Credit Risk

In this book, two of America's leading economists provide the first integrated treatment of the conceptual, practical, and empirical foundations for credit risk pricing and risk measurement. Masterfully applying theory to practice, Darrell Duffie and Kenneth Singleton model credit risk for the purpose of measuring portfolio risk and pricing defaultable bonds, credit derivatives, and other securities exposed to credit risk. The methodological rigor, scope, and sophistication of their state-of-the-art account is unparalleled, and its singularly in-depth treatment of pricing and credit derivatives further illuminates a problem that has drawn much attention in an era when financial institutions the world over are revising their credit management strategies.


Duffie and Singleton offer critical assessments of alternative approaches to credit-risk modeling, while highlighting the strengths and weaknesses of current practice. Their approach blends in-depth discussions of the conceptual foundations of modeling with extensive analyses of the empirical properties of such credit-related time series as default probabilities, recoveries, ratings transitions, and yield spreads. Both the "structura" and "reduced-form" approaches to pricing defaultable securities are presented, and their comparative fits to historical data are assessed. The authors also provide a comprehensive treatment of the pricing of credit derivatives, including credit swaps, collateralized debt obligations, credit guarantees, lines of credit, and spread options. Not least, they describe certain enhancements to current pricing and management practices that, they argue, will better position financial institutions for future changes in the financial markets.


Credit Risk is an indispensable resource for risk managers, traders or regulators dealing with financial products with a significant credit risk component, as well as for academic researchers and students.

Preface xi Acknowledgments xiii 1. Introduction 1 1.1. A Brief Zoology of Risks 3 1.2. Organization of Topics 7 2. Economic Principles of Risk Management 12 2.1. What Types of Risk Count Most?13 2.2. Economics of Market Risk 15 2.3. Economic Principles of Credit Risk 26 2.4. Risk Measurement 29 2.5. Measuring Credit Risk 38 3. Default Arrival: Historical Patterns and Statistical Models 43 3.1. Introduction 43 3.2. Structural Models of Default Probability 53 3.3. From Theor to Practice: Using Distance to Default to Predict Default 57 3.4. Default Intensity 59 3.5. Examples of Intensity Models 64 3.6. Default-Time Simulation 72 3.7. Statistical Prediction of Bankruptcy 74 4. Ratings Transitions: Historical Patterns and Statistical Models 85 4.1. Average Transition Frequencies 85 4.2. Ratings Risk and the Business Cycle 87 4.3. Ratings Transitions and Aging 91 4.4. Ordered Probits of Ratings 92 4.5. Ratings as Markov Chains 94 5. Conceptual Approaches to Valuation of Default Risk 100 5.1. Introduction 100 5.2. Risk-Neutral versus Actual Probabilities 102 5.3. Reduced-Form Pricing 106 5.4. Structural Models 112 5.5. Comparisons of Model-Implied Spreads 114 5.6. From Actual to Risk-Neutral Intensities 118 6. Pricing Corporate and Sovereign Bonds 122 6.1. Uncertain Recover 122 6.2. Reduced-Form Pricing with Recover 125 6.3. Ratings-Based Models of Credit Spreads 137 6.4. Pricing Sovereign Bonds 146 7. Empirical Models of Defaultable Bond Spreads 156 7.1. Credit Spreads and Economic Activity 156 7.2. Reference Curves for Spreads 162 7.3. Parametric Reduced-Form Models 166 7.4. Estimating Structural Models 169 7.5. Parametric Models of Sovereign Spreads 171 8. Credit Swaps 173 8.1. Other Credit Derivatives 173 8.2. The Basic Credit Swap 175 8.3. Simple Credit-Swap Spreads 178 8.4. Model-Based CDS Rates 185 8.5. The Role of Asset Swaps 190 9. Optional Credit Pricing 194 9.1. Spread Options 194 9.2. Callable and Convertible Corporate Debt 201 9.3. A Simple Convertible Bond Pricing Model 215 10. Correlated Defaults 229 10.1. Alternative Approaches to Correlation 229 10.2. CreditMetrics Correlated Defaults 230 10.3. Correlated Default Intensities 233 10.4. Copula-Based Correlation Modeling 237 10.5. Empirical Methods 242 10.6. Default-Time Simulation Algorithms 243 10.7. Joint Default Events 247 11. Collateralized Debt Obligations 250 11.1. Introduction 250 11.2. Some Economics of CDOs 252 11.3. Default-Risk Model 255 11.4. Pricing Examples 260 11.5. Default Loss Analytics 271 11.6. Computation of Diversity Scores 280 12. Over-the-Counter Default Risk and Valuation 285 12.1. Exposure 285 12.2. OTC Credit Risk Value Adjustments 295 12.3. Additional Swap Credit Adjustments 304 12.4. Credit Spreads on Currency Swaps 311 13. Integrated Market and Credit Risk Measurement 314 13.1. Market Risk Factors 315 13.2. Delta-Gamma for Derivatives with Jumps 326 13.3. Integration of Market and Credit Risk 332 13.4. Examples of VaR with Credit Risk 334 Appendix A Introduction to Affine Processes 346 Appendix B Econometrics of Affine Term-Structure Models 362 Appendix C HJM Spread Curve Models 367 References 371 Index 385