Contents. Preface. Introduction The Basics of Credit Derivatives 1. Chapter 1 The Market for Credit Derivatives 3

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1 Preface xii Introduction The Basics of Credit Derivatives 1 What is Credit Risk? 1 What are Credit Derivatives? 1 Why Credit Derivatives? 2 Chapter 1 The Market for Credit Derivatives 3 Credit Events That Have Led to the Birth of Credit Derivatives 3 Market Size and Products 6 Credit Derivatives Have Been Around in Different Forms 8 The QBI Contract 9 Creditex and CreditTrade 11 Trac-x and Iboxx 12 Summary of Chapter 1 12 References and Suggestions for Further Readings 13 Questions and Problems 13 Notes 14 Chapter 2 Credit Derivatives Products 15 Default Swaps 15 What is a default swap? 15 Why default swaps? 16 The terminology 17

2 viii Contents Features of default swaps 17 The default swap premium 17 The reference obligation 17 What constitutes default? 18 Cash versus physical settlement 19 Hedging with default swaps 20 Does a default swap hedge credit deterioration risk? 21 Does a default swap hedge against market risk? 23 Types of default swaps 23 Key benefits of default swaps 25 Total Rate of Return Swaps (TRORs) 25 What is a TROR? 26 Why TRORs? 26 Hedging with TRORs 27 The difference between a TROR and a default swap 27 The difference between a TROR and an asset swap 28 The difference between a TROR and an equity swap 29 The relationship between a TROR and a Repo 29 Key benefits of TRORs 31 Credit-spread Products 31 Credit-spread options 31 Hedging with credit-spread options 34 Credit-spread forwards 35 Credit-spread swaps 36 When to hedge and with what credit-spread product 38 Summary of Chapter 2 38 References and Suggestions for Further Readings 39 Questions and Problems 39 Notes 40 Chapter 3 Synthetic Structures 42 Credit-Linked Notes (CLNs) 42 A More Complex Credit-Linked Note Structure 44 Collateralized Debt Obligations (CDOs) 44 Synthetic CDOs 46 A two-currency, partly cash, partly synthetic CDO with embedded hedges 46 Motivation for CDOs 48 Market value CDOs and cash flow CDOs 48 Tranched Portfolio Default Swaps (TPDS) 49 Tranched Basket Default Swaps (TBDSs) 49 CDO Squared Structures 50 Rating 51 Recovery rates 53 Coverage ratios 54 Notching 55

3 Successful Synthetic Structures 55 Investing in Synthetic Structures A Good Idea? 57 Summary of Chapter 3 59 References and Suggestions for Further Readings 60 Questions and Problems 61 Notes 61 Chapter 4 Application of Credit Derivatives 62 Hedging 62 Market risk 63 Credit risk 65 How are market risk and credit risk related? 65 Operational risk 66 Which credit derivative hedges which risk? 67 Yield Enhancement 70 Cost Reduction and Convenience 75 Cost reduction 75 Convenience 78 Arbitrage 78 Regulatory Capital Relief 85 The Basel II Accord 86 Standardized versus IRB approach 87 Banking book versus trading book 88 Risk weights for positions hedged by credit derivatives in the banking book 88 Risk weights for positions hedged by credit derivatives in the trading book 90 The BIS minimum capital requirement for combined credit, market, and operational risk 91 Summary of Chapter 4 91 References and Suggestions for Further Readings 93 Questions and Problems 94 Notes 94 Chapter 5 The Pricing of Credit Derivatives 96 Credit Derivatives Pricing Approaches 97 Simple Approaches 97 The default swap premium derived from asset swaps 97 Deriving the default swap premium using arbitrage arguments 100 I price it where I can hedge it: Pricing default swaps using hedging arguments 100 Deriving the default probability and the upfront default swap premium on a binomial model 102 Basic properties of the Black-Scholes-Merton model 107 Valuing credit-spread options on a modified Black-Scholes equation where the credit-spread is modeled as a single variable 110 ix

4 x Contents Valuing credit-spread options on a modified Black-Scholes equation as an exchange option 112 Valuing credit-spread options on a term-structure based model 114 Structural Models 118 The original 1974 Merton Model 118 The Black-Cox 1976 model 122 The Kim, Ramaswamy, and Sundaresan 1993 model 123 The Longstaff-Schwartz 1995 model 124 The Briys-de Varenne 1997 model 125 Critical appraisal of first-time passage models 128 Reduced Form Models 128 The Jarrow-Turnbull 1995 model 128 Critical appraisal of the Jarrow-Turnbull 1995 model 138 The Jarrow-Lando-Turnbull 1997 model 138 Critical appraisal of the Jarrow-Lando-Turnbull 1997 model 146 Other Reduced Form Models 147 Duffie and Singleton (1999) 147 Das and Sundaram (2000) 149 Hull and White (2000) 151 Hull and White (2001) 152 Kettunen, Ksendzovsky and Meissner (2003) 156 The KKM model in combination with the Libor Market Model (LMM) 167 Pricing TRORs 171 Further research in valuing credit derivatives 171 Summary of Chapter References and Suggestions for Further Readings 172 Questions and Problems 174 Notes 175 Chapter 6 Risk Management with Credit Derivatives 178 The VAR Concept 178 Market VAR for a single linear asset 178 Market VAR for a portfolio of linear assets 182 Market VAR for non-linear assets 183 Market VAR for a portfolio of options 183 Credit at Risk (CAR) 185 Determining CAR of investment grade bonds 187 Accumulated expected credit loss 189 CAR for a portfolio of assets 189 Reducing portfolio CAR with credit derivatives 191 Reducing CAR with default swaps 191 Reducing CAR with TRORs 192 Reducing CAR with credit-spread options 193 The correlation of credit risk management with market risk management and operational risk management 193

5 Recent Advances in Credit Risk Management A Comparison of Five Models 194 Credit risk models structural versus reduced form 194 Key features of credit risk models 195 The Models in Detail 198 KMV s Portfolio Manager 198 JP Morgan s CreditMetrics 200 Kamakura s Risk Manager 201 CSFP s Credit Risk+ 202 McKinsey s Credit Portfolio View 203 Results 204 So what s the best model? 204 Summary of Chapter References and Suggestions for Further Readings 206 Questions and Problems 208 Notes 208 xi Appendix 211 Table A.1 The cumulative standard normal distribution 211 Table A.2 The cumulative lognormal distribution 213 Glossary of Notation 214 Glossary of Terms 217 Index 226