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 Theory 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
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 Recovery 122
6.2. Reduced-Form Pricing with Recovery 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