HSBC Instrument Specifications .pdf



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HSBC Instrument Specifications

September 2007

CONFIDENTIAL INFORMATION

Copyright © 2007 QuIC Financial Technologies Inc.
All rights reserved.

Document Revision: 2.47

HSBC Instrument Specifications
Document version: 2.47
DO NOT COPY OR DISTRIBUTE

TERMS OF USE
This document, the contents of this document and the software and script
technology described by this document (collectively the Property) are
Copyright © 2007, QuIC Financial Technologies Inc. (QuIC), and constitute
proprietary and confidential information of QuIC that is subject to protection
under Canadian and international trademark and copyright legislation. QuIC
reserves all rights in and to the Property.
Any copying, reproduction, distribution, transmission or disclosure of all or any
part of this document or its contents, in any form or by any means, is strictly
prohibited without the prior written consent of QuIC.
This document is provided to you (as an individual and as a representative of
your company) subject to QuIC’s standard Confidentiality Agreement, Evaluation
License and Agreement, Software License and Support Agreement or similar
document, and you agree to the terms of use of the Property as laid out therein
respectively. Notwithstanding the terms and conditions as may be applicable to
this document, you agree to treat the Property as confidential information unless
advised otherwise by QuIC in writing.
While every effort has been made to ensure that the information contained in this
documentation is correct, QuIC does not warrant the information is free of errors
or omissions, unless agreed to otherwise in writing. The information contained in
this document is subject to change without notice.
QuIC™, the QuIC logo, and QuIC Analytics™, QuIC Analytics - XL™,
QuIC Analyzer™, QuIC Dispatch™, QuIC Engine™, QuIC Functions™,
QuIC Integration™, QuIC Links™, QuIC Mechanics™, QuIC Network Engine™,
QuIC Platform™, QuIC Product Suite™, QuIC Publisher™, QuIC Script™,
QuIC Simulation Framework™, QUIC Run™, QuIC View™, and QuIC Workbench™
product names are trademarks of QuIC Financial Technologies Inc. or a licensor in
Canada, the United States and/or other countries.

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CONTACTING QUIC
Head Office
QuIC Financial Technologies Inc.
1095 W. Pender Street, Suite 1105
Vancouver, BC V6E 2M6
CANADA

EMEA
QuIC Financial Technologies (UK) Ltd.
1 Cornhill
London, EC3V 3ND
UNITED KINGDOM

Research & Development
QuIC Financial Technologies Inc.
3553 – 31st Street NW, Suite 225
Calgary, AB T2L 2K7
CANADA

Americas
QuIC Financial Technologies Inc.
39th Floor, 245 Park Avenue
New York, NY 10167
USA
Asia Pacific
QuIC Financial Technologies Inc.
One Marina Boulevard #28-00
SINGAPORE 018989

www.quic.com
Within North America:
Outside North America:

1.877.689.1888
1.306.337.1446

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CONTENTS
1

INTRODUCTION .................................................................................. 12
1.1
Purpose of This Document .......................................................... 12
1.2
Document Audience ................................................................... 12
1.3
Where to Go for Help ................................................................. 12
1.4
Document Version History .......................................................... 13

2

SIGN-OFFS ........................................................................................ 21

3

PROJECT SCOPE ................................................................................. 22
3.1
PFE Simulation .......................................................................... 22
3.1.1
Equity Risk Simulation ................................................... 22
3.1.2
Credit Spread Simulation ............................................... 26
3.1.3
Jumps ......................................................................... 26
3.1.4
Default ........................................................................ 26
3.1.5
Basket ......................................................................... 26
3.2
Pricing Models ........................................................................... 26
3.2.1
Equity ......................................................................... 26
3.2.2
Inflation....................................................................... 27
3.3
Financial Instruments ................................................................. 27
3.4
QuiC Financial Engineers per Instrument / Model ........................... 29

4

INSTRUMENT SPECIFICATIONS ............................................................ 30
4.1
Cross Instrument Inputs ............................................................. 30
4.1.1
Map Inputs: MultiLeg ..................................................... 30
4.2
American Exercise Vanilla Equity Option ....................................... 30
4.2.1
Description................................................................... 30
4.2.2
Performance Options ..................................................... 37
4.2.3
Finite Difference Solution Preferences .............................. 38
4.2.4
Transaction File Inputs .................................................. 38
4.2.5
Auxiliary Transaction Data File Inputs .............................. 41
4.2.6
Market Data Curves ...................................................... 43
4.2.7
Definition of Daycounts .................................................. 49
4.2.8
Testing Methodology ..................................................... 50
4.3
European Exercise Vanilla Equity Option ....................................... 50
4.3.1
Description................................................................... 50
4.3.2
Settlement Lag ............................................................. 51
4.3.3
Performance Options ..................................................... 52
4.3.4
Transaction File Inputs .................................................. 52
4.3.5
Market Data Curves ...................................................... 54
4.3.6
Testing Methodology ..................................................... 55
4.4
Inflation Swap ........................................................................... 55
4.4.1
Notations ..................................................................... 55
4.4.2
Payoff Definitions .......................................................... 56
4.4.3
Pricing Methodology ...................................................... 56
4.4.4
Seasonality Adjustment ................................................. 58
4.4.5
Potential Future Exposure Calculations ............................ 59
4.4.6
Transaction File Inputs .................................................. 60
4.4.7
Market Data Curves ...................................................... 65
4.4.8
Logging Intermediate Results ......................................... 70

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4.5

4.6

4.7

4.8

4.9

5

4.4.9
Testing Methodology ..................................................... 71
Total Return Swap (TRS) ............................................................ 71
4.5.1
Description................................................................... 71
4.5.2
Analytic Price ............................................................... 72
4.5.3
Risky Discount Factors ................................................... 74
4.5.4
Bond Spread Calibration ................................................ 75
4.5.5
Bond Valuation ............................................................. 76
4.5.6
PRICE_TR .................................................................... 76
4.5.7
AI_TR .......................................................................... 76
4.5.8
LIBOR ......................................................................... 77
4.5.9
AI_PREM ...................................................................... 78
4.5.10 LOCKOUT ..................................................................... 78
4.5.11 Transaction File Inputs .................................................. 78
4.5.12 Market Data Curves ...................................................... 88
Constant Maturity (Treasury) Swaps (CMS and CMT) ..................... 91
4.6.1
Pricing Methodology ...................................................... 91
4.6.2
Transaction File Inputs .................................................. 99
4.6.3
Coupon Map Definitions ................................................100
4.6.4
Observables ................................................................108
4.6.5
Market Data Curves .....................................................113
Equity Swap.............................................................................116
4.7.1
Description..................................................................116
4.7.2
Valuing the Equity Leg ..................................................117
4.7.3
Calculating the Forward Equity Price ...............................118
4.7.4
Fixed Index Leg ...........................................................120
4.7.5
IR Leg ........................................................................120
4.7.6
Performance Return Swap .............................................121
4.7.7
Baskets ......................................................................122
4.7.8
Compo Equity Swaps ....................................................122
4.7.9
Instrument Format .......................................................123
4.7.10 Transaction File Inputs .................................................124
4.7.11 Auxiliary Transaction Data File Inputs .............................125
4.6.12 Market Data Curves .....................................................132
4.6.13 Testing Methodology ....................................................137
Bond Repo ...............................................................................137
4.8.1
Description..................................................................137
4.8.2
Transaction File Inputs .................................................138
4.8.3
Testing Methodology ....................................................139
Equity Repo .............................................................................140
4.9.1
Description..................................................................140
4.9.2
Transaction File Inputs .................................................140
4.9.3
Testing Methodology ....................................................142

MODEL SPECIFICATIONS ....................................................................143
5.1
PFE Model for Equity Risk with Jumps ..........................................143
5.1.1
Accounting for Jumps ...................................................143
5.1.2
Alternative Equity Pricing Model .....................................144
5.2
Model Simulation Data Requirements ..........................................147
5.2.1
Market Data CSV file ....................................................147
5.2.2
Model Parameters CSV file ............................................151
5.2.3
External Scenarios CSV File ...........................................155
5.2.4
Stress Testing Data ......................................................156

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5.2.5
6

Input codes .................................................................156

ABBREVIATIONS ................................................................................158

TABLES
Table 1: Document Version History .............................................................. 13
Table 2: PFE and Stress Testing – Definitions Data Requirements .................... 24
Table 3: Instrument Modelling Approach ...................................................... 27
Table 4: QuIC Financial Engineers – Instrument Assignments ......................... 29
Table 5: MultiLeg Map Definiton .................................................................. 30
Table 6: Instrument 1: Model and Solver ..................................................... 30
Table 7: Instrument 1: Transaction File Inputs.............................................. 38
Table 8: EQOptionAmericanExerice Instrument: oSolverPrefs_ information Map 41
Table 9: Sample Yield Data ........................................................................ 44
Table 10: Sample Equity Implied Volatility Data ............................................ 46
Table 11: Sample Dividend Schedule Data.................................................... 47
Table 12: Sample Dividend Yield Data ......................................................... 48
Table 13: Day count Convention Codes ........................................................ 49
Table 14: Instrument 2: Model and Solver.................................................... 50
Table 15: Instrument 2: Transaction File Inputs ............................................ 52
Table 16: Instrument Inflation Swap: Model and Solver ................................. 55
Table 17: Inflation Instrument: Transaction File Inputs .................................. 60
Table 18: Inflation Instrument: Leg Information Map ..................................... 61
Table 19: CouponInflationFixed Map Definition .............................................. 63
Table 20: Inflation Instrument: Observable Map Input ................................... 65
Table 21: Sample Yield Data ....................................................................... 67
Table 22: Sample Yield Data ....................................................................... 68
Table 23: Total Return Swap on a Corporate Bond: Model and Solver .............. 71
Table 24: Generic Instrument: Transaction File Inputs ................................... 78
Table 25: CouponBondTotalReturnSpot Map Definition ................................... 80
Table 26: ObservableBond Map Definition .................................................... 81
Table 27: mpRateSchedule Definition........................................................... 83
Table 28: CouponTRPremSpot Map Definition ............................................... 84
Table 29: LiborObservable Map Definition ..................................................... 86
Table 30: Sample Yield Data ....................................................................... 89
Table 31: Generic Instrument: Transaction File Inputs ................................. 100
Table 32: CouponLibor and CouponCMS Map Definition ................................ 101
Table 33: CouponFixed Map Definition ....................................................... 104
Table 34: Option Payoffs Supported for strOptionType Field .......................... 105
Table 35: CouponLiobrCapFloor and CouponCMSCapFloor Map Definition ....... 106
Table 36: ObservableSwapRate Map Definition ............................................ 108
Table 37: ObservableLibor Map Definition ................................................... 111
Table 38: Sample Yield Data ..................................................................... 113

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Table 39: Sample ATM Swaption Volatility Data .......................................... 115
Table 40: Sample Swaption Smile Data ...................................................... 115
Table 41: Instrument 1: Model and Solver .................................................. 116
Table 42: Instrument 1: Transaction File Inputs .......................................... 124
Table 43: EQSwap Instrument: CouponLiborEquityIRLeg Information Map...... 125
Table 44: EQSwap Instrument: CouponFixedEquityIRLeg Information Map ..... 126
Table 45: EQSwap Instrument: IRLeg Information Map: ObservableLiborRate Map
Definition ............................................................................................... 128
Table 46: EQSwap Instrument: CouponTotalReturnEquity Information Map .... 129
Table 47: EQSwap Instrument: EQLeg Information Map: mpEquityObservable
Information Map ..................................................................................... 131
Table 48: Sample Yield Data ..................................................................... 133
Table 49: Sample Dividend Schedule Data.................................................. 135
Table 50: Sample Continuous Dividend Yield Data ....................................... 136
Table 51: Instrument BondRepo : Model and Solver .................................... 137
Table 52: Instrument BondRepo: Transaction File Inputs ............................. 138
Table 53: Instrument EquityRepo: Model and Solver .................................... 140
Table 54: Instrument BondRepo: Transaction File Inputs ............................. 140
Table 55: Sample Yield Data ..................................................................... 149
Table 56: Sample Par Credit Spread Data ................................................... 150
Table 57: Data Type Codes ....................................................................... 151
Table 58: Equity Risk Simulation Model Parameters ..................................... 152
Table 59: External Scenario CSV File’s Rows ............................................... 155
Table 60: Day Count Convention Codes ..................................................... 157

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FIGURES
Figure 1: Sample Yield Curve (CSV Format) .................................................. 44
Figure 2: Sample EquityIndex Curve (CSV Format) ....................................... 45
Figure 3: Sample EquityImpliedVolMtx Curve (CSV Format)............................ 46
Figure 4: Sample DiscreteAbsoluteDividend Curve (CSV Format) ..................... 47
Figure 5: Sample DividendYield Curve (CSV Format) ..................................... 49
Figure 6: CPI Fixing in PFE Calculations Example ........................................... 60
Figure 7: Sample Yield Curve (CSV Format) .................................................. 67
Figure 8: Sample Yield Curve (CSV Format) .................................................. 68
Figure 9: Sample RealYield Curve (CSV Format)............................................ 69
Figure 10: Sample HistoricalInflationIndex Curve (CSV Format) ...................... 69
Figure 11: DerivedInflationIndex Curve (CSV Format) ................................... 70
Figure 12: Sample InflationSeasonality Curve (CSV Format) ........................... 70
Figure 13: Bond Spread Calibration ............................................................. 75
Figure 14: Accrued Interest Example ........................................................... 77
Figure 15: Accrued Interest Example ........................................................... 77
Figure 16: Example of Generic Transaction Input for TRSB ............................. 79
Figure 17: Example of TRLegInfo Map Inputs ................................................ 81
Figure 18: Example of BondObservable Map Inputs ....................................... 83
Figure 19: Example of RateScheduleMap Inputs ............................................ 83
Figure 20: Example of CouponTRPremSpot Map Inputs .................................. 86
Figure 21: Examples of LIBOR Map Inputs .................................................... 88
Figure 22: Sample Yield Curve (CSV Format) ................................................ 89
Figure 23: Par Credit Spread Curve ............................................................. 91
Figure 24: Generic Configuration of a Single Cash Flow Based on a Swap Rate . 91
Figure 25: Caplet and Floorlet Payoff ........................................................... 93
Figure 26: j-th Coupon In-Advance.............................................................. 98
Figure 27: j-th Coupon In-Arrears ............................................................... 98
Figure 28: Sample Yield Curve (CSV Format) .............................................. 114
Figure 29: Sample EquityImpliedVolMtx Curve (CSV Format) ........................ 115
Figure 30: Sample EquityImpliedVolMtx Curve (CSV Format) ........................ 116
Figure 31: Sample Yield Curve (CSV Format) .............................................. 134
Figure 32: Sample EquityIndex Curve (CSV Format) .................................... 134
Figure 33: Sample DiscreteAbsoluteDividend Curve (CSV Format) ................. 135
Figure 34: Sample ContinuousDividendYield Curve (CSV Format) .................. 137
Figure 35: Sample Exchange Curve (CSV Format) ....................................... 148
Figure 36: Sample Yield Curve (CSV Format) .............................................. 149
Figure 37: Sample ParCreditSpread Curve (CSV Format) .............................. 150
Figure 38: Sample EquityIndex Curve (CSV Format) .................................... 151
Figure 39: Sample Equity Index Simulation Model Parameters ...................... 155

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EQUATIONS
Equation 1 – Equity Risk Simulation............................................................. 22
Equation 2 – Equity Options ....................................................................... 30
Equation 3 – Equity Options ....................................................................... 31
Equation 4 – Equity Options ....................................................................... 31
Equation 5 – Equity Options ....................................................................... 31
Equation 6 – Equity Options ....................................................................... 32
Equation 7 – Equity Options ....................................................................... 33
Equation 8 – Equity Options ....................................................................... 33
Equation 9 – Equity Options ....................................................................... 34
Equation 10 – Equity Options ...................................................................... 34
Equation 11 – Equity Options ...................................................................... 35
Equation 12 – Equity Options ...................................................................... 35
Equation 13 – Equity Options ...................................................................... 36
Equation 14 – Equity Options ...................................................................... 36
Equation 15 – Equity Options ...................................................................... 36
Equation 16 – Equity Options ...................................................................... 36
Equation 17 – Equity Options ...................................................................... 37
Equation 18 – Equity Options ...................................................................... 37
Equation 19 – Equity Options ...................................................................... 50
Equation 20 – Equity Options ...................................................................... 50
Equation 21 – Equity Options ...................................................................... 50
Equation 22 – Equity Options ...................................................................... 50
Equation 23 – Equity Options ...................................................................... 51
Equation 24 – Equity Options ...................................................................... 51
Equation 25 – Equity Options ...................................................................... 51
Equation 26 – Equity Options ...................................................................... 51
Equation 27 – Inflation Swaps .................................................................... 56
Equation 28 – Inflation Swaps .................................................................... 56
Equation 29 – Inflation Swaps .................................................................... 56
Equation 30 – Inflation Swaps .................................................................... 56
Equation 31 – Inflation Swaps .................................................................... 57
Equation 32 – Inflation Swaps .................................................................... 57
Equation 33 – Inflation Swaps .................................................................... 57
Equation 34 – Inflation Swaps .................................................................... 57
Equation 35 – Inflation Swaps .................................................................... 57
Equation 36 – Inflation Swaps .................................................................... 58
Equation 37 – Inflation Swaps .................................................................... 58
Equation 38 – Inflation Swaps .................................................................... 58
Equation 39 – Inflation Swaps .................................................................... 59
Equation 40 – Inflation Swaps .................................................................... 59

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Equation 41 – Total Return Swap ................................................................ 72
Equation 42 – Total Return Swap ................................................................ 74
Equation 43 – Total Return Swap ................................................................ 75
Equation 44 – Total Return Swap ................................................................ 76
Equation 45 – Total Return Swap ................................................................ 76
Equation 46 – Total Return Swap ................................................................ 77
Equation 47 – Total Return Swap ................................................................ 77
Equation 48 – Total Return Swap ................................................................ 78
Equation 49 – Total Return Swap ................................................................ 78
Equation 50 – CMS and CMT ....................................................................... 92
Equation 51 – CMS and CMT ....................................................................... 92
Equation 52 – CMS and CMT ....................................................................... 93
Equation 53 – CMS and CMT ....................................................................... 94
Equation 54 – CMS and CMT ....................................................................... 94
Equation 55 – CMS and CMT ....................................................................... 94
Equation 56 – CMS and CMT ....................................................................... 94
Equation 57 – CMS and CMT ....................................................................... 95
Equation 58 – CMS and CMT ....................................................................... 95
Equation 59 – CMS and CMT ....................................................................... 95
Equation 60 – CMS and CMT ....................................................................... 95
Equation 61 – CMS and CMT ....................................................................... 95
Equation 62 – CMS and CMT ....................................................................... 96
Equation 63 – CMS and CMT ....................................................................... 96
Equation 64 – CMS and CMT ....................................................................... 96
Equation 65 – CMS and CMT ....................................................................... 97
Equation 66 – CMS and CMT ....................................................................... 97
Equation 67 – CMS and CMT ....................................................................... 97
Equation 68 – CMS and CMT ....................................................................... 97
Equation 69 – Equity Swap ....................................................................... 117
Equation 70 – Equity Swap ....................................................................... 118
Equation 71 – Equity Swap ....................................................................... 118
Equation 72 – Equity Swap ....................................................................... 118
Equation 73 – Equity Swap ....................................................................... 119
Equation 74 – Equity Swap ....................................................................... 119
Equation 75 – Equity Swap ....................................................................... 119
Equation 76 – Equity Swap ....................................................................... 120
Equation 77 – Equity Swap ....................................................................... 120
Equation 78 – Equity Swap ....................................................................... 120
Equation 79 – Equity Swap ....................................................................... 121
Equation 80 – Equity Swap ....................................................................... 121
Equation 81 – Equity Swap ....................................................................... 122
Equation 82 – Equity Swap ....................................................................... 122

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Equation 83 – Equity Swap ....................................................................... 122
Equation 84 – Equity Swap ....................................................................... 122
Equation 85 – Equity Swap ....................................................................... 123
Equation 86 – Equity Swap ....................................................................... 123
Equation 87 – Model Specifications ............................................................ 143
Equation 88 – Model Specifications ............................................................ 144
Equation 89 – Model Specifications ............................................................ 144
Equation 90 – Model Specifications ............................................................ 145
Equation 91 – Model Specifications ............................................................ 145
Equation 92 – Model Specifications ............................................................ 145
Equation 93 – Model Specifications ............................................................ 145
Equation 94 – Model Specifications ............................................................ 145
Equation 95 – Model Specifications ............................................................ 145
Equation 96 – Model Specifications ............................................................ 146
Equation 97 – Model Specifications ............................................................ 146
Equation 98 – Model Specifications ............................................................ 146
Equation 99 – Model Specifications ............................................................ 147

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1

INTRODUCTION
1.1

Purpose of This Document

This document provides detailed specifications of the risk-factor scenariogeneration models and financial instruments that are to be added to HSBC’s
counterparty credit exposure calculations. For a description of the requirements
on which these specifications are based, see the document ‘QuIC Response to
HSBC Credit Risk New Products RFP’.
This is a working document, owned by QuIC, which will evolve throughout the
discovery phase of the workstream 2 (‘WS2’) project.
Chapter 4 Instrument Specifications, starting on page 30, has a section per
financial instrument, explaining the financial model and its variables, and the
parameterization within QuIC Script. Each instrument-specific section will be
signed off by both HSBC (TMR) and QuIC incrementally, to allow the staggered
development and delivery of each product by the QuIC Financial Engineering
team in Vancouver.
1.2

Document Audience

This document is for:


Callum Wingrove, HSBC Project Team, TMR team



QuIC’s project team, financial engineers and QuIC Script programmers.
1.3

Where to Go for Help

For additional help with information covered in this document, contact:
Jay Rao, Project Manager
+44 20 7743 6325 (O)
+44 7852434033 (M)
Email: jay.rao@quic.com
Alternatively call the QuIC customer service at 1.877.689.1888 within North
America, or 1.306.337.1446 outside North America.
Technical support is also available by email at techsupport@quic.com.

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1.4

Document Version History

The following table (Table 1: Document Version History) shows changes made to
this document from V2.14 onwards:
Table 1: Document Version History
Version

Updated by

Change Description

2.14

Julian Maynard-Smith,
Technical Author

General literary edit (correcting typos, simplifying descriptions,
etc).
Added ‘Document Version History’ section.
Changed appendices to chapters, to address heading
numbering problems when pasting instrument-specific
information from other documents.
Added 5.2 Model Simulation Data Requirements, starting on
page 147.
Added new version of the CMS document (‘HSBC CMS
specification 1.5’).
Added new versions of the American Exercise Vanilla Equity
Option, and European Exercise Vanilla Equity Option, sections
(Equity Option Instrument Specification v5).

2.15

Julian Maynard-Smith,
Technical Author

Added new section, 4.7 Equity Swap, starting on page 116.

2.16

Julian Maynard-Smith,
Technical Author

Changes requested by Horst for sign-off on the equity/credit
simulation model. All the changes are in section 3.1 PFE
Simulation, starting on page 22:
The equation in 3.1.1 Equity Risk Simulation on page 22
adjusted so that there is no factor
term

Fn

multiplying the drift

n .

Table 2 (page 24): For the first row of the table, Risk factor n
at time tj under scenario i , the text in the two Data
Requirements columns has been adjusted to mention Calypso
as well as Sophis.
Table 2 (page 24): For the sixth row of the table, Trigger time
step, the word ‘stress’ has been removed from the sentence:
‘The trigger time step is defined in the scenario set.’
New section added, 3.1.3 Jumps, starting on page 26.
Also, removed the tables in Chapter 2 Sign-Offs, on page 21,
since this information is already captured in both the weekly
project status reports and the instrument build matrix. In its
place, there is a description of where the weekly project status
reports are stored.
2.17

Julian Maynard-Smith,
Technical Author

Added new versions of American and European Exercise Vanilla
Options.
The sections come from Equity Option Instrument
Specification_v6, and include descriptions on physically settled
options and a delay for cash-settled American options.

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Version

Updated by

Change Description

2.18

Julian Maynard-Smith,
Technical Author

Added new section for the benefit of HSBC staff: 3.4 QuiC
Financial Engineers per Instrument / Model, on page 29.
Added new versions of American and European Exercise Vanilla
Options. The sections come from Equity Option Instrument
Specification_v7, the changes for which are as follows:
“Cleaned up definition of forward equity prices for dividend
calculations. Changed value of physically settled options on
exposure dates within the settlement lag to be the value of the
forward contract, strike being exchanged for the equity on the
settlement date.” (Allan Cowan, QuiC financial engineer)

2.19

Julian Maynard-Smith,
Technical Author

Added new versions of American and European Exercise Vanilla
Options, from Equity Option Instrument Specification_v7:
contain major modifications to the formulation of physically
settled options.
Fixed some formatting bugs in the document.

2.20

Julian Maynard-Smith,
Technical Author

Replaced the existing section 5.2 Model Simulation Data
Requirements, starting on page 147, with ‘Equity Risk
Simulation Model Data Requirements’ as written by David
Orford, Technical Author.

2.21

Julian Maynard-Smith,
Technical Author

Added new versions of American and European Exercise Vanilla
Options, from Equity Option Instrument Specification_v9. The
new sections contain new dividend and physical settlement
descriptions.

2.22

Julian Maynard-Smith,
Technical Author

CMS/CMT section: removed a number of redundant sections.

Julian Maynard-Smith,
Technical Author

New sections for American/European-exercise equity options:
updates to describe how the settlement lag will be specified (as
clarified in an email from John Ballaram).

2.23

Changes related to equity options:
Removed references to baskets for equity options, as they have
been removed from the project scope. Note that baskets for
equity swaps and total-return swaps are still in scope.
Added new versions of equity option sections (from Equity
Option Specification_v10): daycount and compounding
attributes added to the definition of the dividend yield curve.
Added further changes to the American/Equity Option sections,
affect equations 2.8 and 2.9 and the surrounding text and
equations 3.7 and 3.8 and the surrounding text.

Source document: Equity Option Instrument Specification_v12,
written by Allan Cowan.
2.24

Julian Maynard-Smith

New Equity Swap section, taken from v4 of the Equity Swap
specification, written by Allan Cowan, who describes the
changes as follows:
Updated description of forward price calculation to be consistent
with equity derivative spec. Introduced dividend ratio
parameter to unify description of total return and price return
swaps - this resulted in significant changes to the document
format. Split IR leg into a separate Fixed and Floating leg map
in the input file.

2.25

Kirstie Wilson

New Total Return Swap section, from TRS Instrument
Specification (V1.4), written by Jeff Hawkins.

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Updated by

Change Description

2.26

Kirstie Wilson

New Equity Option section from v13 of the Equity Option
Instrument Specification by Allan Cowan to include:
A description of the performance option and how we will value
it, and relevant changes to the instrument inputs.
Further details about the user settings available to set
preferences in the FD solver.

2.27

Jay Rao

Updated TRS specifications from Jeff Hawkins. This document
defines the pricing methodology in details as per the latest
discussions between Jeff and Dong –

Bonds are valued using a risky discount factor which is
based on swap yield curve, CDS spreads and a basis
adjustment (this needs further definition)

Data inputs

Minor notational changes

2.28

Jeff Hawkins

Minor changes to TRS specifications in line with discussions with
Horst

2.29

Jay Rao

Equity Swaps
Changes to sections – Baskets, Quanto
Additions to Table 33: EQSwap instrument: EQLeg information map – Field
apFXInfo
Table 31: EQSwap instrument: IRFixedLeg information map –
field pFXInfo
Equity Options – Performance Options

Performance option section has the notation changes
as suggested in an email.
Minor changes to reflect the comments from Thomas
in the attached email – adding a nominal amount that
is separate from the number of shares input.

Added a FX curve, this will be needed so that all option
prices in a portfolio are converted to a common
currency for reporting PFE

2.36

Allan Cowan

Equity Swaps
Updating with v8 of the equity swap spec: Fixed a few
typos, and clarified that apFXUnderlying will be a FX rate from
equity currency to USD.
TRS
Updated pricing methodology and data inputs to make a clearer
distinction of bond currency, TR currency, and reporting
currency.
Updated description of the credit spread curve market data
type in the TRS section

Jeff Hawkins

2.37

Jeff Hawkins

TRS
Updated data inputs and to allow for a different funding leg
currency and funding riskless discount factors.
Updated exchange rates so they all convert to the reporting
currency.

2.38

Jeff Hawkins

TRS
Updated some the bond return so that the previous bond price
is converted at what was the FX spot rate at the time.
Updated the MTM of Lockout coupons to be discounted by
riskless discount factor.

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Version

Updated by

Change Description

2.39

Bernadette McGovern,
Technical Author

Inflation Swaps
Added Inflation Swaps section from Inflation Swap Specification
V1 originated by Curtis Sam. The input and testing
requirements for Inflation zero coupon and year on year swap
are specified here.
General
Edited this HSBC Instrument Specifications document from
general formatting, typos and consistency perspective – and
specifically:



Spelling errors.
Wrong numbering of tables ie the captions have been
typed manually therefore the numbering was not
updated.

Inconsistency as regards use of Initial Capital in
headings.

References are to page numbers and sections - which,
shouldn't be done because if anything shifts, it creates
an issue. Replacing them with hyperlinked references
to the section number and name.

Incorrect use of styles resulting in 'Error' messages
and not the actual content in a table.

"<>" left in several places, instead of it being replaced
with actual text.

References to documents but not the actual location of
them or how to get them.

Inconsistent use of styles for "Example" – and
sometimes numbered – also the example name not
put in full, so too vague.

Some sections badly numbered and manually typed –
this affected the numbering in the whole document.

The automatic fields for the version number were
overwritten manually.

Tables not formatted consistently or the paragraph
spacing.
Additional editing to be done to correct more of these items.
2.40

Section 3.2.2 Inflation added to 3 Project Scope.
Section 3.3 Financial Instruments of 3 Project Scope – removed
the third and fourth rows in the inflation section ie the hybrid
and inflation-linked bonds are not in scope. Changed "JY
Model" to "Arbitrage free".
Awaiting responses on some reference queries see “<hold…>”,
which will be put in next draft.

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2.41

Bernadette McGovern,
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Inflation Swaps
4.4.2 Payoff Definitions of 4 Instrument Specifications edited to
add paragraph regarding leverage factor and spread.
4.4.6.4.1 Example – Inflation Leg Observable Map Input – third
line of amended.
4.4.7.2 Nominal Yield Curve – changes to variable attributes.
4.4.7.4 Real Yield Curve – changes to variable attributes.
Example changed.
4.4.7.5 Historical Inflation Index Curve – change to title of
Figure.
4.4.7.6 Spot Inflation Index Curve – change to format and
additional description of curve, updated to Figure to reflect this.
4.4.7.7 Inflation Seasonality Curve – change to curve format
and sample in the Figure.
4.4.8 Logging Intermediate Results – new section added.
Equity Options
4.2.1 Description – paragraphs added “Early exercise of a
scenario… used in the equation (2.5).”
4.2.1.1 Cash Settled Options – equations renumbered through
to the end of entire Equity Options section. Text changes in the
last two paragraphs.
4.2.1.2 Physically Settled Options – equation change made.
Last paragraph removed.
4.2.7 Definition of Daycounts – new section added.
The word ‘Exercise’ has been removed from each instrument
name.
Total Return Swap
New section added – 4.5.4 Bond Spread Calibration. 4.5.5 Bond
Valuation updated.
Figures in Figure 13: Bond Spread Calibration and Figure 14:
Accrued Interest Example replaced.
CMS/CMT
New section added – 4.1 Cross Instrument Inputs
Map Inputs: MultiLeg.
General Updates
All equations numbered and referenced where necessary. Table
of contents put in for Equations, Figures and Tables. General
editing as regards formatting. Some obsolete references to
Appendices removed.

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Updated by

Change Description

2.42

Bernadette McGovern,
Technical Author

Inflation Swaps
4.4.3 Pricing Methodology edited to add paragraph regarding
ST_MONTH and OATI prior to Equation 37 – Inflation Swaps,
where the equation has also been changed. Equation 38 –
Inflation Swaps – the equation has been changed, line
regarding PFE calculation added in the subsequent paragraph.
4.4.5 Potential Future Exposure Calculations edited to add
paragraph regarding CPI reference month.
4.4.6.3 Map Inputs: CouponInflationFixed entire section edited.
4.4.7.6 Spot Inflation Index Curve – line added about ‘historical
index fixing’ added.
Equity Swaps
4.7.9 Instrument Format – first paragraph edited to reword
sentence about LIBOR.
4.7.10 Transaction File Inputs, Table 42: Instrument 1:
Transaction File Inputs – constraints column content edited and
the subsequent sample transaction line.
4.7.11 Auxiliary Transaction Data File Inputs – several general
edits eg input names and formats throughout the section and in
the following sections –
4.7.11.1 CouponLiborEquityIRLeg Data Structure, 4.7.11.2
CouponFixedEquityIRLeg Data Structure, 4.7.11.3
mpObservable Structure of CouponLiborEquityIRLeg Map,
4.7.11.9 Dividend Yield Curve – the word 'continuous' removed
from 'ContinuousDividendYield' curve.
CMS/CMT
4.6.2 Transaction File Inputs – Example Entry changed, Table
31: Generic Instrument: Transaction File Inputs – Constraint
updated for Field 2.
4.6.3.2 Floating Leg Map Inputs: CouponLibor and CouponCMS
– title changed from '.. CouponFloat'. Table 32: CouponLibor
and CouponCMS Map Definition – Map Key and Type Code
changed for Daycount convention, constraint changed for
mpObservable, arPastFixing changed from arPastReset and
constraint changed. 4.6.3.2.1 Examples Map Key references
changed.
4.6.3.3 Map Inputs: CouponFixed, Table 33: CouponFixed Map
Definition – strDaycount put in and 4.6.3.3.1 Examples
updated.
4.6.3.4 Cap/Floor Map Inputs: CouponLiborCapFloor and
CouponCMSCapFloor – title changed from '…CouponCap Floor'.
Table 35: CouponLiobrCapFloor and CouponCMSCapFloor Map
Definition – strDaycount put in, mpObservable constraint
changed, arPastFixing put in, bUseMoneyness added. 4.6.3.4.1
Examples – Map Key names updated and bUseMoneyness
added. Table 37: ObservableLibor Map Definition –
'pHistoricalRate put in and last row pVol updated.
4.6.4.1 Map Inputs: ObservableSwapRate, Table 36:
ObservableSwapRate Map Definition – last 2 rows updated,
4.6.4.1.1 Example: 5 Year, Semi-Annual Swap Rates –
updated.
4.6.4.2 Map Inputs: ObservableLibor – title changed and Table
37: ObservableLibor Map Definition. 4.6.4.2.1 Examples – Map
Key name updated.
4.5.4.3 Map Inputs: ObservableBond – section removed. 4.6.5
Market Data Curves – whole new section added.

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Bernadette McGovern,
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Total Return Swap
4.5.11 Transaction File Inputs, Table 24: Generic Instrument:
Transaction File Inputs – changed instrument name from 'TRSB'
to 'LegFrameGeneric' because it uses the LegFrameGeneric
input structure. Field No. 3 updated. Figure 16: Example of
Generic Transaction Input for TRSB – all updated.
4.5.11.2 Map Inputs: CouponBondTotalReturnSpot – updated.
Table 25: CouponBondTotalReturnSpot Map Definition –
stryType is changed from 'TRBondLeg' to
'CouponBondTotalReturnSpot' to be more specific - this is just a
user input, not a data item, Map key changed from
mpBondObservable to mpObservable - this is a user input, not
a data item. Map key changed from 'pFXBondInfo' to
'pExchangeBond'. This is a user input, not a data item. Figure
17: Example of TRLegInfo Map Inputs – updated.
4.5.11.3 Map Inputs: ObservableBond – updated. Table 26:
ObservableBond Map Definition – the method for describing
bond coupon dates has been changed from supplying adjusted
dates (adtStart, adtEnd) to supplying dtSettle, dtMaturity,
dtFirstPayment, strPayFreq. This is an additional map that
allows for reuse of schedules. Figure 18: Example of
BondObservable Map Inputs – all updated.
4.5.11.4 Map Inputs: mpRateSchedule – updated. The standard
bond input calls for a single fixed rate, single notinoal amount
and single leverage. If these inputs vary by coupon then a rate
schedule map must be used.
4.5.11.5 Map Inputs: CouponTRPremSpot – updated. Table 28:
CouponTRPremSpot Map Definition – name change from
‘TRFundingLeg’ to ‘CouponTRPremSpot’. Daycount required for
calculating accrued interest. Figure 20: Example of
CouponTRPremSpot Map Inputs – all updated.
Error! Reference source not found. Error! Reference
source not found. – a map describing the lockout features has
been added (the previous method had these inputs in the
funding leg description).
4.5.11.6 Map Inputs: LiborObservable – updated. Table 29:
LiborObservable Map Definition – first row updated, the strType
value changed from 'ObservableLibor' to 'LiborObservable'.
Figure 21: Examples of LIBOR Map Inputs – all updated.

2.44

Equity Swaps
4.7.2 Valuing the Equity Leg – sentence added "We allow for a
lag…".
4.7.9 Instrument Format – sentence edited "For an equity
leg..".
4.7.11.4 CouponTotalReturnEquity Data Structure, Table 46:
EQSwap Instrument: CouponTotalReturnEquity Information
Map – Map Key 'adtEnd' description edited, Map key
'adtpayment' added. 4.7.11.4.1 Example – 'adtPayment…' row
added.
More detail added to reasons for updates in 2.43 updates to
TRS.

2.45

Inflation Swaps
4.4.6 Transaction File Inputs, 4.4.6.2 Map Inputs:
CouponInflation, Table 18: Inflation Instrument: Leg
Information Map – May Key 'strDaycount' and Type Code 'S'
added.
4.1 Cross Instrument Inputs, 4.1.1 Map Inputs: MultiLegTable
5: MultiLeg Map Definiton – Map Key 'strType' and Type Code
'S', Map Key 'ampLegs' and Type Code 'AL' added, table moved
to common area within Instrument section.

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Bernadette McGovern,
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CMS/CMT
4.6.3.2 Floating Leg Map Inputs: CouponLibor and CouponCMS,
Table 32: CouponLibor and CouponCMS Map Definition – Title
changd, Constraint for 'strType' changed to 'CouponLibor or
CouponCMS'.
4.6.3.4 Cap/Floor Map Inputs: CouponLiborCapFloor and
CouponCMSCapFloor,
Table 35: CouponLiobrCapFloor and CouponCMSCapFloor Map
Definition – Title changed, Constraint for 'strType' changed to
'CouponLiobrCapFloor or CouponCMSCapFloor', Constraint for
'mpObservable' changed to 'CouponLiobrCapFloor or
CouponCMSCapFloor, Constraint for 'arPastFixing' changed to
'Optional – if omitted, uses the underlying’s pHistoricalRate'.

2.47

TRS
4.5 Total Return Swap (TRS) - Entire section replaced.

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2

SIGN-OFFS

Before QuIC Script development on a specific simulation model or instrument can
start, both HSBC and QuIC must sign off the specification.
The latest sign-off status per simulation model and instrument is available in the
latest HSBC Project Status Report, available in the following locations:


For HSBC personnel, the Lotus Notes team room entitled ‘Credit Risk new
Products Programme’



For QuIC personnel, the QuIC portal at: http://tinyurl.com/2m54vs.

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3

PROJECT SCOPE
3.1

PFE Simulation

The key risk factors to be simulated are equity prices and five-year par credit
spreads1. Risk factors specific to FX rates, interest rates, and inflation trades will
be provided via external scenarios.
3.1.1

Equity Risk Simulation

Both equity prices and five-year par spreads will be simulated as follows:
Equation 1 – Equity Risk Simulation



 F 2 
  n  n n t j  t j 1 

2




S in t j   S in t j 1 At j exp 
  Bt j 


 F 
 nxyz z i (t j 1 , t j ) xyz   Fn  ni (t j ) t j  t j 1 
 n  xyz {Market
Driver Indices}




Here ‘n’ indexes the risk factor (be it an equity price or a par spread), ‘i’ indexes
the scenario, and ‘j’ indexes the time step. This model extends the existing HSBC
credit spread model in the following respects:


There is a risk factor-specific drift rate n



There is a new term

 nequity index z i (t j 1 , t j ) equity index

arising from contributions

from an equity index


The idiosyncratic shocks n may be correlated.

The existing HSBC credit-spread model handles three market driver indices:
region, sector and rating. In principle, the current model will support an
additional equity index. Please note that users can change the number of market
driver indices. The idiosyncratic shocks n are correlated

N (0,  n2 ) -distributed

random variables independent of the market drivers. The parameters A, B, and Fn
are used for stress testing.

1

The benchmark spread is a five-year par spread. This is to be consistent with HSBC’s existing QuIC
implementation for CDS/CDX PFE calculations.

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HSBC will explicitly specify pairwise correlations for an arbitrary (but typically
small) subset of idiosyncratic shock pairs. For all pairs where a correlation is
unspecified, a correlation of zero will be assumed. Consequently, the correlation
matrix of the idiosyncratic components will have a block structure, where risk
factors that have been assigned nonzero correlations are put in one block with
correlation matrix C, and all other risk factors are put in another block with a
correlation matrix equal to the identity. To generate idiosyncratic shocks, PCA will
be applied to C to obtain a square-root representation C
terms will then be simulated via the equation

   (1) 

 U
    

 0
  (N ) 

 UU T . The idiosyncratic

   (1) 

0 
  
I 

  ( N ) 

where  is a permutation taking the correlated components into the first block.
The ns are uncorrelated

N (0,  n2 ) random variables.

The market-driver indices in Equation 1 – Equity Risk will be provided to QuIC in
the form of external scenarios having the same format as the existing creditspread model. HSBC will specify all model parameters as inputs. QuIC will
generate idiosyncratic shocks and use Equation 1 – Equity Risk to create
scenarios for equity prices and credit spreads.

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Table 2: PFE and Stress Testing – Definitions Data Requirements
Notation

Definition

Data Requirements
PFE

Stress Testing

Risk factor n at time tj under scenario i.

Initial values will be passed in from Calypso for
credit spreads and from Sophis for equity spot
prices.

Initial values will be passed in from Calypso for
credit spreads and from Sophis for equity spot
prices.

Time-varying parameter used for applying relative
stress changes. Unless explicitly specified, this
parameter has a default value of 1.

Will not be passed in, and should take on its
default value of 1 at all time steps.

May be passed in by Scenario Modulator, but
should otherwise take on its default value of 1 at
all time steps.

Btj

Time-varying parameter used for applying absolute
stress changes. Unless explicitly specified, this
parameter has a default value of 0.

May be passed in by Scenario Modulator, but
should otherwise take on its default value of 0 at
all time steps

May be passed in by Scenario Modulator, but
should otherwise take on its default value of 0 at
all time steps.

 n , n

Annualised volatility, annualised drift rate.

May be passed in by Scenario Modulator, but
should otherwise be obtained from data file output
from the regression tool.

May be passed in by Scenario Modulator, but
should otherwise be obtained from data file output
from the regression tool.

Fn

Volatility scaling factor obtained through a backtesting algorithm.

Will be provided to QuIC as a data file output from
the regression tool.

Will be provided to QuIC as a data file output from
the regression tool.

tj

Trigger time step.

Defined in the scenario set.

Defined in the scenario set.

 nxyz

Beta (or regression coefficient) of risk factor n,
relative to market index xyz. Typically obtained
through standard multi-factor regression analysis.

Will be provided to QuIC as a data file output from
the regression tool.

Will be provided to QuIC as a data file output from
the regression tool.



Si t j
n

 

Atj

 

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Notation

Definition

Data Requirements
PFE

z i (t j 1 , t j ) xyz

Log-return scenario for a market index between tj-1
and tj, for scenario path i. ASE provide scenario
data in the form
computes

 ni (t j )

i

i

z (0, t j )

z (t j 1 , t j )

xyz

xyz

from which QuIC

.

Idiosyncratic random return, drawn from a normal
distribution with zero mean and standard deviation

n.

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Stress Testing

Will be passed in by Scenario Modulator in the
form z

i

(0, t j ) xyz . Must be converted to

Will be passed in by Scenario Modulator in the
form z

i

(0, t j ) xyz . Must be converted to

z i (t j 1 , t j ) xyz by subtracting

z i (t j 1 , t j ) xyz by subtracting

z i (0, t j 1 ) xyz from z i (0, t j ) xyz .

z i (0, t j 1 ) xyz from z i (0, t j ) xyz .

Must be drawn by QuIC for each issuer (ie not per
contract or per trade) and output to a file under
each scenario and time step for each issuer.

Must be drawn by QuIC for each issuer (ie not per
contract or per trade) and output to a file under
each scenario and time step for each issuer.

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3.1.2

Credit Spread Simulation

Like the existing credit spread simulation model used for HSBC’s CDS/CDX
portfolio, the initial term structure of credit spreads will be bootstrapped from the
initial par spread curve. Simulated future simulated credit spread term structures
will be based on this initial term structure and the simulated five-year par spread.
Thus, on any PFE simulation date, the full term structure of credit spreads (the
‘spread curve’) can be recovered. For pricing simple instruments like CDSs or
CDXs, the stochastic nature of credit spreads is irrelevant in that we can price
these instruments ‘off the spread curve’ at any time step in any PFE simulation.
To calculate a CDS price, we need not know anything about the volatility of the
credit spread eg we only need to know the simulated spread curve.
3.1.3

Jumps

Equity spot prices and credit spreads exhibit jump returns, which can have a
material impact on PFE. Such jumps will not be in scope for the initial release of
the simulation model. Where required, the simulation will be adjusted for the
effects of jumps through the volatility-scaling factors Fn .
3.1.4

Default

Another aspect of the PFE simulation process is the simulation of default by
individual equities. This requires that we make a link between credit spreads and
default probabilities – we must ensure that default is more probable when credit
spreads are high.
Note: The simulation of defaults is not part of the initial release.
3.1.5

Basket

As equity swaps of a basket are in scope they will be simulated by individually
simulating each stock in the basket and summing to find the return of the basket.
Dividends yields will be provided for each name in the basket to be used as with
the equity options.
3.2
3.2.1

Pricing Models
Equity

Equity derivatives will be priced using the Black-Scholes model. Given a simulated
equity price at any time step of a given PFE scenario, a Black-Scholes volatility
will be looked up from an input volatility surface, indexed by time-to-maturity and
option moneyness. The option will then be priced based on this volatility. For the
sake of consistency with front-office methodology, credit spreads will not be

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accounted for in equity option pricing.2 For the same reason, a combination of
dividend types will be supported. A time-indexed array of explicit dividends up to
a certain date, followed by a continuous dividend yield, will be supported. Explicit
dividends may either be expressed in absolute (eg dollar amount) terms, or in
relative (eg proportion of stock price) terms.
3.2.2

Inflation

Zero coupon inflation swap and year-on-year inflation swap are supported.
Features such as arbitrary index lag and payment frequency are allowed, as well
as leverage factor and spread. They are priced with the nominal and real yield
curves with the consideration of the seasonality adjustment's term structure of
the inflation index. The convexity adjustment due to the payment lag is assumed
to be small and therefore neglected. For PFE calculations, the inflation index is
not treated as a primary risk factor, but is driven by the nominal and real yield
curves and is taken to assume the expected forward index value, viewing from
the last PFE date.
3.3

Financial Instruments

Financial instruments within the scope of WS1 are:
Table 3: Instrument Modelling Approach

2

No.

Instrument
Type

Exists
(Y/N/
Proto)

Instrument
Features

Pricing
Model

Solver

QuIC
Name

1

Vanilla
Equity
Derivatives

Yes

Call / Put
(American)

BlackScholes

Finite
Difference

EQ:
Option
Vanilla
American

Comments

For equity options subject to default risk, this approach is somewhat more controversial since
textbook pricing methods only allow us to “price off the curve” if the curve is deterministic.
However, the model calibration and computation involved in a fully rigorous treatment of stochastic
credit spreads is highly complex; and the exposure contribution of an equity option is far more
sensitive to the underlying equity price than it is to the credit spread. Therefore we choose to make
the following modeling compromise: when calculating the exposure of equity options, the option
pricer will assume that the simulated equity spread at any given time step, in any given PFE
scenario, is deterministic for the remainder of the option’s lifetime, despite the fact that at the next
PFE time step the entire spread curve will be subject to a stochastic shock. An alternative two-factor
methodology, in which spreads are driven by a CIR square-root default intensity process, is also
conceivable. However, the attendant model calibration challenges are substantial since they require
a parameter-freezing technique (cf. Piterbarg (2005), Risk Magazine) and the numerical inversion of
two complex characteristic functions (cf. Bakshi et al (1997), Journal of Finance). Moreover, it is not
clear how to capture reasonable volatility surface behaviour with this type of model without
introducing a third stochastic volatility state variable (Bakshi et al (1997)). The attendant model
dimensionality issues rule out this approach for large-scale PFE calculations.

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No.

2

3

4

Instrument
Type

Inflation
Swap (with
leverage
and lag)
Inflation
Swap

Instrument
Features

Pricing
Model

Solver

QuIC
Name

Yes

Call / Put
(European)

BlackScholes

Analytic

EQ:
Option
Vanilla
European

No

Zero
Coupon

Arbitrage
Free

Analytic

No

Year-onYear

Arbitrage
Free

Analytic

TRS

Proto

Single Name

Arbitrage
Free

Analytic

TRS

Proto

Basket

Arbitrage
Free

Analytic

Yes

Vanilla
Swap

Linear
Swap
Rate

Analytic

No

Caps/Floors

Linear
Swap
Rate

Analytic
approximation

No

Digitals

Linear
Swap
Rate

Analytic
approximation

No

Swaptions

Linear
Swap
Rate

Analytic
approximation

Yes

Vanilla
Swap

Linear
Swap
Rate

Analytic

No

Caps/Floors

Linear
Swap
Rate

Analytic
approximation

No

Digitals

Linear
Swap
Rate

Analytic
approximation

No

Swaptions

Linear
Swap
Rate

Analytic
approximation

No

PRS
(dividend
not
included)

Arbitrage
Free

Analytic

CMS (inarrears and
in-advance)

CMT (inarrears and
in-advance)

5

Exists
(Y/N/
Proto)

Non-callable
Equity
(Index)
Swap

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Comments

CMS

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No.

6

Instrument
Type

Repo

3.4

Exists
(Y/N/
Proto)

Instrument
Features

Pricing
Model

Solver

No

TRS
(dividend
included)

Arbitrage
Free

Analytic

No

PS (either
leg could be
PRS or TRS
or both)

Arbitrage
Free

Analytic

No

Govt
Underlying

Arbitrage
Free

Analytic

No

Corporate
Underlying

Arbitrage
Free

Analytic

No

Equity
Underlying

Arbitrage
Free

Analytic

QuIC
Name

Comments

QuiC Financial Engineers per Instrument / Model

The following table (Table 4: QuIC Financial Engineers – Instrument Assignments)
shows which QuIC financial engineer is assigned to which instrument or
simulation model. The QuIC FE is responsible both for developing the software
and for writing the specification (see relevant section in Chapter 4 Instrument
Specifications.
Note:

See CRISP New Products Testing Strategy V0.3 (located in the
HSBC Credit Risk New Products Programme Lotus Notes work
space and QFT Instrument Testing.
Table 4: QuIC Financial Engineers – Instrument Assignments

Instrument /Model

QuIC Financial Engineer

Simulation model

Rodrigo Rivas-Cortes

Vanilla Equity Derivatives

Allan Cowan

Inflation Swap

Curtis Sam
(Youngsuk Lee)

TRS and Repo

Jeff Hawkins
(Youngsuk Lee)

CMS and CMT

Jeremy Watson
(Paul Jones)

Non-callable Equity (Index) Swap

Allan Cowan

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4

INSTRUMENT SPECIFICATIONS
4.1

4.1.1

Cross Instrument Inputs
Map Inputs: MultiLeg

A MultiLeg aggregates a number of legs, for example a CMS payment and a Cap
on the payment.
Table 5: MultiLeg Map Definiton
Map key

Type
code

Description

Default

Constraints

strType

S

Object type

None

MultiLeg

ampLegs

AL

List of the legs to be
aggregated

Blank

Legs must exist as
maps

4.2

American Exercise Vanilla Equity Option
Table 6: Instrument 1: Model and Solver

Instrument

EQOptionAmerican

Type

Equity

Model

Black Scholes

Solution Method

Finite Difference

4.2.1

Description

The American exercise vanilla equity option will be priced with the Black-Scholes
model using a finite-difference solver. For convenience we will work with forward
equity prices
Equation 2 – Equity Options
T
S (t ) exp    (u )du 
 t

F (t ; T ) 
,
DF (t , T )

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where (t) is the equity dividend yield at time t and DF(t, T) is the time t discount
factor corresponding to the deal maturity date T.3 Relative to the time T forward
measure, we have the dynamics
Equation 3 – Equity Options

dF (t ; T )
  (t )dW (t )
F (t; T )
where W is a standard Brownian motion, and (t) is the volatility of the equity
S (t ) .
In this case the valuation PDE for an equity option takes the form
Equation 4 – Equity Options

1
Vt   2 (t ) F 2VFF  0,
2
where V(t, F) denotes the option price divided by the discount factor DF(t, T). The
terminal condition at maturity of the option is given by
Equation 5 – Equity Options

V (T , F (T ; T ))  max ( S (T )  K ),0
V (T , F (T ; T ))  max ( K  S (T )),0
for the call and put option respectively. Note that
strike price

F (T ; T ) = S (T ) . The constant

K is a user defined input.

To allow for pricing to be done with a unique volatility for each scenario of each
time step in the PFE simulation, the volatility will be considered an independent
parameter in the PDE solution. From the simulated scenarios the maximum and
minimum volatility required for all risk-factor scenarios and exposure dates will be
determined, and from this we create an auxiliary axis that represents the
volatility value. The effect is that we will solve the PDE for a range of volatilities in
parallel, producing a state space indexed by time, forward stock price and
volatility: V (t , F ,  ) .
The state space is generated as follows. Starting from the known payoff at the
expiration date (terminal condition), we step the PDE solver back to the valuation
date. For American calls, exercise need only take place on dividend dates, while

3

Working with forward prices means that interest-rate and dividend-yield parameters make no explicit
appearance in the valuation PDE. This allows us to “cheat” in the sense that we can account for the
stochastic nature of interest rates by embedding them in the forward price instead of introducing
yet another state variable to the pricing state space. The dividend yield can be determined as
described in the HSBC document entitled "Fast CRISP Equity Options Pricing Version 1.1”, 28
February 2007.

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American puts must account for the possibility of early exercise at each
intermediate step. For simplicity in implementation, calls will be treated in the
same way as puts with exercise being account for on each intermediate time step
of the PDE solution.

At the exercise dates (dividend dates, or each time step), the continuation value
is compared to the exercise value and used as the terminal value at the next
backwards step.

Repeating this backwards recursion to the valuation date produces both the
option price as of the valuation date and a state space of option prices as a
function of forward equity price and volatility between times t and T.
The American style early exercise condition implemented at each time step of the
FD solution takes the form
Equation 6 – Equity Options

 ( S (t )  K )

V (t , F (t ; T ),  )  max 
,V (t , F (t ; T ),  )
 DF (t , T )

 ( K  S (t ))

V (t , F (t ; T ),  )  max 
, V (t , F (t ; T ),  )
 DF (t , T )

for the call and put respectively.
The presence of the discount-factor term in this boundary condition forces a
modelling approximation. In general we would have to reconfigure and re-solve

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the free boundary problem every time a new PFE simulation is generated, as
DF (t , T ) is unique for each scenario. This is not practical. Instead, we
approximate by replacing the discount factor by the forward value as of the PFE
simulation start date.
Once the state space has been generated, all PFE exposure dates are looped over
to determine the value of the option for each scenario on each date. On the PFE
exposure date t scenario i is found to have the simulated equity price S i (t ) . For
this scenario we calculate the moneyness as

K / S i (t ) and time-to-maturity as

T  t and interpolate into the user provided volatility matrix to find the volatility,

 i , for this particular PFE date and scenario. We then calculate the forward price
Fi (t; T ) from the simulated price S i (t ) , with dividends accounted for as described
below. The value of the option on this PFE date and for this scenario, Value (t , i) , is
determined by interpolating into the state space at
multiplying by the discount factor between

i

and Fi (t ; T ) , and

t and T :

Equation 7 – Equity Options

Value (t , i)  bNV (t , Fi , i ) DF (t , T )
where N is the number of shares and b is +1 if the option was bought and -1 if
sold. If this particular path was determined to be exercised at an earlier date the
price is instead set to zero. Early exercise of a scenario is determined by checking
whether the exercise value is greater than or equal to the continuation value
Equation 8 – Equity Options

wSi (t )  K   V (t , Fi , i )
This exercise condition is checked every business day for puts in order to ensure
the PFE profile accurately captures the actual date the exercise occurs. If less
frequent monitoring is desired then that can be set with the parameter
strSamplingFreq in the oSolverPrefs_ input. We allow for both discrete and
continuous dividend schedules (as we will see in 4.2.1.3 Dividends). For call
options, in the regime of continuous dividends the exercise condition will be
checked daily as is done for the puts. However, in the regime of discrete
dividends the exercise condition will be checked only on the dividend payment
dates because theoretically those are the only dates that the exercise will occur.
It should be noted that daily checking in this regime could result in some
scenarios being incorrectly exercised due the under estimation of the option value
resulting from the approximation to the discount factor used in Equation 6 –
Equity Options.
The aforesaid discussion and equations in this section have assumed that the
option settles on the same day that the exercise decision is made. We will not
restrict ourselves to this settlement procedure and allow for a user specified lag
between the exercise date and settlement date. The type of settlement can have

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an impact on the exposure when a lag exists. We allow for cash settled and
physically settled options.
4.2.1.1

Cash Settled Options

A cash-settled option has the value of the option paid (received) at some date
after the exercise date. The settlement date corresponding to the final exercise
date will be provided, from this QuIC will calculate the settlement lag and this will
be used to determine the settlement date t s for each early exercise date t . The
provided holiday list and business day convention will be used to calculate the lag
and the variable settlement dates. If no final settlement date is given then there
is an nSettlementLag input that can be used to directly specify the settlement lag.
The settlement lag for cash settled options is captured in the payoff by modifying
the state space reset condition that is executed on each exercise date. Equation 6
– Equity Options becomes
Equation 9 – Equity Options

 ( S (t )  K ) DF (t , t s )

V (t , F (t ; T ),  )  max 
,V (t , F (t ; T ),  )
DF (t , T )


 ( K  S (t )) DF (t , t s )

V (t , F (t ; T ),  )  max 
,V (t , F (t ; T ),  )
DF (t , T )


where

DF (t , t s ) is the discount factor between t and t s which accounts for the

delay in payment. As with the discount factor term in the denominator we
approximate DF (t , t s ) as the forward value as calculated from the yield curve on
the simulation start date. Note that the terminal condition (Equation 5 – Equity
Options) is modified in an analogous fashion. The effect of the lag is captured in
the state space, so the value of the trade on exposure date t for scenario i is still
given by Value (t , i)  bNV (t , Fi , i ) DF (t , T ) .

However, if an option gets exercised it still has a non-zero trade value up to the
settlement date Ts . If the option expires then the trade value is zero. The value of
an exercised scenario for exposure dates between the exercise date and the
settlement date, T  t  Ts , is given by
Equation 10 – Equity Options

Value (t , i)  bNwSi (T )  K DF (t , Ts )
where

Si (T ) is the simulated equity price on the option exercise date, Ts is the
settlement date associated with exercise date T , and w is +1 for a call option
and -1 for a put option.

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Since the exercise reset condition (Equation 9 – Equity Options) contains the
discount factor for settlement the early exercise condition must be changed
accordingly when a settlement lag exists. With a settlement lag equation
(Equation 8 – Equity Options) becomes

wSi (t )  K   V (t , Fi ,  i ) / DF (t , Ts )
4.2.1.2

Physically Settled Options

For consistency with the front office, physically settled options are priced exactly
the same as cash-settled options except that during the settlement lag the
reported value contributing to the exposure is still subject to fluctuations in the
stock price. Hence, for exposure dates falling part way between exercise and
settlement, T  t  Ts , the value is a function of the simulated equity price on the
exposure date S i (t ) , rather than the price on the exercise date Si (T ) . Thus for
physically settled options equation (Equation 10 – Equity Options) becomes
Equation 11 – Equity Options

Value (t , i)  bNwSi (t )  K DF (t , Ts )
For exposure dates less than the exercise date t  T the state space reset
condition is again given by Equation 9 – Equity Options due to the fact that we
treat the pricing of physically and cash-settled options the same in this time
regime.
4.2.1.3

Dividends

We now consider how dividends are handled within this formulation and give
details of how the forward equity prices are calculated.
The dividend payments can be provided in two formats, either as a schedule of
discrete payments or as a continuous dividend yield. A switching date, Td , will be
provided – for dates earlier than this date we will use the discrete dividend
schedule, while for dates after the switching date we will use the dividend yield
curve to calculate a forward dividend rate.
Due to the choice of working with forward equity prices the dividends do not
enter into the solution of the PDE. However, dividends are accounted for when
calculating the forward equity price from the simulated equity prices.
On an ex-dividend date we have a jump condition for the forward price,
Equation 12 – Equity Options

F  t; t j   F t; t j   Q j F  t; t j ,

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where

F  t; t j  is the forward price prior to going ex-dividend on t j , F t; t j  is the

forward price after going ex-dividend and
a fraction of the forward price F



Q j is the dividend amount specified as

t; t . Alternatively, we can write
j

Equation 13 – Equity Options

F t; t j   1  Q j F  t; t j .
For dates t

 Td  T , equation (Equation 2 – Equity Options) becomes
Equation 14 – Equity Options


 DF T , T 
F t ;T   S (t )  1  Q j  q d
,
 t  t T
 DF t , T 
 j d

where each discrete dividend with ex-dividend date

t  t j  Td results in a factor

1  Q  and the continuous dividend yield is captured through a forward discount
j

factor, DFq Td , T  , calculated from the dividend yield curve.

T  Td only discrete dividends apply and the forward price is obtained by
setting Td  T in equation (Equation 14 – Equity Options), or
If

Equation 15 – Equity Options



1
F t; T   S (t )  1  Q j 
.
 t t T
 DF t , T 
j


Note:

If

T falls on an ex-dividend date T  t j then the factor 1  Q j  is

included since we are interested in the forward price after going
ex-dividend.

t  Td only continuous dividends apply and the forward price is obtained by
setting Td  t in equation (Equation 14 – Equity Options), or
If

Equation 16 – Equity Options

F t; T   S (t )

DFq t , T 
DF t , T 

.

If the discrete dividend schedule is provided in terms of absolute dividend
amounts D j these will be converted to relative dividends Q j at the start of

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simulation. Specifically, if the simulation start date is

T0 then the dividends

Q j are determined iteratively through
Equation 17 – Equity Options

Qj 

Dj

F T0 ; t j 


,



1
F  T0 ; t j   S (T0 )  1  Q k 
,
 T t t
 DF T0 , t j 
0 k j

where the

Qk have been determined already.

To apply the exercise condition for American options we need to invert (Equation
14 – Equity Options) to obtain the spot price in terms of the forward price,
Equation 18 – Equity Options



S (t )  F t; T   1  Q j 
 t t T

 j d

This is used to calculate the

1

DF t , T 
.
DFq Td , T 

S (t ) needed in Equation 6 – Equity Options.

The instrument will allow for the grid to be concentrated around the strike price.
User inputs in the oSolverPrefs_ field will be available to specify the degree of
concentration as well as the location of strike price with respect to the grid points.
4.2.2

Performance Options

The American exercise instrument will also allow for the valuation of performance
options. Performance options have the payoff

  S (t )
 
Nom * max  w
 Kˆ ,0 
 
  S Fix
where

S (t ) is the equity price on the exercise date and S Fix is the equity price on
a specified fixing date TFix , and Nom in the nominal amount in the currency of the
equity. Kˆ is the strike expressed as a decimal amount. Once S
is fixed the
Fix

valuation of this option follows exactly as described above but with

K  Kˆ * S Fix

and the number of shares is scaled by Nom / S Fix . The value of the option is

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Value (t , i)  bN

Nom
V (t , Fi ,  i ) DF (t , T )
S Fix

The early exercise condition, cash and physical settlement value are the same as
given in equation (Equation 8 – Equity Options), (Equation 9 – Equity Options)

K  Kˆ * S Fix and
N  N * Nom / S Fix . If the simulation start date T0 is after TFix then S Fix will be

and (Equation 10 – Equity Options) respectively, but with

provided as an input to the trade. If the simulation start date is before the fixing
date TFix then S Fix will be approximated as the forward price as of the simulation
start date,

S Fix  F (T0 ; TFix ) . This approximated value for S Fix will be used

throughout the calculation, both for the PDE solution and pricing on each PFE date
(same value for all scenarios).
To value a performance option the input bPerformanceOption_ must be set to
TRUE. When bPerformanceOption_ is TRUE a nominal amount must be given,
rStrike must be given as a decimal amount, and dtContractStart_ will be used as
the fixing date. If the simulation starts after dtContractStart_ a historical curve
must be given or the strike and nominal must be appropriately scaled by the fixed
equity price.
4.2.3

Finite Difference Solution Preferences

The instrument will allow for various preferences to be set for the FD solution.
The number of grid points of the equity forward price and volatility axes can be
set. A Crank-Nicholson or Krylov solver can be chosen as well as a maximum time
step for the PDE solver. The grid can be concentrated around the strike price and
the volatility corresponding to the time to maturity and moneyness prevailing on
the simulation start date. Parameters indicating the degree of concentration can
be set by the user. The user can also set a frequency at which exercise is checked
during the PFE loop.
4.2.4

Transaction File Inputs

This section defines the inputs for the American exercise equity option
instrument, which is named EQOptionAmerican. All inputs must be provided and
must conform to any specification listed in the constraints column.
Table 7: Instrument 1: Transaction File Inputs
Field
No.

Input Field (Internal
Name)

Description

Type

1

strId_

Transaction ID.

String

2

strInstrument_

Instrument name.

String

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Constraints

EQOptionAmerican

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Field
No.

Input Field (Internal
Name)

Description

Type

3

strCounterparty_

String identifying
the counterparty
to which the
transaction
belongs.

String

4

strNettingGroupID_

String identifying
any netting group
to which the
transaction
belongs.

String

5

dtContractStart_

Option contract
start date.

Date

6

dtContractEnd_

Option expiry date.

Date

> dtContractStart_

7

strSettlementType_

Type of settlement
for the option.

String

CASH or PHYSICAL

8

dtSettlement_

Date on which
option is settled.
QuIC will calculate
a lag from this
date and
dtContractEnd_,
and use this lag to
calculate
dtSettlement_ for
early exercise
date.

Date

9

nSettlementLag_

Number of days
after exercise that
settlement occurs.
If cash settled, this
is date payoff is
paid, if physically
settled this is date
equity is held to.
Only used if
dtSettlement_ is
void.

Integer

≥ 0.0

10

strBoughtOrSold_

Position type.

Enum

BOUGHT, SOLD

11

strOptionType_

Option type.

Enum

CALL, PUT

12

rShares_

Number of shares.

Float

≥ 0.0

13

rStrike_

Option strike price
(in units of the
equity currency).

Float

≥ 0.0 (in units of the
equity currency)

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Constraints

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Field
No.

Input Field (Internal
Name)

Description

Type

Constraints

14

pYieldInfo_

Reference to a
yield curve
structure for the
equity currency.

String

Curve name must
exist in the market
data HDF5 file

15

pEquityInfo_

Reference to an
equity curve
structure.

String

Curve name must
exist in the market
data HDF5 file

16

pImpliedVol_

Reference to an
equity implied
volatility matrix,
matrix indexed by
time-to-maturity
and option
moneyness.

String

Curve name must
exist in the market
data HDF5 file

17

pDiscreteDividend_

Reference to a
discrete dividend
schedule
containing
dividend dates and
amounts paid per
share.

String

Curve name must
exist in the market
data HDF5 file

18

pDividendYield_

Reference to a
forward dividend
yield curve.

String

Curve name must
exist in the market
data HDF5 file

19

dtSwitchDividendType_

Date on which we
stop using
pDiscreteDividend_
and start using
pDividendYield_.

Date

20

strBusDayConv_

Business date
convention, used
to calculate
settlement date.

Enum

AFTER, BEFORE,
MODFOLLOWING

21

pg1dtHolidays_

Reference to a
holiday schedule,
used to calculate
settlement date.

String

Schedule name must
exist in the holidays
HDF5 file

22

bPerformanceOption_

Indicates if this
trade is a
performance
option.

Boolean

TRUE, FALSE

23

rNominal_

Nominal amount
used for
performance
option.

Real

This can be left blank
if
bPerformanceOption_
is FALSE

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Field
No.

Input Field (Internal
Name)

Description

Type

Constraints

24

pHistoricalEquity_

Reference to a
historical equity
curve in the
market date file,
this curve provides
the equity price on
the fixing date
(dtContractStart_).

String

Curve name must
exist in market data
HDF5 file. This input
can be left blank if
not needed. If this is
left blank when
bPerformanceOption_
is true then it is
assumed that both
rNominal and
rStrike_ have been
properly scaled by
the fixed equity
price.

25

pFXInfo_

Reference to a FX
curve used to
convert equity
currency (currency
of payoff) into the
reporting currency.

String

Curve name must
exist in the market
data HDF5 file.

26

oSolverPrefs_

Reference to a
solver preference
structure.

String

Solver ID specified in
valuation module

A sample transaction line is shown next:
Trade649,EQOptionAmerican,CPY1,GRP1,2007/05/05,2008/05/05,CASH,2008/0
5/10,5,SOLD,CALL,100,10,USD.Yield.USD,Nikkei.EquityIndex.USD,Nikkei.E
quityVolMtx.USD,Nikkei.DiscreteRelativeDividend.USD,Nikkei.Continuous
DividendYield.USD,2008/01/01,MODFOLLOWING,USD,FALSE,,,EUR.Exchange.EU
R,mpSolverPrefs
4.2.5

Auxiliary Transaction Data File Inputs
Table 8: EQOptionAmericanExerice Instrument: oSolverPrefs_ information Map

Map Key

Type
Code

Description

Constraints

anFactorGridPoints

AN

Array of number of grid
points for the forward
equity price, and
volatility.

Array of two
elements, first is the
number of grid points
for forward equity
price – second is for
volatility. Defaults is
100,50

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Map Key

Type
Code

Description

Constraints

strSamplingFreq

S

Frequency of sampling
during PFE loop to
determine if American
exercise takes place.
Default is DAILY. IF NONE
is chosen, then sampling
is on PE/EPE dates only.

NONE, DAILY,
WEEKLY, MONTHLY,
QUARTERLY,
SEMIANNUAL,
ANNUAL

rMaxTimeStep

R

Maximum time step of FD
solver.

>0.0
Defaults to 5[dy] if
blank

strSolver

S

String indicating the FD
solver type.

_xfnModExpKyrlov or
_xfnModExpCN
Defaults to
_xfnModExpKrylov if
blank

nStdDevs

N

Number of standard
deviations to use when
calculating axis
boundaries.

Defaults to 3 if blank

bUseGridConc

B

Boolean to indicate if grid
concentration should be
used.

TRUE, FALSE, Default
is TRUE

rStrikeAlpha

R

Grid concentration
parameter for
concentration around
strike price.

Default is 0.13

rVolAlpha

R

Grid concentration
parameter for
concentration around vol
as of simulation start
date.

Default is 0.4

bPlotStateSpace

B

Boolean to indicate if
state space should be
plotted, can be useful for
testing but should be
FALSE for production
runs.

TRUE, FALSE, Default
is FALSE

4.2.5.1.1

Example

An example of this solver preference map is shown next. This map will be located
in the Schedules.txt file.
mpSolverMap,{
anFactorGridPoints,AN,100

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nVolGridPoints,N,50
strSamplingFrequency,S,WEEKLY
rMaxTimeStep,R,5
strSolver,S,_xfnModExpKrylov
nStdDev,N,3
aaPts,AR,void
aaAlpha,AR,0.1
aaOnGrid,AR,FALSE
}

4.2.6

Market Data Curves

This section introduces QuIC market data curves in general, and then describes
the following types of market data curves needed to price this instrument:






Yield curve
Equity index
Equity implied volatility matrix
Discrete dividend schedule
Dividend yield curve

A complete example is provided for each of these curve types.
4.2.6.1

General Information

Transaction inputs refer to curves in a QuIC market data file with names that are
a combination of three fields in the curve data structure, in the following format:
curve-ID.curve-type.currency-ID
For example, the sample transaction in Section 4.2.2 Performance Options
specifies the equity index curve as Nikkei.EquityIndex.USD. This means that the
curve identifier is Nikkei, the curve type is EquityIndex, and the currency
identifier is USD. The curve ID is an arbitrary user-specified name, the curve type
is a predefined name determined by the QuIC curve definitions, and the currency
identifier is the standard 3-character code.
Each curve data structure includes at least these fields plus the observation date
and the data values. In addition, most curve types include certain variable
attributes and the ordinate values of the axis or axes.
Initially, you enter market data curves in text files in comma-separated value
(CSV) format. Then you use a QuIC Script program (provided with the QuIC
Analytics package) to convert these files to a single HDF5 database file.
4.2.6.2

Yield

The pYieldInfo_ transaction input (USD.Yield.USD in the sample transaction)
refers to a curve of type Yield in a market data HDF5 file.
The general format for a Yield curve in a CSV file is as follows:

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Yield, curve-ID, observation-date, currency-ID, interpolationtype, extrapolation-type, day-count-convention, compoundingfrequency, maturity-1, ..., maturity-n, yield-1, ..., yield-n
The sample yield curve includes the following variable attributes (and lets the rest
take on their default values):



Day count convention: ACT360
Compounding frequency: annual.

Table 9: Sample Yield Data shows the sample data that the curve includes.
Table 9: Sample Yield Data
Days to Maturity

Yield

30

0.0309

60

0.0315902

91

0.032243

182

0.0340263

273

0.0354036

365

0.036532

730

0.039369

1096

0.04095

1460

0.0421268

1825

0.0431881

2555

0.0451795

3650

0.0480538

5475

0.0488034

7300

0.0503278

10950

0.0510875

Figure 1: Sample Yield Curve (CSV Format) shows how the sample curve is coded
in a CSV file. In the file, the curve occupies a single line, but in this figure it
wraps to show the whole line.
Figure 1: Sample Yield Curve (CSV Format)
Yield,USD,2005/05/05,USD,,,ACT360,ANNUAL,30,60,91,182,273,365,730,1096,1460,
1825,2555,3650,5475,7300,10950,0.0309,0.0315902,0.032243,0.0340263,
0.0354036,0.036532,0.039369,0.04095,0.0421268,0.0431881,0.0451795,0.0480538,
0.0488034,0.0503278,0.0510875

4.2.6.3

Equity Index

The pEquityInfo_ transaction input (Nikkei.EquityIndex.USD in the sample
transaction) refers to a curve of type EquityIndex in a market data HDF5 file.

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The general format for an EquityIndex curve in a CSV file is as follows:
EquityIndex, curve-ID, observation-date, currency-ID, index-value
Figure 2: Sample EquityIndex Curve (CSV Format) shows an example of the
equity curve as it appears in a CSV file.
Figure 2: Sample EquityIndex Curve (CSV Format)
EquityIndex,Nikkei,2005/03/09,USD,11073.77

4.2.6.4

Equity Implied Volatility

The pImpliedVol_ transaction input (Nikkei.EquityImpliedVolMtx.USD in the
sample transaction) refers to a curve of type EquityImpliedVolMtx in a market
data HDF5 file.
The general format for an EquityImpliedVolMtx curve in a CSV file is as follows:
EquityImpliedVolMtx, curve-ID, observation-date, currency-ID,
moneyness-interpolation-type, moneyness-extrapolation-type,
expiry-interpolation-type, expiry-extrapolation-type, day-countconvention, days-per-annum, moneyness-1, volatility-1,...,
volatility-n
...
EquityImpliedVolMtx, curve-ID, observation-date, currency-ID,
moneyness-interpolation-type, moneyness-extrapolation-type,
expiry-interpolation-type, expiry-extrapolation-type, day-countconvention, days-per-annum, moneyness-m, volatility-1,...,
volatility-n
The curve is specified by multiple lines, one for each row of the matrix. The
moneyness axis in this matrix is defined as K/S(t=0), where S(t=0) is the spot
equity price on the simulation start date, and K is the strike price.
The sample volatility matrix curve specifies the following variable attributes:


Moneyness interpolation method: linear



Moneyness extrapolation method: nearest



Expiry interpolation method: linear



Expiry extrapolation method: nearest



Day count convention: ACT360



Days per annum: 360.

Table 10: Sample Equity Implied Volatility Data shows the sample data that the
curve includes (for simplicity, only a subset of a typical matrix is included in this
example).

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Table 10: Sample Equity Implied Volatility Data
Maturity (months)
Moneyness

1

2

3

6

9

12

18

0.9

0.219123

0.202728

0.19436

0.183323

0.179931

0.176813

0.176943

0.95

0.181194

0.172552

0.168963

0.164444

0.1643

0.163275

0.166247

0.975

0.162097

0.157358

0.156172

0.15494

0.156427

0.156516

0.16087

1.0

0.143746

0.142771

0.143874

0.145719

0.148816

0.150071

0.155677

1.025

0.127188

0.129412

0.132495

0.137071

0.141624

0.14395

0.150716

1.05

0.112311

0.117199

0.121977

0.12896

0.134825

0.138135

0.145974

1.075

0.1

0.10606

0.112264

0.121354

0.128397

0.132607

0.141439

Figure 3: Sample EquityImpliedVolMtx Curve (CSV Format) shows how this curve
is coded in a CSV file. In this figure, each line wraps to show the whole line.
Figure 3: Sample EquityImpliedVolMtx Curve (CSV Format)
EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,0.9,1,
2,3,6,9,12,18,0.219123,0.202728,0.19436,0.183323,0.179931,0.176813,0.176943
EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,0.95,1,
2,3,6,9,12,18,0.181194,0.172552,0.168963,0.164444,0.1643,0.163275,0.166247
EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,0.975,
1,2,3,6,9,12,18,0.162097,0.157358,0.156172,0.15494,0.156427,0.156516,0.16087
EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1,1,2,
3,6,9,12,18,0.143746,0.142771,0.143874,0.145719,0.148816,0.150071,0.155677
EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1.025,
1,2,3,6,9,12,18,0.127188,0.129412,0.132495,0.137071,0.141624,0.14395,
0.150716
EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1.05,1,
2,3,6,9,12,18,0.112311,0.117199,0.121977,0.12896,0.134825,0.138135,0.145974
EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1.075,
1,2,3,6,9,12,18,0.1,0.10606,0.112264,0.121354,0.128397,0.132607,0.141439

4.2.6.5

Discrete Dividend Schedule

The pDiscreteDividend_ transaction input
(Nikkei.DiscreteAbsoluteDividend.USD in the sample transaction) refers to a
curve of type DiscreteAbsoluteDividend in a market data HDF5 file.
The general format for a DiscreteAbsoluteDividend curve in a CSV file is:
DiscreteAbsoluteDividend, curve-ID, observation-date, currency-ID,
interpolation-type, extrapolation-type, date-1, ..., date-n,
dividend-1, ..., dividend-n

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The sample dividend schedule curve does not specify any variable attributes (it
lets them take their defaults). Table 11: Sample Dividend Schedule Data shows
the sample data the curve includes.
Table 11: Sample Dividend Schedule Data
Date

Absolute Dividend Amount

2005/05/26

20

2005/06/27

20

2005/07/26

20

2005/08/26

20

2005/09/27

20

2005/11/25

20

2005/12/27

20

2006/01/26

20

2006/02/15

20

2006/02/23

20

2006/03/28

20

2006/05/26

20

2006/06/27

20

2006/07/26

20

2006/08/28

20

2006/09/26

20

2006/11/27

20

2006/12/26

20

2007/01/26

20

2007/02/15

20

2007/02/23

20

Figure 4: Sample DiscreteAbsoluteDividend Curve (CSV Format) shows how this
curve is coded in a CSV file. In the file, the curve occupies a single line, but in
this figure it wraps to show the whole line.
Figure 4: Sample DiscreteAbsoluteDividend Curve (CSV Format)
DiscreteAbsoluteDividend,Nikkei,2005/03/09,USD,,,2005/05/26,2005/06/27,
2005/07/26,2005/08/26,2005/09/27,2005/11/25,2005/12/27,2006/01/26,
2006/02/15,2006/02/23,2006/03/28,2006/05/26,2006/06/27,2006/07/26,
2006/08/28,2006/09/26,2006/11/27,2006/12/26,2007/01/26,2007/02/15,
2007/02/23,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,
20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0

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When the discrete dividend schedule is provided as an absolute amount (as
shown in the example), it will be converted to a relative amount with respect to
forward prices calculated on the simulation start date, as shown in Equation 16 –
Equity Options.
The discrete dividend schedule can also be provided directly as a relative amount.
The curve has the same format as above, however the name is now
DiscreteRelativeDividend. These amounts will be directly used as the relative
dividend amounts on each date.
4.2.6.6

Dividend Yield Curve

The pDividendYield_ transaction input (Nikkei.USD in the sample transaction)
refers to a curve of type DividendYield in a market data HDF5 file.
The general format for a DividendYield curve in a CSV file is as follows:
DividendYield, curve-ID, observation-date, currency-ID,
interpolation-type, extrapolation-type, day-count-convention,
compounding-frequency, date-1, ..., date-n, yield-1, ..., yield-n
The sample dividend yield curve specifies the following variable attribute (and lets
the others take on their default values):



Day count convention: ACT365
Compounding frequency: continuous

Table 12: Sample Dividend Yield Data shows the sample data that the curve
includes.
Table 12: Sample Dividend Yield Data
Date

Dividend Yield

2005/06/05

0.02

2005/07/05

0.021

2005/08/05

0.022243

2005/11/05

0.0240263

2006/02/05

0.0254036

2006/05/05

0.026532

2007/05/05

0.029369

2008/05/05

0.03095

2009/05/05

0.0321268

2010/05/05

0.0331881

2011/05/05

0.0351795

2012/05/05

0.0380538

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Date

Dividend Yield

2013/05/05

0.0388034

2014/05/05

0.0403278

2015/05/05

0.0410875

Figure 5: Sample DividendYield Curve (CSV Format) shows how this curve is
coded in a CSV file. In the file, the curve occupies a single line, but in this figure
it wraps to show the whole line.
Figure 5: Sample DividendYield Curve (CSV Format)
DividendYield,Nikkei,2005/05/05,USD,,,ACT365,CONTINUOUS,2005/06/05,2005/07/0
5,2005/08/05,2005/11/05,2006/02/05,2006/05/05,2007/05/05,2008/05/05,2009/05/
05,2010/05/05,2011/05/05,2012/05/05,2013/05/05,2014/05/05,2015/05/05,0.02,0.
021,0.022243,0.0240263,0.0254036,0.026532,0.029369,0.03095,0.0321268,0.03318
81,0.0351795,0.0380538,0.0388034,0.0403278,0.0410875

4.2.7

Definition of Daycounts

The following table defines the daycounts that can be used with the above curves.
Table 13: Day count Convention Codes
Value

Meaning

ACTACT

Uses the actual number of days in the month
and year.

ACT365

Same as ACTACT.

ACT365FIXED

Uses the actual number of days in the month
and year, but days in a leap year count as
1/365th of a year.

ACT360

Interest is calculated over the actual number of
calendar days, on the basis of a 360-day year.

THIRTY360

Assumes there are 30 days in a month and 360
days in a year.

EURO30360

Essentially the same as 30360 but used for
Eurobonds and many foreign bonds.
The one distinction is that whenever the start or
end date is the 31st of the month, it is reset to
the 30th. The 30360 version only resets the end
date when the start date is on the 30th or 31st.

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