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The Credit Risk of Complex Derivatives

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The Credit Risk of Complex Derivatives THE CREDIT RISK OF COMPLEX DERIVATIVES The Credit Risk of Complex Derivatives Third Edition ERIK BANKS © Erik Banks 2004 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1T 4LP. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The author has asserted his right to be identified as the author of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2004 by PALGRAVE MACMILLAN Houndmills, Basingstoke, Hampshire RG21 6XS and 175 Fifth Avenue, New York, N.Y.10010 Companies and representatives throughout the world PALGRAVE MACMILLAN is the global academic imprint of the Palgrave Macmillan division of St. Martin’s Press, LLC and of Palgrave Macmillan Ltd. Macmillan® is a registered trademark in the United States, United Kingdom and other countries. Palgrave is a registered trademark in the European Union and other countries. ISBN 978-1-349-51299-7 ISBN 978-1-4039-4609-6 (eBook) DOI 10.1057/9781403946096 This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. A catalogue record for this book is available from the British Library. A catalog record for this book is available from the Library of Congress. Editing and origination by Curran Publishing Services, Norwich 10987654321 13 12 11 10 09 08 07 06 05 04 To my wife, Milena Contents List of Figures x List of Tables xiv Preface xvi PART I DERIVATIVES, CREDIT, AND RISK MANAGEMENT 1 An Overview of the Derivatives Marketplace 3 Derivatives Market Scope 4 Market Volatility and the Growth of Derivatives 10 General Derivative Risk and Return Considerations 15 Addressing Derivative Risk Management Issues 19 Overview of the Text 25 2 Derivative Losses 27 Sources of Derivative Losses 27 A Sampling of Derivative Losses 30 3 Risk Governance and Risk Management 42 Corporate and Risk Governance 42 Credit Risk Management Processes 43 4 Regulatory and Industry Initiatives 54 Regulatory Efforts 54 Industry Efforts 68 vii viii CONTENTS Part II THE CREDIT RISK OF COMPLEX DERIVATIVES 5 Classification and Quantification of Credit Risk 81 Background 81 Market Risk 82 Risk Equivalency 86 Risk Factors 88 The Risk Equivalency Framework 98 Refining Risk Equivalent Exposure 101 Simulation: An Alternative Methodology 105 6 Quantifying Option Credit Risk 108 An Overview of Option Credit Risk 109 7 The Credit Risk of Compound Option Strategies 121 Product Description 122 Credit Risk Quantification 138 8 The Credit Risk of Complex Options 160 Product Description 164 Credit Risk Quantification 202 9 Quantifying Swap Credit Risk 241 Actual Exposure of Swap Contracts 242 Fractional Exposure of Swap Contracts 246 Swap Credit Risk in a Complete Framework 248 A Model for Calculating Swap Credit Risk 250 Empirical Findings on Swap Risk Factors 256 10 The Credit Risk of Complex Swaps 260 Product Description 261 Credit Risk Quantification 288 Part III CREDIT PORTFOLIO RISK MANAGEMENT ISSUES 11 Credit Risk Management of Derivative Portfolios: Quantitative Issues 321 Consolidating Individual Credit Exposures into Portfolios 322 Portfolios of Counterparties 341 Quantifying Credit Losses 342 12 Credit Risk Portfolio Models 367 Value-at-Risk and Regulatory Models 367 CONTENTS ix The Ideal Generic Credit Portfolio Model 369 An Overview of Specific Credit Risk Portfolio Models 376 13 Credit Risk Management of Derivative Portfolios: Qualitative Issues 385 Managing Derivative Credit Exposures Dynamically 385 Addressing Ancillary Credit Risk Management Issues 412 Appendix 1: Option Valuation 420 Appendix 2: Twenty Questions for the Derivatives Desk 428 Appendix 3: ISDA 2002 Master Agreement 430 Notes 467 Glossary 494 Bibliography 541 Index 549 List of Figures 1.1 General classification of derivatives 6 1.2 General classification of swaps 8 1.3 General classification of options 8 1.4 Derivative asset classes 9 1.5 Eurodollars (US$ Libor), 15-year average volatility (%), 1988–2002 11 1.6 30-Year US Treasury bond, 15-year average volatility, 1988–2002 12 1.7 S&P500 index, 15-year average volatility, 1988–2002 12 1.8 Crude oil (light sweet crude), 15-year average volatility, 1988–2002 12 1.9 Gold, 15-year average volatility, 1988–2002 13 1.10 US$/Japanese yen, 15-year average volatility, 1988–2002 13 1.11 US$/Pound Sterling, 15-year average volatility, 1988–2002 13 1.12 Notional outstandings, OTC derivative contracts, 1987–2002 14 1.13 Gross replacement cost, OTC derivative contracts, 1998–2002 15 1.14 Risk-adjusted returns 17 1.15 Common credit risk mitigation techniques 23 3.1 Board level credit risk management duties 44 3.2 Corporate risk management duties 45 3.3 Sources of credit risk in a financial institution 46 3.4 Credit risk governance process 53 4.1 Forms of regulatory and economic capital 57 4.2 BIS IRB approaches 65 x FIGURES xi 5.1 Normal distribution 89 5.2 Lognormal distribution 89 5.3 Path of the risk factor at 10% volatility, 97.5% confidence level 98 5.4 Path of the risk factor at 10% volatility, varying confidence levels (90–99%) 98 5.5 Path of the risk factor at 97.5% confidence level, varying volatilities (10–30%) 99 5.6 The risk equivalency process 100 5.7 Alternative risk exposure paths 104 5.8 Sample asset price paths 107 7.1 Long call payoff profile 123 7.2 Long put payoff profile 123 7.3 Short call payoff profile 124 7.4 Short put payoff profile 124 7.5 Bullish vertical call spread payoff profile 126 7.6 Bearish vertical put spread payoff profile 127 7.7 Long straddle payoff profile 128 7.8 Short straddle payoff profile 129 7.9 Long strangle payoff profile 130 7.10 Short strangle payoff profile 130 7.11 Long butterfly payoff profile 131 7.12 Short butterfly payoff profile 132 7.13 Long condor payoff profile 133 7.14 Short condor payoff profile 133 7.15 Call backspread payoff profile 135 7.16 Call ratio vertical spread payoff profile 136 7.17 Synthetic long payoff profile 139 7.18 Synthetic short payoff profile 139 7.19 Bullish vertical call spread with a single counterparty 143 7.20 Bullish vertical call spread with multiple counterparties 144 8.1 Up and out call option 167 8.2 Down and in put option 167 8.3 Average price put option 168 8.4 Average strike put option 170 8.5 Floating strike lookback call option 171 8.6 Put option on the minimum 172 8.7 High–low option 173 8.8 Partial lookback call option 175 8.9 Ladder call option 176 8.10 Cliquet put option 177 xii FIGURES 8.11 Shout put option 179 8.12 Installment call option 180 8.13 Cash-or-nothing at hit put option 182 8.14 Option on the best of two assets and cash 183 8.15 Put option on the worst of two assets 185 8.16 Multiple strike call option 187 8.17 Spread call option 188 8.18 Basket call option 191 8.19 Compound call option 193 8.20 Regular chooser option 194 8.21 Contingent premium call option 195 8.22 Deferred payment American call option 196 8.23 Quanto option on put structure 197 8.24 Exploding call option 199 8.25 Squared power call option 200 9.1 The simulation approach to credit risk valuation 249 9.2 Swap replacement cost curve 256 10.1 Inverse floater swap 264 10.2 Pay/receive flows of leveraged swaps 265 10.3 Leveraged swap 266 10.4 Leveraged inverse floater swap 266 10.5 Differential swap 267 10.6 Creation of a US$ Libor/Euribor differential swap 268 10.7 Amortizing swap 269 10.8 Mortgage swap 271 10.9 Index principal swap 272 10.10 Reverse index principal swap 273 10.11 Credit forward 275 10.12 Default swap 276 10.13 Total return swap 279 10.14 Equity call swap 280 10.15 Equity call–put swap 281 10.16 Realized volatility swap 283 10.17 Zero coupon inflation swap 285 10.18 Peak electricity swap 286 10.19 Cooling degree day swap 288 10.20 Decomposing a leveraged inverse floater swap 292 11.1 Credit transaction decision process 325 11.2 Maximum peak and forward point exposures 336 11.3 Forward point exposures 1 337 FIGURES xiii 11.4 Forward point exposures 2 338 11.5 Derivation of possible credit losses 342 11.6 REE probability distribution 345 11.7 Default rate probability distribution 350 11.8 Recovery rate probability distribution 352 11.9 Creation of a credit loss distribution function 353 11.10 Expected credit losses 354 11.11 Worst-case credit losses 357 11.12 Expected, unexpected, and worst-case credit losses 360 11.13 Generalized credit process 366 12.1 PDF of future asset value and probability of default 373 12.2 Inputs and outputs of the generic credit risk portfolio model 375 13.1 Systematic and idiosyncratic credit risks 388 13.2 Credit forward to create credit capacity 399 13.3 Dynamic credit exposure management 413 List of Tables 1.1 Countries amending legislation to accept netting 23 4.1 BIS CEM factors, 1988 (percentages) 59 4.2 BIS OEM factors, 1988 (percentages) 60 4.3 BIS CEM factors, 1994–5 (percentages 60 4.4 Best practice self-regulation 72 5.1 PMR and AMR over trade life 85 5.2 Counterparty risk, market risk, and losses 86 5.3 Probabilities and z factors 94 5.4 Confidence levels and z factors 95 5.5 Sample table of Nikkei risk factors: constant 10% volatility, varying confidence levels 97 5.6 Sample table of Nikkei risk factors: constant 97.5% confidence
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