
of the components. When Keep Market Value is switched on, the system adjusts component inputs
that are not marked with Keep Input. Otherwise the market value can be re-calculated.
When the input method is Weight %, the Keep Market Value flag is forced to True.

Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate...

flags the base with the attribute Error, and the instrument cannot be saved. It is possible to

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temporarily save an index with an inconsistent base by unswitching the attributes
manually, but the user must fix the problem before using the index.

7.2.2.3 Composition
Defines the composition of the index for a given base
Information

Description

Base Date

Reference of the base (corresponds to Base "From").

Component

Id of the component; available components are filtered according to index type.

Currency

Read-only. Currency of the component, retrieved from component characteristics.

Calendar

Calendar of the component, retrieved from component characteristics.

FX Rate

Cross-rate between Component currency and index currency, defaulted from fixing
scenario. Can be changed by the user. It is the base rate used in calculation relative
to this base for this component.

Component Value

Price of the component. This is defaulted from the fixing scenario and can be
changed by the user. It is the base price used in calculations relative to this base for
this component.

Input

It is the base weight for this component. The significance of this weight depends on
the input method defined in the index structure (see 7.2.2.1 Structure on page
427).

Units/Nominal

Read-only. This is the absolute weight in units (for equities) or in nominal (for
bonds) which is calculated for the component depending on the input method.

Accrued Interest

For bond index, amount of accrued interest for the component at base date.

Amount

Read-only. Shows the amount of the component for the base in index currency. The
sum of the amount of all components for a base gives the base market value of the
index.

Attributes

Keep Input forces the Calculate action to keep the input for this component.

7.2.2.4 Rebase
Stores the impact of cashflows, depending on the method of calculation. This is used when
cashflows are impacted at index level.
Information

Description

Date

Date of the market value shift

Old Value

Market value of the index before the external event was taken into account

New Value

Market value of the index including the impact of the external event.

Cash

Amount to be added to index MV from the specified date onwards.

Source

Read-only. Shows what event triggers the rebasing. Manual means that the user
can enter it manually, and in which case, it is modifiable in the editor.
Other choices are: Amortization, Cash Dividend, Coupon, Split.

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7.2.2.5 Rebalance
Stores the impact of cashflows, depending on the method of calculation. This is used when
cashflows are impacted at component level. It is also used to compensate for the effect of equity
splits.
Information

Description

Date

Date of the CA to be balanced.

Component

Id of the component; available components are filtered according to index type.

Old Units/Nominal

Number of units before rebalancing

New Units/Nominal

Number of units after rebalancing

Cash

Amount to be added to component MV from the specified date onwards.

Source

Read-only. Shows what event triggers the rebasing. Manual means that the user
can enter it manually, and in which case, it is modifiable in the editor.

7.2.3 Derived Index
Features INDEX-DERIVED (primary) and QUOTED must be used.

7.2.3.1 Structure
Defines the currency, index type, and maximum weight for any component for the corresponding
index composition.
Information

Description

Currency

Reference currency for the index, used as the basis of index calculations.

Composition Type

Index is the only available type.

Weight Cap

The max % of the market value a single component can attain.

Input Method

Defines how weightings are input (see 7.2.3.3 Composition on page 431). Available
methods are:
•

Units/Nominal: the absolute units for the component

•

Weight %: the % of the total market value of the component.

Rounding Precision

Rounding precision to be applied in calculations.

Rounding Method

Rounding method to be applied in calculations.

Calculation Method

Not used for a derived index.

7.2.3.2 Base
Periodically models the revisions of the index including the initial definition

430

Information

Description

From

Date of the revision

To

Read-only. Date up to which this revision is valid.

Index Value

•

For the initial base the default is 100. This can be changed if you want to start
the index with another value.

•

For revision bases this is defaulted to the last known frozen base (from the
previous day). It can be changed (if incorrect in the database for example) but
should normally not be changed: it will be used as the base for index
calculations for every date until the next revision.

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7 Index
7.2 Instrument setup

Information

Description

Market Value

The total market value of the index in the index currency. It is automatically set
with the Calculate... button (see Actions). It can also be forced, and then calculate
will adjust composition to match it.

Last Market Value

Read-only.

Attributes

•

Error: calculation of the base is impossible (incorrect base/component attributes
and/or inputs/market value)

•

Keep Market Value: affects Calculate button behavior (see below); always on
when method is %.

•

Modified: composition has been modified for this base and calculation must be
done before saving

Actions
•

Copy composition from template
Initializes an index from one or more template indexes, available only for the initial base. The
template must be selected for the action to be visible. A factor can be used to scale template
composition. The action can be executed several times to combine several templates.

•

Duplicate previous composition
Duplicates composition which can be then manually revised. Only on revision bases (when there
is more than one base).

•

Update composition attributes
Automatically sets or resets the Keep Input flag for all the components of the base: this is a
shortcut (see 7.2.3.3 Composition on page 431).

•

Calculate...
This button recalculates the specified base when Components are added, removed, or modified.
The calculation makes sure that the setup of the base is consistent: that the sum of all the
components amount matches the market value of the base and, if input method is Weight %,
that the inputs sum to 100%.
The calculation is affected by the Keep Market Value switch of the base and the Keep Inputs flags
of the components. When Keep Market Value is switched on, the system adjusts component inputs
that are not marked with Keep Input. Otherwise the market value can be re-calculated.
When the input method is Weight %, the Keep Market Value flag is forced to True.

Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate...

flags the base with the attribute Error, and the instrument cannot be saved. It is possible to
temporarily save an index with an inconsistent base by unswitching the attributes
manually, but the user must fix the problem before using the index.

7.2.3.3 Composition
Defines the composition of the index for a given base.
Information

Description

Base Date

Reference of the base (corresponds to Base "From").

Component

Id of the component; available components are indexes.

Currency

Read-only. Currency of the component, retrieved from component characteristics.

Calendar

Read-only. Calendar of the component, retrieved from component characteristics.

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Information

Description

FX Rate

Cross-rate between Component currency and index currency, defaulted from fixing
scenario. Can be changed by the user. It is the base rate used in calculation relative
to this base for this component.

Component Value

Price of the component. This is defaulted from the fixing scenario and can be
changed by the user. It is the base price used in calculations relative to this base for
this component.

Input

It is the base weight for this component. The significance of this weight depends on
the input method defined in the index structure (see above).

Units/Nominal

Read-only. This is the absolute weight in units which is calculated for the component
depending on the input method.

Amount

Read-only. Shows the amount of the component for the base in index currency. The
sum of the amount of all components for a base gives the base market value of the
index.

Attributes

Keep Input forces the Calculate action to keep the input for this component.

7.2.3.4 Schedule
Defines rebalance schedules, which will be used to generate rebalance dates.
Information

Description

Start Date

Date from when rebalancing starts.

End Date

Date when rebalancing stops (if you do not know if it will stop, just use a distant
future date).

Method

Specifies how the rebalancing dates are calculated.

Frequency

A function of the Method selected. For example, if method is Months, entering 3
here gives a frequency of 3 months.

Convention

Business convention to be followed.

Roll from Start

Yes or No.

Date Type

Select Re-balance.

7.2.3.5 Rebalance Date
Shows rebalance dates.
Information

Description

Date

Date when rebalancing is executed.

Actions
•

Generate
Generates a set of rebalance dates according to the schedules. If Method is "Days" or "Business
Days" and Frequency is 1, only the first rebalance date is generated; next rebalance dates are
generated by clicking Rebalance (see below).

•

Rebalance
Performs index rebalancing. The input method for the index must be Weight %. The system
creates rows in the Rebalance page for the components of the index to adjust their units so that
the percentages match the definition of the base. It is possible to trigger this action
automatically via an activity (see 7.4 Processing on page 440).

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7.2.3.6 Rebalance
Stores the impact of re-balancing.
Information

Description

Date

Date of rebalancing.

Component

Id of the component.

Old Units/Nominal

Number of units before rebalancing.

New Units/Nominal

Number of units after rebalancing.

Cash

Amount to be added to component MV from the specified date onwards.

Source

Read-only. Shows what event triggers the rebasing. Manual means that the user
can enter it manually, and in which case, it is modifiable in the editor.

7.2.4 Performance averaging index
•

Main characteristics
Features INDEX-AVERAGING (primary) and QUOTED must be used.
See A.2.204 Index Averaging on page 813.
This feature allows you to define the following information in the instrument setup tabs:

7.2.4.1 Structure
Defines the currency, index type, and maximum weight for any component for the corresponding
index composition.
Information

Description

Currency

Reference currency for the index, used as the basis of index calculations.

Composition Type

Defines the component types used in this index: equities, bonds or indexes.

Weight Cap

The max % of the market value a single component can attain.

Calculation Method

Clean Price is the only method supported.

Rounding Precision

Rounding precision to be applied in calculations.

Rounding Method

Rounding method to be applied in calculations.

Input Method

Defines how weightings are input (see 7.2.4.3 Composition on page 435). Available
methods are:
•

Units/Nominal: the absolute units for the component

•

Market value: the market value of the component in index currency

•

Weight %: the % of the total market value of the component

•

Outstanding: the number of times the outstanding units/nominal (typically 1).
Available for Bond and Equity.

•

Free Float: same as above, but with the units available for trading. Available only
for Equity.

7.2.4.2 Base
Periodically models the revisions of the index including the initial definition
Information

Description

From

Date of the revision

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Information

Description

To

Read-only. Date up to which this revision is valid.

Index Value

•

For the initial base the default is 100.

•

For revision bases this is defaulted to the last known frozen base (from the
previous day). It can be changed (if incorrect in the database for example) but
should normally not be changed: it will be used as the base for index
calculations for every date until the next revision.

Market Value

The total market value of the index in the index currency. It is automatically set
with Calculate (see Actions). It can also be forced and then Calculate will adjust
composition to match it.

Last Market Value

Read-only.

Attributes

•

Error: calculation of the base is impossible (incorrect base/component attributes
and/or inputs/market value)

•

Keep Market Value: affects Calculate button behavior (see below); always on
when method is %.

•

Modified: composition has been modified for this base and calculation must be
done before saving

Actions
•

Copy composition from template
Initializes an index from one or more template indexes, available only for the initial base. The
template must be selected for the action to be visible. A factor can be used to scale template
composition. This action can be repeated to combine several templates.

•

Duplicate previous composition
Duplicates composition which can then be manually revised: when using outstanding and
free-float methods, this does automatic revision without manual intervention (it re-fetches new
market information at revision time). Only on revision bases.

•

Update composition attributes
Automatically sets or resets the Keep Input flag for all the components of the base: this is a
short cut (see 7.2.4.3 Composition on page 435).

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7.2 Instrument setup

•

Calculate...
This button recalculates the specified base when Components are added, removed, or modified.
The calculation makes sure that the setup of the base is consistent: that the sum of all the
components amount matches the market value of the base, and if the input method is Weight %,
that the inputs sum to 100%.
The calculation is affected by the Keep Market Value switch of the base, and the Keep Inputs flags of
the components. When Keep Market Value is switched on, the system adjusts component inputs
that are not marked with Keep Input. Otherwise the market value can be re-calculated.
When input method is Weight %, the Keep Market Value flag is forced to True; when the input
method is Outstanding or Free Float, it is forced to False.

Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate...
flags the base with attribute Error, and the instrument cannot be saved. It is possible to
temporarily save an index with an inconsistent base by unswitching the attributes
manually, but the user must fix this problem before using the index.

7.2.4.3 Composition
Defines the composition of the index for a given base.
Information

Description

Base Date

Reference of the base (corresponds to Base "From").

Component

Id of the component; available components are filtered according to index type.

Currency

Read-only. Currency of the component, retrieved from component characteristics.

Calendar

Read-only. Calendar of the component, retrieved from component characteristics.

FX Rate

Cross-rate between Component currency and index currency, defaulted from fixing
scenario. Can be changed by the user. It is the base rate used in calculation relative
to this base for this component.

Component Value

Price of the component. This is defaulted from the fixing scenario and can be
changed by the user. It is the base price used in calculations relative to this base for
this component.

Input

It is the base weight for this component. The significance of this weight depends on
the input method defined in the index structure (see above).

Units/Nominal

Read-only. This is the absolute weight in units (for equities) or in nominal (for
bonds) which is calculated for the component depending on the input method.

Amount

Read-only. Shows the amount of the component for the base in index currency. The
sum of the amount of all components for a base gives the base market value of the
index.

Attributes

Keep Input forces the Calculate action to keep the input for this component.

7.2.4.4 Rebalance
Balances the impact of any equity splits.
Information

Description

Date

Date of the CA to be balanced.

Component

Id of the component; available components are filtered according to index type.

Old Units/Nominal

Number of units before split.

New Units/Nominal

Number of units after split.

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Information

Description

Cash

Amount to be added to component MV from the specified date onwards.

Source

Read-only. Shows what event triggers the rebasing. Manual means that the user
can enter it manually, and in which case, it is modifiable in the editor.

7.2.4.5 Schedule
Defines schedules, used to generate numerator and denominator dates.
Information

Description

Start Date

Date from when generation starts.

End Date

Date when generation stops (if you do not know when generation will stop, just use
a distant future date).

Method

Defines how the generation dates are calculated.

Frequency

A function of the Method selected. For example, if method is Months, entering 3
here gives a frequency of 3 months.

Convention

Business convention to be used.

Roll from Start

Yes or No.

Date Type

Use Avg. Numerator and Avg. Denominator.

7.2.4.6 Denominator Date and Numerator Date
These pages show the dates when performance calculations are performed
Information

Description

Date Input

Date of the calculation.

Observation Date

Date when the price is retrieved for the components following the given calendar.

Calendar

For each Date Input there must be as many records as distinct calendars in the
components. Observation date might be different for each calendar.

Actions
•

Generate
Generates a set of Numerator and Denominator dates according to the schedules and individual
calendars of the components.

7.2.5 Performance totaling index
•

Main characteristics
Features INDEX-TOTALING (primary) and QUOTED must be used.
See A.2.215 Index Totaling on page 821.
This feature allows you to define the information in the instrument setup tabs described in the
following sections.

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7.2 Instrument setup

7.2.5.1 Structure
Defines the currency, index type, and maximum weight for any component for the corresponding
index composition.
Information

Description

Currency

Reference currency for the index, used as the basis of index calculations.

Composition Type

Defines the component types used in this index: equities, bonds or indexes.

Weight Cap

The max % of the market value a single component can attain.

Calculation Method

Clean Price is the only supported method.

Rounding Precision

Rounding precision to be applied in calculations.

Rounding Method

Rounding method to be applied in calculations.

Input Method

Defines how weightings are input (see 7.2.5.3 Composition on page 438). Available
methods are:
•

Units/Nominal: the absolute units for the component

•

Market value: the market value of the component in index currency

•

Weight %: the % of the total market value of the component

•

Outstanding: the number of times the outstanding units/nominal (typically 1).
Available for Bond and Equity.

•

Free Float: same as above but with the units available for trading. Available only
for Equity.

7.2.5.2 Base
Periodically models the revisions of the index including the initial definition
Information

Description

From

Date of the revision

To

Read-only. Date up to which this revision is valid.

Index Value

•

For the initial base the default is 100.

•

For revision bases this is defaulted to the last known frozen base (from the
previous day). It can be changed (if incorrect in the database for example) but
should normally not be changed: it will be used as the base for index
calculations for every date until the next revision.

Market Value

The total market value of the index in the index currency. It is automatically set
with Calculate (see Actions). It can also be forced and then calculate will adjust
composition to match it.

Last Market Value

Read-only.

Attributes

•

Error: calculation of the base is impossible (incorrect base/component attributes
and/or inputs/market value)

•

Keep Market Value: affects Calculate button behavior (see below); always on

•

Modified: composition has been modified for this base and calculation must be

when method is %.
done before saving

Actions
•

Copy composition from template

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7.2 Instrument setup

Initializes an index from one or more template indexes, available only for the initial base. The
template must be selected for the action to be visible. A factor can be used to scale template
composition. This action can be repeated to combine several templates.

•

Duplicate previous composition
Duplicates composition which can be then manually revised: when using outstanding and free
float methods this does automatic revision without requiring manual intervention (it re-fetches
new market information at revision time). Only on revision bases.

•

Update composition attributes
Automatically sets or resets the Keep Input flag for all the components of the base: this is a
short cut (see 7.2.5.3 Composition on page 438).

•

Calculate...
This button recalculates the specified base when Components are added, removed, or modified.
The calculation makes sure that the setup of the base is consistent: that the sum of all the
components amount matches the market value of the base and, if input method is Weight %, that
the inputs sum to 100%.
The calculation is affected by the Keep Market Value switch of the base and the Keep Inputs flags of
the components. When Keep Market Value is switched on, the system adjusts component inputs
that are not flagged with Keep Input. Otherwise the Market Value can be re-calculated.
When input method is Weight %, the Keep Market Value flag is forced to True; when method is
Outstanding or Free Float it is forced to False.

Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate...

marks the base with attribute Error, and the instrument cannot be saved. It is possible to
temporarily save an index with an inconsistent base by unswitching the attributes
manually, but the user must fix this problem before using the index.

7.2.5.3 Composition
Defines the composition of the index for a given base

438

Information

Description

Base Date

Reference of the base (corresponds to Base "From").

Component

Id of the component; available components are filtered according to index type.

Currency

Read-only. Currency of the component, retrieved from component characteristics.

Calendar

Read-only. Calendar of the component, retrieved from component characteristics.

FX Rate

Cross-rate between Component currency and index currency, defaulted from fixing
scenario. Can be changed by the user. It is the base rate used in calculation relative
to this base for this component.

Component Value

Price of the component. This is defaulted from the fixing scenario and can be
changed by the user. It is the base price used in calculations relative to this base for
this component.

Input

It is the base weight for this component. The significance of this weight depends on
the input method defined in the index structure (see above).

Units/Nominal

Read-only. This is the absolute weight in units (for equities) or in nominal (for
bonds) which is calculated for the component depending on the input method.

Amount

Read-only. Shows the amount of the component for the base in index currency. The
sum of the amount of all components for a base gives the base market value of the
index.

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7.2 Instrument setup

Information

Description

Attributes

Keep Input forces the Calculate action to keep the input for this component.

7.2.5.4 Rebalance
Balances the impact of any equity splits
Information

Description

Date

Date of the CA to be balanced.

Component

Id of the component; available components are filtered according to index type.

Old Units/Nominal

Number of units before rebalancing

New Units/Nominal

Number of units after rebalancing

Cash

Amount to be added to component MV from the specified date onwards.

Source

Read-only. Shows what event triggers the rebasing. Manual means that the user
can enter it manually, and in which case, it is modifiable in the editor.

7.2.5.5 Totaling
Defines cap and floor to use in totaling formula (see – Performance Totaling Index on page 426).
Information

Description

Floor

The floor to use in the totaling formulae.

Cap

The cap to use in the totaling formulae.

7.2.5.6 Schedule
Defines schedules, used to generate totaling dates.
Information

Description

Start Date

Date from when generation starts.

End Date

Date when generation stops (if you do not know if it will stop, just use a date very
far in the future).

Method

Defines how the generation dates are calculated.

Frequency

A function of the Method selected. For example, if method is Months, entering 3
here gives a frequency of 3 months.

Convention

Business convention to be used.

Roll from Start

Yes or No.

Date Type

Use average numerator and denominator for date types.

7.2.5.7 Totaling Date
This page shows the dates when performance calculation is done.
Information

Description

Date Input

Date of the calculation.

Observation Date

The date when the price will be retrieved for the components following the given
calendar.

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7.3 Market information

Information

Description

Calendar

For each Date Input there must be as many records as there are distinct calendars
in the components. The Observation Dates for each calendar can be different.

Actions
•

Generate
Generates a set of totaling dates according to the schedules and individual calendars of the
components.

7.3 Market information
Rate Monitor is used to visualize and maintain index prices. See the TRM User Guide for more
information.

7.4 Processing
This section describes the processing that you can perform, either manually in the relevant
application, or automatically, as an activity, in Activity Monitor.

7.4.1 Revision
Revision is a manual process which consists of updating an index to reflect the market more
accurately. This operation is done in the Instrument Editor by creating a new base and a new
composition.

Note: It is also possible to import revisions using one of the TRM connectivity tools.

7.4.2 Freezing Index Values
Rate Monitor enables you to view both calculated and quoted (Q) values, but only the quoted values
are used by the rest of the system. Values of composite, derived and performance indexes are
calculated automatically in real time according to market data changes (FX rates or component
values). It is nevertheless important to be able to freeze these results at any time.
In Rate Monitor, use the command Command - Freeze to freeze these values; the current content of
the calculated cells are copied to the Quoted (Q) cells. When you have frozen these values, use the
Save button to store them in the database like any other standard price. Both index values and
detailed composition information are stored.

Note: You can import Quoted (Q) values directly from an external data feed, either as a
replacement or in parallel, by using another scenario and/or subscenario.

You can also use the Index Freeze activity in Activity Manager to perform the freeze.

Note: See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

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7.4 Processing

7.4.3 Updating Factors and Cash
Use the activity Index Adjustment in Activity Manager to automatically update factors and cash. This
activity reads the characteristics of the underlyings, and depending on the Index Type and the
Calculation Method, inserts the relevant information into the Rebase and Rebalance pages.

Note: See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

7.4.4 Rebalancing
A common use for a derived index is to rebalance the index periodically, so that each component
weight is readjusted to the original percentage weighting. After the setup of rebalancing dates is
done, (see setup above), you can execute rebalancing for an index directly in the editor, by clicking
Rebalance.
You can also use the Index Rebalance activity in Activity Manager to perform this task.

Note: See the TRM User Guide for general information on running activities, and also specific
information on the activity parameters.

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7.4 Processing

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Chapter 8

Cash

8.1 Bank account
Bank account balances and any interest accrued on a bank account are displayed in the system as
transactions.
Bank accounts can be used either: to track your own bank balance by checking your current position
adjusted by the existing balance, and to calculate the estimated accrued interest on the bank
account; or, if you represent an In-house Bank (that is, you hold accounts for your subsidiaries),
you can calculate end-of-day balances and provide your subsidiaries with the appropriate
information, as well as calculating any accrued interest on the accounts.
You need to set up one instrument to calculate bank balances, and another which is specifically used
to calculate accrued interest. Both instruments are assigned to accounts in the Accounts page of
Client Editor: see the TRM User Guide for more information.
It is recommended that a separate Balance portfolio is defined for the balance and
interest-calculation transactions. One reason is that you can restrict update access to the balance
information to people in the back office, while the trading portfolios can only be updated by people
in the front office and middle office.
If you operate as an In-house Bank, you may also find it useful to have a Balance portfolio for each
of the bank accounts of your subsidiaries.

Note: Information about how to assign balance instruments to accounts and how to create
Balance portfolios is described in the TRM User Guide.

Bank account balances and interest-calculation instruments belong to the instrument class
BANK-ACCOUNT.

8.1.1 Instrument setup
Both bank account balance and bank account interest instruments share the same primary feature.

8.1.1.1 Bank account balance
Bank account balance instruments are assigned to the accounts for which you want to calculate the
balance. The balance can either be derived from payable cashflows in the system, or from paid
cashflows. It is also possible to define in how much detail you want the balance to be calculated, for
example, if you need one balance transaction per counterparty.
Balance instruments do not require any specific set up. They are simply recognized by the following
features in the Bank-Account instrument class:

•

The primary feature Bank Account Balance (see A.2.45 Bank Account Balance on page 729)

•

The valuation feature Bank Account Method (see A.2.47 Bank Account Valuation on page 732).

8.1.1.2 Bank account interest-calculation
Interest-calculation instruments are assigned to the accounts for which you want to calculate the
accrual of interest.

•

Main characteristics

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8.1 Bank account

The bank account interest instrument uses the same primary feature as the bank account
balance instrument (see 8.1.1.1 Bank account balance on page 443).

•

Trading information

–

Interest accrual parameters
For bank balances, you can specify the interest rates used, and the method and frequency
that interest is accrued.
Information

Description

Date Basis

Date basis used to calculate accrued interest for this instrument.

Interest Rate Curve

Underlying yield curve (set up in IR Quote and Yield Curve Editor) used for
interest calculation.
Note: If you specify a yield curve (and/or Period, Positive Spread, or
Negative Spread), you do not need to specify any Ladder values (see
Ladder Rule and Ladder).

–

Period

Period of the underlying yield curve to be used for interest calculation (for
example, O/N).

Scenario

Rate scenario to be used for calculating interest for this instrument.

Interest realization parameters
You can specify how the accrued interest is realized on the balance.
Information

Description

Frequency

Frequency of interest realization (if Method = Periodically).

Frequency Unit
Method

Unit of time to use for interest realization: Business Days, Days, Months,

Weeks, or Years.

Method of realizing interest:
•

At Withdrawal - not applicable.

•

Periodically - interest is realized at regular intervals (see Frequency
field).

•
Settlement Method

At Expiration - not applicable.

Interest payment method: Capitalize to compound interest or Settle to
receive or pay interest.

See A.2.46 Bank Account Interest on page 730.

8.1.2 Deal capture
Bank account balances and interest transactions are system-generated transactions, performed by
scheduled activities (see the TRM User Guide for more information). Once the activity has run, the
transactions are generated in the Bank Account Balances application.

8.1.2.1 Generated data
•

Transaction
Transaction Type = Balance
Counterparty = Bank that holds the balance, unless the balances are calculated
by counterparty

•

Cashflows

–

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8 Cash
8.1 Bank account

–

If the interest is unrealized: daily accrued interest

–

If the interest is realized: realized interest cashflows or the capitalizing balance cashflow.

8.1.3 Processing
This section describes the processing that you can perform, either manually in the relevant
application, or automatically, as an activity, in Activity Manager. See the TRM User Guide for
information about these activities and how to set up activities in general.

8.1.3.1 Calculating bank account balance and interest
Bank account balance and accrued interest-calculation transactions are generated by the activity
Bank Account Balances which you can schedule to run as often as required (see the TRM User Guide
for more information).

8.1.3.2 Realize AI
Bank account accrued interest can be realized automatically or manually (for automatic realization,
see the TRM User Guide).
You can realize interest manually, by right-clicking on the transaction in the Transaction view of the
Bank Account Balances application and selecting the Realize AI action.

•

Execution
The following information is needed to process the realization:
Information

Description

Date

Date of the action i.e. the realization date.

Opening Date

The opening date of the transaction.

Payment Date

By default, the Payment Date is the realization date. However, you can change
the default.

Amount

Amount of the realized interest cashflow.
By default, this is the total amount of accrued interest, but it can be changed to
a lesser amount if you do not want to realize the total amount.

Interest Sign

Positive: To receive interest.
Negative: To pay interest.

Settlement Method

Capitalize or Settle. The accrued interest is either settled or capitalized.
Note: By default, the settlement method will be the one defined in the Interest
Realization page of Instrument Editor.

Interest Bank

ID of a bank if you want to settle the interest realization in a specific bank,
which differs from the default bank.

Interest Account

ID of a bank account if you want to settle the interest realization in a specific
account, which differs from the default bank account.

Update Realization Date

Switch on to allow the next interest realization date to be automatically
updated.

Note: It is not possible to realize accrued interest for future dates using the Realize AI action.
•

Cancellation

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8.2 Call account

You can cancel interest manually by right-clicking on the transaction in the Transaction view of
the Bank Account Balances application and selecting the Undo Realize AI action. The following
information is needed to process the cancellation:
Information

Description

Date

Date of the action i.e. the undo realization date.
By default the date is today's date.

8.2 Call account
Call Account is similar to a normal bank account. The client can withdraw and deposit funds (lend or
borrow) from the account whenever it is necessary. The funds earn interest on the account at a rate
that is fixed daily. The interest is accrued and paid or capitalized at regular intervals. The client can
withdraw all or part of the interest from the account when interest is payable (without first having to
capitalize the interest).
The main difference between Call Money and Call Account is the presumed length of the transaction.
Call Money is assumed to mature on a daily basis, while Call Account is automatically rolled over
every day.
In TRM, call account instruments belong to the instrument class CALL-ACCOUNT.

8.2.1 Instrument setup
Call accounts are based on an instrument type derived from the instrument class CALL-ACCOUNT.

•

Main characteristics
The following basic information may be captured when defining a call account instrument.
Information

Description

Currency

Currency of the call account.

Balance
information

Minimum and maximum balance allowed on the call account.

Notice period
information

Required notice period for calling the money.

–

Interest accrual parameters
For call accounts, you can specify the interest rates used, and the method and frequency
that interest is accrued on the call account.

–

Interest realization parameters
You can also specify how the accrued interest is realized on the call account.

See A.2.82 Call Account on page 747.
For a call account instrument, it is also possible to set up:

•

Spot date calculation

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes.

See Appendix A Features on page 713.

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8.2 Call account

8.2.2 Deal capture
Call account transactions are entered in the Call Account trading mode of Transaction Manager’s Call
Manager layout.

Note: See the TRM User Guide for more information about this Transaction Manager layout.

8.2.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a call
account transaction:

•

Transaction view
Information

Description

Movement/Initial
Balance

Initial movement (inflow or outflow) on the call account.

Interest Rate

At contract level, this is the last roll over rate.

Roll Over Date

Date of the next roll over.

Capitalize Account

Transaction number of an alternative call account on which to realize the capitalized
interest.

This amount can be zero if the initial movement is intended to open the account only,
and does not involve a deposit or withdrawal of funds.

Interest rate and balance information defined at instrument level default to the date in the Roll
Over Date field. If the Roll Over Date field is empty, then today’s date is used. If no interest rate
is available for today, then the rate applied yesterday is used. Similarly, if no balance is
available, then the closing balance from the previous day is shown.

8.2.2.2 Generated data
Movements on call accounts can be viewed in the Movement view of Call Manager.

•

Movement view
Information

Description

Movement ID

Log number for each movement carried out on a transaction.
This number is used to identify individual movements when multiple identical
movements are performed on the same transaction on the same day.

Interest Rate

At movement level, this is the interest rate of the movement.
If the transaction has not yet been rolled over, the previous interest rate is displayed.
Once the transaction has been rolled over, the rate is updated from the underlying
yield curve. If no underlying curve has been defined and a rate change has been
agreed with the counterparty, this rate needs to be updated manually.

8.2.3 Processing
This section describes the actions that can be done throughout the life of a call account transaction.

8.2.3.1 Update account
A call account instrument needs to be updated each day.

•

Execution

–

Automatic updating of a call account is done using the Call Money Account Update activity.
This activity should be scheduled to run on a daily basis to ensure that the call account
instrument is updated each day.

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8.2 Call account

The following information is needed to process the activity:
Parameter

Description

Minimum Transaction
State

Minimum transaction state the call account transaction needs to have to be
included in the process

Portfolio

Portfolio containing the call account transaction.

Owner

Client (portfolio owner) of the portfolio.

Counterparty

Counterparty of the call account transaction.

Counterparty Main
Group

Counterparty main group of the call account transaction.

Counterparty Group

Counterparty group of the call account transaction.

Instrument

ID of the call account instrument.

Instrument Group

Instrument group to which the call account instrument belongs.

Currency

Currency of the call account transaction.

Interest Rate Curve

Yield curve attached to the call money or call account instrument.

Note: See the TRM User Guide for information about these activities and how to set up activities
in general.

8.2.3.2 New movement
It is possible to make a deposit or withdrawal (movement) on a call account.

•

Execution
To include new movements on call account transactions, execute the New Movement processing
action on the transaction for which you want to include additional lending or borrowing.
In the new row that is added in the Movement view, the following data is required.
Information

Description

Interest Rate

Interest rate for the new movement.

Amount

Amount of the movement.

8.2.3.3 Change interest
It is possible to change the interest rate but not create a new movement on a call account using the
Change Interest processing action.

•

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Execution
Information

Description

Date

Date from when the new interest rate applies.

Rate

New interest rate.

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8.2 Call account

8.2.3.4 Expire
A call account with no outstanding balance can be closed by selecting the Expire right-click action on
the call account transaction.

•

Execution
Information

Description

Closing Date

Date when the call account expires.

Note that call accounts can have a zero balance and still remain active in the system for future
transactions if required; they are not automatically closed when the balance is zero.

8.2.3.5 Update balance
You can update the balance using the Update Balance right-click action.

•

Execution
Information

Description

From

Start and end dates of the period for which you want to update the balance.

To

8.2.3.6 Update AI
You can update accrued interest on call account transactions using the Update AI action.

•

Execution
Information

Description

Date

Date on which you want to recalculate the accrued interest.

Rate

New interest rate you want to use to recalculate the accrued interest.

8.2.3.7 Realize interest
You can realize accrued interest on call account transactions using the Realize AI action.

•

Execution
Information

Description

Date

Date of the action.

Opening Date

Opening date of the realized interest cashflow.

Payment Date

By default, the Payment Date is the realize date + payment offset. However, you can
change the given default date.

Amount

Amount of the realized interest cashflow.
By default, this is the total amount of accrued interest, but it can be changed to a
lesser amount if you do not want to realize the total.

Settlement
Method

Capitalize or Settle.
The accrued interest is then either settled or capitalized with the nominal amount of
the transaction, depending on the Settlement Method.

Note that it is not possible to realize AI for future dates using this action.

•

Cancellation
You can cancel the action using Undo Realize AI.

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8.3 Call money

8.2.3.8 Dormant/Pledged
You can mark call accounts as being dormant (no transactions allowed) or pledged (restricted
movements).

•

Execution
Use the Dormant/Pledged processing action. You are then prompted for new minimum/maximum
values: for a dormant account, the minimum and maximum values are both zero.

8.3 Call money
Call Money is an overnight deposit used in the wholesale banking market. Although such
transactions are normally expired the following day, they can also be rolled over and the interest
rate changed. It is possible to increase/decrease the principal of the original deal. In addition, the
interest can be paid, capitalized, or simply accrued.
The main difference between Call Money and Call Account is the presumed length of the transaction.
Call Money is assumed to mature on a daily basis, while Call Account is automatically rolled over
every day.
In TRM, call money instruments belong to the instrument class CALL-MONEY.

8.3.1 Instrument setup
Call Money instruments are based on an instrument type derived from the class CALL-MONEY.

•

Main characteristics
The following basic information may be captured when defining a call money instrument.
Information

Description

Currency

Currency of the call money.

Balance
information

Minimum and maximum balance allowed on the call money.

Notice period
information

Required notice period for calling the money.

–

Interest accrual parameters
For call money, you can specify the interest rates used, and the method and frequency that
interest is accrued on the call money.

–

Interest realization parameters
You can also specify how the accrued interest is realized on the call money.

–

Roll over parameters
You can define the frequency of the roll over and the convention used.

See A.2.84 Call Money on page 750.

•

Valuation approach
See A.2.85 Call Money Valuation on page 750.

For a call money instrument, it is also possible to set up:

•

Spot date calculation

•

Cashflow and transaction charge rules

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8.3 Call money

•

Manual charges

•

Branch codes.

See Appendix A Features on page 713.

8.3.2 Deal capture
Call money transactions are entered in the Call Money trading mode of Transaction Manager’s Call
Manager layout.

Note: See the TRM User Guide for more information about this Transaction Manager layout.

8.3.2.1 Input data
•

Transaction view
In addition to the standard deal parameters, the following information is required to enter a call
money transaction:
Information

Description

Movement/Initial
Balance

Change in amount (inflow or outflow) that occurs.

Interest Rate

Interest rate of the movement.
If the transaction has not yet been rolled over, the previous interest rate is displayed.
Once the transaction has been rolled over, the rate is updated from the underlying
yield curve. If no underlying curve has been defined and a rate change has been
agreed with the counterparty, this rate needs to be updated manually.

Roll Over Date

Date of the next roll over.

Capitalize Account

Transaction number of an alternative call money instrument on which to realize the
capitalized interest.

Interest rate and balance information defined at instrument level default to the date in the Roll
Over Date field. If the Roll Over Date field is empty, then today’s date is used. If no interest rate
is available for today, then the rate applied yesterday is used. Similarly, if no balance is
available, then the closing balance from the previous day is shown.

8.3.2.2 Generated data
Movements of call money can be viewed in the Movement view of Call Manager.

•

Movement view
Information

Description

Movement ID

Log number for each movement carried out on a transaction.

Settlement instructions are also displayed in this view.

8.3.3 Processing
This section describes the actions that can be done throughout the life of a call money transaction.

8.3.3.1 Roll over
Call money is assumed to mature on a daily basis, unless it is prolonged through roll over. Roll over
of call money can be done either manually or automatically using an activity.
Normally, the roll over of call instruments should be done as soon as the relevant fixing rates are
available.

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•

Setup
The frequency and conventions for the roll over are determined in the instrument definition.

•

Execution

–

Manual roll over of call money instruments is done using the Roll Over action in the
Transaction view of Call Manager.
If you want to change the amount or interest rate for a call money transaction during roll
over, you can enter the changes directly in the following fields: Interest %, Movement, or
Closing Amount).
If you enter changes in any of these fields, the selected transaction is automatically rolled
over. You can enter changes in the fields even after you have selected the Roll Over
command.

–

Automatic roll over is done using the Call Money Roll Over activity.
This activity ensures that any unrolled transactions are prolonged automatically at the end of
the business day instead of the system creating expiry instruments.
The Call Money Account Update activity is then used to update the balances after the roll
over.

Note: See the TRM User Guide for information on the activity parameters for these activities and
how to set up activities in general.

•

Undo Roll Over
You can also undo this action by selecting Undo Roll Over.

8.3.3.2 New movement
When rolling over call money transactions, it is possible to include additional lending or borrowing
(movements). It is also possible to include new movements after the roll over has been carried out.

•

Execution
To include new movements in call money transactions, execute the New Movement action on the
transaction for which you want to include additional lending or borrowing.
This command is only available for transactions that have been rolled over and applied.
In the new row that is added in the Movement view, the following data is required.
Information

Description

Interest Rate

Interest rate for the new movement.

Amount

Amount of the movement.

8.3.3.3 Expire
Call money transactions are expired when there is no longer any lending or borrowing (balance is
zero).

Note: TRM will not allow you to expire the transaction before the current roll over date.

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•

Execution

–

Call money transactions are manually expired using the Expire action in Call Money Manager.
Information

Description

Opening Date

Date on which the call money transaction is expired.

Value Date

Value date for the call money transaction. This date defaults from the Roll Over
Date.

(Interest) Payment
Date

By default, it is the expiry date. However, you can change this date to a later
date at which you want interest to be paid.

When the transaction is expired, the interest is realized and a payable cashflow is created for
the realized interest.

8.3.3.4 Update balance
To update the balance, use the Update Balance right-click action.

•

Execution
Information

Description

From

Start and end dates of the period for which you want to update the balance.

To

8.3.3.5 Update AI
You can update accrued interest on call money transactions using the Update AI action.

•

Execution
Information

Description

Date

Date on which you want to recalculate the accrued interest.

Rate

New interest rate you want to use to recalculate the accrued interest.

8.3.3.6 Realize interest
•

Execution
You can realize accrued interest on call money transactions using the Realize AI action.
Information

Description

Date

Date of the action.

Opening Date

Opening date of the realized interest cashflow.

Payment Date

By default, the Payment Date is the realize date + payment offset. However, you can
change the given default date.

Amount

Amount of the realized interest cashflow.
By default, this is the total amount of accrued interest, but it can be changed to a
lesser amount if you do not want to realize the total.

Settlement
Method

Capitalize or Settle.
The accrued interest is then either settled or capitalized with the nominal amount of
the transaction, depending on the Settlement Method.

Note that it is not possible to realize AI for future dates using this action: you cannot enter a
date that is equal to or later than the transaction’s roll over date.

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•

Cancellation
You can cancel the action using Undo Realize AI.

8.3.4 Position monitoring
8.3.4.1 Setup
Call money transactions are valued by discounting the future cashflows from the maturity date of
the roll-over.

8.4 Cash
Movements in cash, be it payments or receipts, or transfers, that are not generated directly from a
transaction need to be defined as individual instruments. They can then be entered in Transaction
Manager as deals in the same way as any other type of instrument.
Payment cash instruments are based on an instrument type derived from the class CASH.

Note: It is also possible to define cash forecast instruments: see 8.5 Forecast on page 459.

8.4.1 Payment
Payment cash instruments represent stand-alone movements of cash, and can be either a negative
flow (payment) or a positive flow (receipt).

8.4.1.1 Instrument setup
The following basic information may be captured when defining the instrument. This information is
relevant to any kind of payment (or receipt).

•

Main characteristics
Information

Description

Transaction Sign

Sign of the payment.
If the sign is not defined at instrument level, it needs to be specified separately for
each payment transaction.

Currency

Currency of the payment.
Leave this field blank if you want to specify the currency when you enter the payment
in Transaction Manager.

Rounding
parameters

Method and precision used to round cashflow amounts.

Cashflow Type
details

Type and subtype assigned to a cashflow. For a generic payment instrument: select
Payment.

Attribute
parameters

Attributes of the cashflow: Nominal Amount, Not Bookable, Not Payable, or Pseudo.

Client and bank
account details

The client (portfolio-owner) making the payment, and the client’s bank account
information.

Counterparty and
bank account
details

The counterparty of the payment, and the counterparty’s bank account information.

See A.2.91 Cash Payment on page 754.

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For a payment instrument it is also possible to set up:

•

Spot date and value date calculations

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes.

See Appendix A Features on page 713.

8.4.1.2 Deal capture
8.4.1.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a
payment instrument:
Information

Description

Currency

Currency of the payment.

Nominal Amount

Amount of the payment.

Value Date

Date when the payment is made. This defaults to the spot date of the transaction if
the value date has not been specified in the instrument definition.

Value Date Code

If the Value Date Setup feature is applied at instrument level, you can enter the value
date period you want to use to calculate the value date for the transaction, for
example, 3M (3 months).
Note: If you specify a value date period in the instrument setup, this is used by
default and cannot be modified.

8.4.1.2.2 Generated data
•

Cashflows

–

One cashflow per payment transaction.

8.4.1.3 Processing
Apart from the standard processing actions which are common to all transactions (such as Duplicate
and Package), there are no other actions in Transaction Manager that are specific to payment
instruments.
Settlement of cashflows and reconciliation of payments and receipts with the bank account are
managed in Settlement Processing and Settlement Reconciliation: see the TRM User Guide for more
information.

8.4.2 Transfer
Transfers are also set up as cash instruments. Transfers differ from a payment transaction in that
they have two cashflows rather than one: one to debit the account making the payment, and the
other to credit the account receiving the payment.
Transfer instruments are based on an instrument type derived from the class CASH.

8.4.2.1 Instrument setup
The following basic information may be captured when defining the instrument. This information is
relevant to any kind of cash transfer.

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Main characteristics

•

Information

Description

Transaction Sign

Sign of the transfer.
If the sign is not defined at instrument level, it needs to be specified separately for
each transfer transaction.

Currency

Currency of the transfer.
Leave this field blank if you want to specify the currency when you enter the transfer
in Transaction Manager.

Rounding
parameters

Method and precision used to round cashflow amounts.

Cashflow Type
details

Type and subtype assigned to a cashflow. For a generic transfer instrument: select
Payment.

Attribute
parameters

Attributes of the cashflow: Nominal Amount, Not Bookable, Not Payable, or Pseudo.

Client and bank
account details

The client (portfolio-owner) making the transfer, and the client’s bank account
information.

Counterparty and
bank account
details

The counterparty of the transfer, and the counterparty’s bank account information.

See A.2.326 Transfer (cash) on page 874.
For a transfer instrument it is also possible to set up:

•

Spot date and value date calculations

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes.

See Appendix A Features on page 713.

8.4.2.2 Deal capture
8.4.2.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a transfer
instrument:
Information

Description

Currency

Currency of the transfer.

Nominal Amount

Amount of the transfer.

Value Date

Date when the transfer is made. This defaults to the spot date of the transaction.

Value Date Code

If the Value Date Setup feature is applied at instrument level, you can enter the value
date period you want to use to calculate the value date for the transaction, for
example, 3M (3 months).
Note: If you specify a value date period in the instrument setup, this is used as the
default in the transaction and cannot be modified: see A.2.339 Value Date
Setup on page 879.

8.4.2.2.2 Generated data
•

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–

A transfer generates two cashflows: one negative cashflow for the source account and one
positive cashflow for the target account.

–

If Counterparty = Owner, then the cash instructions are reversed.

8.4.2.3 Processing
Apart from the standard processing actions which are common to all transactions (such as Duplicate
and Package), there are no other actions in Transaction Manager that are specific to transfer
instruments.
Settlement of cashflows and reconciliation of transfers with the bank account are managed in
Settlement Processing and Settlement Reconciliation: see the TRM User Guide for more information.

8.4.3 Complex payment
A complex payment instrument allows you to define a payment instrument with multiple cashflows
in the same currency. The direction (transaction sign) and cashflow type of each individual cashflow
within the one payment instrument can be configured separately.
Note that if you need to define a complex payment instrument consisting of different currencies, you
should use an FX deal instead.
Complex payment instruments are based on an instrument type derived from the class CASH.

8.4.3.1 Instrument setup
The following basic information may be captured when defining the instrument. This information is
relevant to any kind of complex payment.

•

Main characteristics
Information

Description

Transaction Sign

Sign of the initial payment transaction.
If the sign is not defined at instrument level, it needs to be specified separately for
each payment transaction at deal entry.
The parameters of the initial payment are defined in the Movement Leg page.

•

Cashflow Leg characteristics
Information

Description

ID

Number representing the order in which the payment is made. The ID of the initial
transaction = 0.
The ID is displayed in the Origin column in Transaction Manager’s Cashflow view.

Payment Sign

Select from: Any, Negative, or Positive. The payment sign for the cashflow leg is
relative to the transaction sign of the initial payment transaction.

Currency

Currency of the payment.
Leave this field blank if you want to specify the currency when you enter the payment
in Transaction Manager.

Rounding
parameters

Method and precision used to round cashflow amounts.

Cashflow Type
details

Type and subtype assigned to a cashflow. For a generic transfer instrument: select
Payment.

Attribute
parameters

Attributes of the cashflow: Nominal Amount, Not Bookable, Not Payable, or Pseudo.

Client and bank
account details

The client (portfolio-owner) making the transfer, and the client’s bank account
information.

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Information

Description

Counterparty and
bank account
details

The counterparty of the transfer, and the counterparty’s bank account information.

See A.2.102 Complex Payment (cash) on page 757.
For a complex payment instrument it is also possible to set up:

•

Spot date and value date calculations

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes.

See Appendix A Features on page 713.

8.4.3.2 Deal capture
8.4.3.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter a complex
payment instrument:
Information

Description

Currency

Currency of the payment.

Nominal Amount

Amount of the payment.

Value Date

Date when the payment is made. This defaults to the spot date of the transaction.

Value Date Code

If the Value Date Setup feature is applied at instrument level, you can enter the value
date period you want to use to calculate the value date for the transaction, for
example, 3M (3 months).
Note: If you specify a value date period in the instrument setup, this is used as the
default in the transaction and cannot be modified: see A.2.339 Value Date
Setup on page 879.

8.4.3.2.2 Generated data
•

Cashflows

–

A complex payment generates multiple cashflows

–

All cashflows are in the same currency

–

The sign and type of each cashflow can be different.

8.4.3.3 Processing
Apart from the standard processing actions which are common to all transactions (such as Duplicate
and Package), there are no other actions in Transaction Manager that are specific to complex
payment instruments.
Settlement of cashflows and reconciliation of payments and receipts with the bank account are
managed in Settlement Processing and Settlement Reconciliation: see the TRM User Guide for more
information.

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8.5 Forecast

8.5 Forecast
A cash forecast instrument can be defined to record cashflow forecasts in the system.
Using a dual-currency forecast instrument, it is possible to view cash exposures in two different
currencies.
Forecast instruments are based on an instrument type derived from the class FORECAST.

8.5.1 Instrument setup
The following basic information may be captured when defining a forecast instrument.

•

Main characteristics
Information

Description

Currency

Currency of the cashflow forecast.

Rounding
parameters

Method and precision used to round cashflow amounts.

Price Type

Price type for the quotation used to determine which FX rate is used in risk
calculations.

See A.2.153 Forecast on page 784.
For a forecast instrument it is also possible to set up:

•

Spot date and value date calculations

•

Cashflow and transaction charge rules

•

Manual charges

•

Branch codes.

See Appendix A Features on page 713.

8.5.1.1 Dual-currency forecast
Using a dual-currency forecast instrument, it is possible to view forecast exposures in two different
currencies.
Dual-currency cashflow forecast instruments are set up in the same way as single currency
forecasts, except that they are set up with a different primary feature.
See A.2.126 Dual Currency Forecast on page 772.

8.5.2 Deal capture
Forecast exposures are imported into TRM using the Forecast Exposures from CMM activity which
you can schedule to run as often as required (for example, nightly).
These forecasts can then be retrieved in the Forecast Exposure Board for further monitoring or
processing.

Note: See the TRM User Guide for more information about importing cashflow forecasts into TRM
and managing cashflow forecasts in general.

8.5.3 Processing
This section describes the actions that can be done throughout the life of a forecast exposure.

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8.5.3.1 Adjust
In some rare cases, it may be necessary to adjust the amount of a forecast. This can be done using
the Adjust right-click action on the selected forecast.

•

Execution
Information

Description

Active From

Date from when the adjustment applies.

Adjustment
Amount

Amount of the adjustment.

Active Until
Method

Date until when the adjustment applies:

Active Until

•

Until Next Import – the adjustment applies until the next time the activity to
import the forecasts from CMM is run, at which time the adjustment is deactivated
(but not deleted).

•

Until Specific Date – the adjustment applies until the date defined in the Active Until
field, at which time the adjustment is deactivated (but not deleted).

•

Always – the adjustment applies indefinitely.

Date until when the adjustment applies when Active Until Method = Until Specific

Date.

An Adjustment flow is added to the forecast exposure.

8.5.3.2 Calculate figures
The Calculate Figures right-click action calculates the figures for forecast exposures and displays the
results in Forecast Exposure Board’s Figures view.

8.5.3.3 Drill Down
The Drill Down action on a retrieved forecast exposure allows you to drill down further into the
forecast exposure’s underlying details, for example, to see the underlying component cashflow
forecasts of a global forecast amount at a specific date.
The underlying components are displayed in Forecast Exposure Board’s Exposure Drilldown view.

8.6 Cost-of-carry
Cost-of-carry is used to capture the internal funding cost of outstanding cash. The cost-of-carry
balance can be used to monitor how much cash is outstanding for a position and to calculate the
accrued interest on the balance. Cost-of-carry can be calculated automatically for any portfolios with
a position.
Cost-of-carry balances and any accrued interest are displayed in the system as transactions: there
is one cost-of-carry transaction per currency dealt in the portfolio.
In order to calculate the cost-of-carry of a position, a cost-of-carry instrument needs to be defined
and assigned to the portfolio.
Only one cost-of-carry instrument needs to be set up to calculate both the balances and the accrued
interest.

Note: Information about how to assign cost-of-carry instruments to portfolios is described in the
TRM User Guide.

Cost-of-carry instruments are based on an instrument type derived from the class COST-OF-CARRY.

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8.6 Cost-of-carry

8.6.1 Instrument setup
Cost-of-carry instruments are assigned to the portfolios for which you want to calculate the cost
associated with funding a position. The balance can either be derived from payable cashflows in the
system, or from paid cashflows.
Cost-of-carry balance instruments are assigned to portfolios in the Cost of Carry page of Portfolio
Editor: see the TRM User Guide for more information.

•

Main characteristics
Cost-of-carry instruments (that do not have accrued interest calculated on the balance) do not
require any specific setup. They are simply recognized by the following features in the Cost of
Carry instrument class:

•

–

The primary feature COST-OF-CARRY-BALANCE (see A.2.106 Cost of Carry Balance on page
760)

–

The valuation feature COST-OF-CARRY-METHOD (see A.2.108 Cost of Carry Valuation on
page 761).

Interest information
Cost-of-carry instruments that have accrued interest calculated on the balance use the feature
COST-OF-CARRY-INTEREST and require the following setup:

–

Interest accrual parameters
There are some additional parameters that must be defined to calculate the accrual of
interest on the cost-of-carry balance. You can specify the interest rates used, and the
method and frequency that interest is accrued.
Note that if the feature COST-OF-CARRY-INTEREST is not defined in the instrument setup,
interest will not be calculated on the cost-of-carry balance.
Information

Description

Date Basis

Date basis used to calculate accrued interest for this instrument.

Interest Rate Curve

Underlying yield curve used for interest calculation.
Note: If you specify a yield curve, you do not need to specify any Ladder
values (see Ladder Rule and Ladder).

–

Period

Period of the underlying yield curve to be used for interest calculation (for
example, O/N).

Scenario

Rate scenario to be used for calculating interest for this instrument.

Interest realization parameters
You can specify how the accrued interest is realized on the balance.
Information

Description

Frequency

Frequency of interest realization (if Method = Periodically).

Frequency Unit
Method

Unit of time to use for interest realization: Business Days, Days, Months,

Weeks, or Years.

Method of realizing interest:
•

At Withdrawal - not applicable.

•

Periodically - interest is realized at regular intervals (see Frequency
field).

•
Settlement Method

At Expiration - not applicable.

Interest payment method: Only Capitalize is used for cost-of-carry.

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See A.2.107 Cost of Carry Interest on page 760.

8.6.2 Deal capture
Cost-of-carry transactions are system-generated transactions, performed by scheduled activities
(see the TRM User Guide for more information). When an activity has run, you can view the
transactions in the Cost of Carry application.

8.6.2.1 Generated data
•

Transaction

–

One transaction per currency:
Transaction Type = Balance
Counterparty = Portfolio-owner

•

Cashflows

–

One cashflow per balance (only if the balance has changed)

–

Daily accrued interest (if the Cost of Carry Interest feature is assigned to the instrument).

–

If the interest is realized: realized interest cashflows.

–

If zero-balancing is used: another balance cashflow with the opposite sign. A zero balance
cashflow is also generated the next day.

8.6.3 Processing
This section describes the processing that you can perform, either manually in the relevant
application, or automatically, as an activity, in Activity Manager.

8.6.3.1 Calculating cost-of-carry balance and interest
Cost-of-carry balance and accrued interest-calculation transactions are generated by the activity
Cost of Carry which you can schedule to run as often as required (see the TRM User Guide for more
information).

8.6.3.2 Realizing cost-of-carry interest
Cost-of-carry accrued interest can be realized automatically or manually (for automatic realization,
see the TRM User Guide).
You can realize interest manually, by right-clicking on the transaction in the Transaction view of the
Cost of Carry application and selecting the Realize AI action.

•

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The following information is needed to process the realization:
Information

Description

Date

Date of the action i.e. the realization date.

Opening Date

The opening date of the transaction.

Payment Date

By default, the Payment Date is the realization date. However, you can change
the default.

Amount

Amount of the realized cost-of-carry interest cashflow. By default, this is the
total amount of accrued interest, but it can be changed to a lesser amount if
you do not want to realize the total amount.

Zero Balancing

Yes or No (default).

Update Realization Date

•

Yes - the accrued cost-of-carry interest and the cost-of-carry balance are
closed out, so that the next day, the starting cost-of-carry balance is zero
when the cost-of-carry activity is run.

•

No - the accrued cost-of-carry interest is realized today, and the next day,
the starting cost-of-carry balance is today's balance.

Switch on to allow the next interest realization date to be automatically
updated.

Note: It is not possible to realize accrued interest for future dates using the Realize AI action.
•

Cancellation
You can cancel interest manually by right-clicking on the transaction in the Transaction view of
the Cost of Carry application and selecting the Undo Realize AI action. The following
information is needed to process the cancellation:.
Information

Description

Date

Date of the action i.e. the undo realization date.
By default the date is today's date.

8.6.3.3 Setting the cost-of-carry balance to zero
It is possible to close out the outstanding cost-of-carry balance without realizing any interest using
the activity Cost of Carry Zero Balancing. See the TRM User Guide for more information.

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Chapter 9

Futures

9.1 Forward rate agreement
A Forward Rate Agreement (FRA) is an obligation between two parties to enter into a deposit or
discount contract in the future at a predefined interest rate.
An FRA is an off-balance sheet instrument where the underlying contract is not entered at expiry,
but the difference between the pre-agreed rate and the actual rate at expiry is settled between the
two parties.
The date on which the comparison is made is known as the fixing date. Payment of the interest
differential is made up-front, at the start of the future period. The amount is therefore calculated on
a discounted basis since it is settled in advance.
FRA contracts are traded in reversed sign (the market convention). This means that the purchase of
an FRA creates a negative position and a negative interest rate risk, whereas the sale of an FRA
produces a positive position and a positive interest rate risk.
The most common maturities for FRAs are between 1 and 12 months and the US dollar is the major
currency used. FRAs are labeled by period (for example, 3M/6M means a contract that starts in
three months and ends in six).

9.1.1 FRA deposit and FRA discount
The following basic information may be captured when defining the instrument. This information is
relevant to any kind of FRA contract (discount paper or deposit).
For more information relating to the setup and structure of specific types of FRA, see 9.1.2
Australian FRA on page 476.

9.1.1.1 Instrument setup
Forward rate agreements are based on an instrument type derived from the class FRA.

•

Main characteristics
The following basic information may be captured when defining the instrument. This information
is relevant to any kind of FRA contract (discount paper or deposit).
Information

Description

Currency

Currency of the FRA (that is, if it is a listed forward rate agreement).
Leave this field blank if you want to specify the currency at deal entry (if you are
defining an OTC forward rate agreement).

Date Basis

Date basis of the instrument. If the date basis is not defined at instrument level, it
needs to be specified separately for each transaction.

Rounding
parameters

Method and precision used to round cashflow amounts.

Yield Type

Yield type of the forward rate agreement.

Principal Subtype

Type of principal or interest cashflows, if you want to override the default settings.

Interest Subtype

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9.1 Forward rate agreement

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Netting parameters
Information

Description

Fixing Offset

Minimum number of days’ offset allowed, that is, the difference in days between
the fixing date and the due date (default = 0).
Leave this field blank if you want to specify the fixing offset when you enter the
deal.

Fixing Subscenario

Prices scenario from which the floating rate is retrieved (for example, EUR/USD
Spot 9:00 London, or EUR/USD Spot 9:00 Tokyo).
Leave this field blank if you want to specify it when you enter the deal.

Calendar

Calendar to use when calculating the fixing date.

Switches

Activate the switches that apply to the instrument.
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Settlement Currency

Settlement Currency - switch on if the P/L cashflow is paid in a different currency.

Currency in which the P/L cashflow is paid (if the switch Settlement Currency is
switched on).
Leave this field blank if you want to specify the settlement currency when you enter
the deal.

Payment Offset

Number of business days after which effective payment of the P/L is made

Fixing Rate

ID of the yield curve used to calculate the closing price of the forward contract. The
forward contract is fixed with the price and TRM calculates the profit/loss using this
closing price and the deal rate.
Leave this field blank if you want to specify it when you enter the deal.

Fixing Period

Length of time for which fixing is to be executed (for example, 3M, 6M, 1Y, and so
on).
Leave this field blank if you want to specify the fixing period when you enter the
deal.

See A.2.157 Forward Rate Agreement (Deposit) on page 786 and A.2.158 Forward Rate
Agreement (Discount) on page 787.

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Date information
For listed FRA contracts, you must specify the fixing, settlement, and maturity information.
See A.2.156 FRA Dates on page 785.
For OTC FRA contracts, you need to set up the FRA period information. The maturity date and
value date of the contract is calculated using these values.
Information

Description

Calendar
parameters

Calendars used to calculate the dates.

Gap Set

Gap set used for supplying the available value/maturity periods for an OTC FRA
contract; these in turn are used to define exact dates.

Gap

Specific gap (within the gap set) defined for the FRA period. This value is used to
calculate the value date and maturity date for an OTC FRA contract at deal entry.
If you specify the gap period in the instrument setup, this is used as the default in the
transaction and cannot be modified. If you leave this field blank, you need to select
the gap period in the Maturity Code field at deal entry. The system will then calculate
the FRA periods automatically.

See A.2.163 FRA Periods on page 790.

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Quotation information

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9 Futures
9.1 Forward rate agreement

For listed FRA discount contracts, specify the quote information as Yield.
See A.2.274 Quoted on page 849.
It is also possible to set up:

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Branch codes

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Cashflow and transaction charge rules

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Manual charges

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Spot date calculation.

See Appendix A Features on page 713.

9.1.1.2 Deal capture
9.1.1.2.1 Input data
In addition to the standard deal parameters, the following information is required to enter an FRA
contract:
Information

Description

Currency

Currency of the transaction.
If you specified the currency in the instrument setup (for example, for a US T-Bill),
this is used as the default currency in the transaction and cannot be modified.

Maturity Code

Maturity code used to calculate the FRA periods. From this code, the date for the
maturity of the underlying contract and the official date when money is transferred
(expiry of the FRA) are calculated.
If you defined the specific FRA periods in the instrument setup, these are used as the
default in the transaction and cannot be modified.

Maturity Date

Date when the transaction matures. If you enter a maturity code, the date is
calculated automatically; otherwise you can enter the date manually.
If the maturity definition parameters are defined at instrument level, these are used
by default and cannot be modified.

Value Date

Date when the transaction starts. This defaults to the spot date of the transaction.

Nominal Amount

Amount of the forward rate agreement. This is equal to the principal (the amount on
which the interest is calculated).
FRAs are traded in reversed sign. This means that the nominal amount is negative for
the purchase of an FRA, whereas the sale of an FRA is denoted by a positive nominal
amount.

Deal Rate

Rate of return of the underlying forward contract.

Fixing Rate

Yield curve used when fixing the cashflow.

Fixing Period

Interest period from which the quotation is retrieved when fixing the interest rate of
the transaction, for example, 1M, 3M, or 1Y.

Fixing (Max) Offset

(Maximum) number of business days before the interest date.

Fixing Offset

The fixing of the interest occurs on this date.

Fixing Subscenario

Rate scenario from which the interest rate is retrieved (for example, EUR/USD Spot
9:00 London or EUR/USD Spot 9:00 Tokyo).

Fixing Calendar

Calendar used for fixing.

9.1.1.2.2 Generated data
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Transaction
Book Value (discount style):

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9.1 Forward rate agreement

BV = rounder (A*D)
where:
D = discount factor
A = nominal amount
rounder depends on instrument rounding parameters

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