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 Scope 4 Market and the Growth of Derivatives 10 General 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 Credit Risk 108 An Overview of Option Credit Risk 109

7 The Credit Risk of 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 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 payoff profile 128 7.8 Short straddle payoff profile 129 7.9 Long payoff profile 130 7.10 Short strangle payoff profile 130 7.11 Long 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 payoff profile 135 7.16 Call ratio 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 167 8.2 Down and in 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 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 10.13 279 10.14 Equity call swap 280 10.15 Equity call–put swap 281 10.16 Realized 283 10.17 Zero coupon 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 levels, varying volatilities 97 5.7 Alternative REE computations 104

6.1 Ongoing credit risk of a put option 114

7.1 Option risk sensitivities: simple position directional strategies 125 7.2 Option risk sensitivities: compound position directional strategies 127 7.3 Option risk sensitivities: compound position volatility strategies 136 7.4 Synthetic options 138 7.5 Synthetic underlyings 138

8.1 Complex option variations 162 8.2 Barrier options 165

xiv TABLES xv

8.3 Binary– combinations 182 8.4 Yield curve scenarios 188

9.1 Calculated up/down rate movements (percentages) 252 9.2 Calculated rate movements (percentages) 254 9.3 Discounted replacement costs 254 9.4 Calculated and discounted replacement costs 255 9.5 Sample risk factor for interest rate swaps (%) (fixed payer) 257 9.6 Federal Reserve/Bank of England 257 9.7 Arak, Goodman, and Rones 257 9.8a Whittaker 258 9.8b Whittaker 258 9.9 Ferron and Handjinicolaou 258 9.10 Hull 259 9.11a Giberti, Mentini, and Scabellone 259 9.11b Giberti, Mentini, and Scabellone 259

10.1 Complex swap variations 262 10.2 Amortization schedule 294 10.3 Average life results (millions) 295

11.1 Company ABC credit portfolio 323 11.2 Incremental summation approach: sample portfolio 1 327 11.3 Incremental summation approach: sample portfolio 2 328 11.4 Incremental summation approach: sample portfolio 3 330 11.5 Incremental summation approach: sample portfolio 4 330 11.6 Incremental summation approach: sample portfolio 5 331 11.7 Incremental summation approach: sample portfolio 6 332 11.8 Incremental summation approach: sample portfolio 7 333 11.9 Sample portfolio 1 with correlations 334 11.10 Sample portfolio 2 with correlations 334 11.11 Standard and Poor’s cumulative average default rates 346 11.12 Moody’s cumulative average default rates 347 11.13 Moody’s one-year default rates, 1992–2002 348 11.14 Standard and Poor’s one-year transition matrices 349 11.15 Moody’s one-year transition matrices 349 11.16 Default recovery statistics, 1982–2002 351

12.1 Summary of credit portfolio risk models 381

13.1 Derivatives collateral 389 Preface

Since the publication of the second edition of The Credit Risk of Complex Derivatives in 1997 the world of derivatives has again gone through a period of very dramatic change – in the external operating environment, underlying products and markets, and risk management techniques. Changes in the external operating environment have been dramatic.

ᔢ The global corporate credit environment has deteriorated; after a decade of de-leveraging and re-equitization, a new cycle of leverage (some fuelled by the technology, media, and telecom boom), coupled with an economic slowdown, has brought corporate defaults back to levels not seen since 1991–2.

ᔢ Global stock markets have experienced tremendous bouts of volatility from the late 1990s into the new millennium.

ᔢ Financial and accounting scandals, some ending in bankruptcy, have shaken the corporate world and investor confidence (including Enron, Tyco, Global Crossing, Daewoo, Vivendi, Swissair, and Ahold, among others).

ᔢ The Japanese economy, the second largest in the world, has been crippled by asset deflation and a bad loan crisis for the past decade; Japanese banks and corporations, historically active participants in the derivatives market, have been forced to renegotiate their credit dealing terms to take account of their weakened financial condition.

ᔢ Monetary union has arrived in Europe, causing consolidation of the currency and interest rate markets and growth in pan-European equity and credit investment.

xvi PREFACE xvii

ᔢ Emerging market crises have appeared with frequency, impacting local and offshore credit and derivative counterparties (such as those in Mexico in 1994, Korea, Indonesia, Thailand, and Malaysia in 1997, Russia in 1998, Brazil in 1999 and 2002, Argentina in 2000, Venezuela in 2002 and 2003). Systemic credit problems, which spread and deep- ened throughout the 1990s, continue to plague the banking systems of some Asian countries (Indonesia and Thailand for instance).

ᔢ Hedge funds, always significant derivative players, have been through a boom and bust cycle of their own, culminating in the spectacular bailout of the Long Term Capital Management (LTCM) behemoth by a consortium of international banks in 1998.

The underlying derivative products and markets have changed in tandem, sometimes in response to macro events:

ᔢ Derivative product availability has increased steadily; new structures (such as volatility swaps, first-to-default swaps, and others) and new asset classes (such as non-catastrophic weather, bankruptcy, and inflation) are now part of the financial marketplace.

ᔢ Once-exotic and unique instruments, such as barrier options and credit default swaps, have become part of the mainstream of financial activity.

ᔢ Some of the “pioneering” derivative instruments of the early 1980s, such as vanilla interest rate swaps, have become so common and liquid that they are now traded on leading exchanges as listed futures contracts.

ᔢ Overall trading volumes and liquidity have expanded, bid-offer spreads have tightened, and transaction maturities have lengthened.

ᔢ New players have entered different segments of the market (insurance and reinsurance companies, for example, are increasingly active in credit and catastrophe derivatives, and electronic trading networks are delivering vanilla products) while established players are consolidating (for example, mergers of intermediaries, including some long-standing derivative pioneers, have commenced).

ᔢ Derivative-related losses, from market, credit, operational, and legal risks, have continued to mount, but have not yet created broad systemic problems. Special purpose vehicles, including those with embedded derivatives, have come under accounting and regulatory scrutiny. xviii PREFACE

To cope with these macro and industry changes, risk management techniques and rules are being redesigned:

ᔢ Credit and market risk exposures are drawing closer together and are increasingly being managed on an enterprise-wide basis.

ᔢ New credit analysis tools and portfolio credit risk models have been developed by industry leaders. Computing power and analytical sophistication have increased, allowing for more timely and accurate quantification and management of exposures.

ᔢ Portfolio management of credit exposures has taken greater hold; sensitivity to credit stress scenarios and correlated counterparty credit exposures is becoming standard operating procedure.

ᔢ Use of collateral, third-party clearing services, and other risk mitigation tools and vehicles has expanded.

ᔢ Derivative documentation standards have been strengthened and clari- fied, sometimes as a result of disputes and lawsuits; netting of derivatives has gained wider support around the world.

ᔢ New regulatory capital requirements for the credit risks of derivatives have been created, new disclosure rules have been enacted, and accounting treatments have been refined – all in hopes of creating more meaningful and equitable consideration of risk and capital.

ᔢ Sensitivity to risk issues – including disclosure and governance – is on the rise.

Clients, intermediaries, and regulators continue to focus on risk education, risk management, and risk disclosure in order to make participation in derivatives more secure, transparent, efficient, and beneficial. Given these changes, and a desire to continue conveying valuable information on the state of the derivative credit risk sector, the second edition of The Credit Risk of Complex Derivatives has been fully revised. The new edition has been substantially reorganized, updated, and expanded.

ᔢ Several new chapters have been added, including: – Chapter 2: Derivative Losses. This chapter provides an updated view on market, operational, legal, and credit-related derivative losses. – Chapter 3: Risk Governance and Risk Management. This chapter PREFACE xix

discusses important board-level and executive management governance requirements related to risk, credit risk, and derivatives. – Chapter 4: Regulatory and Industry Initiatives. This chapter outlines unfolding regulatory and industry efforts centered on credit risk, derivatives, capital, and “best practice” risk management. – Chapter 12: Credit Risk Portfolio Models. This chapter reviews advances in “next stage” portfolio credit risk management tools that have appeared in recent years – those applicable to credit sensitive instruments generally (for example, loans and bonds) and derivatives specifically.

ᔢ In addition, the new edition has been updated throughout to convey the latest product and control information. The book includes: – Definitions, explanations, and examples of new derivative structures that have appeared in the marketplace in recent years. – Discussion of documentation issues, including those that have arisen through formal legal proceedings; this has particular relevance for the market, which has been at the center of a host of documentary and definitional issues. – Review of alternate transaction and portfolio quantification tech- niques. As in the second edition, the new edition continues to focus on a volatility-based risk equivalency process as the primary quan- tification framework for discrete derivative transactions. However, alternative credit quantification techniques based on simulation and option statics, are discussed. – Analysis of portfolio risk management models and techniques and capital allocation processes. – An expanded and updated glossary.

I would like to express my sincere gratitude to Andrea Hartill at Palgrave Macmillan for her support and guidance on this project (as well as many others) over the past decade. Thanks are also due to the production and marketing teams at Palgrave Macmillan.

E.B. Redding, Connecticut July 2003 [email protected]