Introduction xi
PART I – CREDIT RISK MANAGEMENT
1 – Overview of Credit Risk 3
1.1 Components of Credit Risk 4
1.2 Factors Determining the Credit Risk of a Portfolio 5
1.3 Traditional Approaches to Managing Credit Risk 8
1.4 Market Risk versus Credit Risk 10
1.5 Historical Data 12
1.6 An Example of Default Loss Distribution 15
1.7 Credit Risk Models 21
1.8 Conclusion 29
2 – Exposure Measurement 31
2.1 Introduction 31
2.2 Exposure Simulation 33
2.3 Typical Exposures 36
2.4 Conclusion 44
3 – A Framework for Credit Risk Management 45
3.1 Credit Loss Distribution and Unexpected Loss 45
3.2 Generating the Loss Distribution 48
3.3 Example – One Period Model 62
3.4 Multiple Period Model 66
3.5 Loan Equivalents 69
3.6 Conclusion 71
Appendix A – Derivation of the Formulas for Loan
Equivalent Exposures 71
Appendix B – Example Simulation Algorithm 73
4 – Advanced Techniques for Credit Risk Management 75
4.1 Analytical Approximations to the Loss Distribution 75
4.2 Monte Carlo Acceleration Techniques 79
4.3 Extreme Value Theory 85
4.4 Marginal Risk 90
4.5 Portfolio Optimisation 99
4.6 Credit Spread Model 106
4.7 Conclusion 115
ContentsPART II – PRICING AND HEDGING OF CREDIT RISK
5 – Credit Derivatives 121
5.1 Introduction 121
5.2 Fundamental Credit Products 122
5.3 Fundamental Ideas on Pricing Credit 126
5.4 Pricing Fundamental Credit Products 127
5.5 Credit Spread Options 146
5.6 Multiple Underlying Products 156
5.7 Conclusion 177
6 – Pricing Counterparty Risk in Interest Rate Derivatives 183
6.1 Introduction 185
6.2 Overview 186
6.3 Expected Loss versus Economic Capital 190
6.4 Portfolio Effect 191
6.5 The Model 192
6.6 Interest Rate Swaps 193
6.7 Cross-Currency Swaps 199
6.8 Caps and Floors 202
6.9 Swaptions 202
6.10 Portfolio Pricing 204
6.11 Extensions of the Model 209
6.12 Hedging 211
6.13 Conclusion 220
Appendix A – Derivation of the Formula for the Expected
Loss on an Interest Rate Swap 221
Appendix B – The Formula for the Expected Loss on an
Interest Rate Cap or Floor 226
Appendix C – Derivation of the Formula for the Expected
Loss on an Interest Rate Swaption (Hull and White
Interest Rate Model) 227
Appendix D – Derivation of the Formula for the Expected
Loss on a Cancellable Interest Rate Swap 236
Appendix E – Market Parameters used for the Computations 246
7 – Credit Risk in Convertible Bonds 245
7.1 Introduction 245
7.2 Basic Features of Convertibles 246
7.3 General Pricing Conditions 247
7.4 Interest Rate Model 248
7.5 Firm Value Model 249
7.6 Credit Spread Model 260
7.7 Comparison of the two Models 269
7.8 Hedging of Credit Risk 272
7.9 Conclusion 274
Appendix A – Firm Value Model – Analytic Pricing Formulae 274Appendix B – Derivation of Formulae for Trinomial Tree
with Default Branch 275
Appendix C – Effect of Sub-optimal Call Policy 276
Appendix D – Incorporation of “Smile” in the Firm
Value Model 278
8 – Market Imperfections 281
8.1 Liquidity Risk 284
8.2 Discrete Hedging 295
8.3 Asymmetric Information 300
8.4 Conclusion 311
Appendix 313
1. Credit Swap Valuation – Darrel Duffie 315
2. Practical use of Credit Risk Models in Loan Portfolio and
Counterparty Exposure Management – Robert A. Jarrow
and Donald R. van Deventer 338
3. An Empirical Analysis of Corporate Rating Migration,
Default and Recovery – Sean C. Keenan, Lea V. Carty
and David T. Hamilton 350
4. Modelling Credit Migration – Bill Demchak 376
5. Haircuts for Hedge Funds – Ray Meadows 389
6. Generalising with HJM – Dmitry Pugachevsky 400
Glossary 409
Index 421