Structured Credit Portfolio Analysis Baskets & CDOs

Preface v About the Authors ix A Brief Guide to the Book xi 1 From Single Credit Risks to Credit Portfolios 1(26) 1.1 Modeling Single-Name Credit Risk 2(15) 1.1.1 Ratings and Default Probabilities 2(8) 1.1.2 Credit Exposure 10(4) 1.1.3 Loss Given Default 14(3) 1.2 Modeling Portfolio Credit Risk 17(10) 1.2.1 Systematic and Idiosyncratic Credit Risk 17(3) 1.2.2 Loss Distribution of Credit Portfolios 20(4) 1.2.3 Practicability Versus Accuracy 24(3) 2 Default Baskets 27(138) 2.1 Introductory Example: Duo Baskets 27(7) 2.2 First- and Second-to-Default Modeling 34(5) 2.3 Derivation of PD Term Structures 39(20) 2.3.1 A Time-Homogeneous Markov Chain Approach 40(12) 2.3.2 A Non-Homogeneous Markov Chain Approach 52(5) 2.3.3 Extrapolation Problems for PD Term Structures 57(2) 2.4 Duo Basket Evaluation for Multi-Year Horizons 59(8) 2.5 Dependent Default Times 67(53) 2.5.1 Default Times and PD Term Structures 67(1) 2.5.2 Survival Function and Hazard Rate 68(1) 2.5.3 Calculation of Default Time Densities and Hazard Rate Functions 69(9) 2.5.4 From Latent Variables to Default Times 78(7) 2.5.5 Dependence Modeling via Copula Functions 85(8) 2.5.6 Copulas in Practice 93(6) 2.5.7 Visualization of Copula Differences and Mathematical Description by Dependence Measures 99(14) 2.5.8 Impact of Copula Differences to the Duo Basket 113(5) 2.5.9 A Word of Caution 118(2) 2.6 Nth-to-Default Modeling 120(27) 2.6.1 Nth-to-Default Basket with the Gaussian Copula 121(6) 2.6.2 Nth-to-Default Basket with the Student-t Copula 127(1) 2.6.3 Nth-to-Default Basket with the Clayton Copula 127(2) 2.6.4 Nth-to-Default Simulation Study 129(7) 2.6.5 Evaluation of Cash Flows in Default Baskets 136(4) 2.6.6 Scenario Analysis 140(7) 2.7 Example of a Basket Credit-Linked Note (CLN) 147(18) 3 Collateralized Debt and Synthetic Obligations 165(138) 3.1 A General Perspective on CDO Modeling 166(24) 3.1.1 A Primer on CDOs 167(5) 3.1.2 Risk Transfer 172(6) 3.1.3 Spread and Rating Arbitrage 178(6) 3.1.4 Funding Benefits 184(2) 3.1.5 Regulatory Capital Relief 186(4) 3.2 CDO Modeling Principles 190(4) 3.3 CDO Modeling Approaches 194(56) 3.3.1 Introduction of a Sample CSO 194(5) 3.3.2 A First-Order Look at CSO Performance 199(3) 3.3.3 Monte Carlo Simulation of the CSO 202(8) 3.3.4 Implementing an Excess Cash Trap 210(3) 3.3.5 Multi-Step and First Passage Time Models 213(7) 3.3.6 Analytic, Semi-Analytic, and Comonotonic CDO Evaluation Approaches 220(30) 3.4 Single-Tranche CDOs (STCDOs) 250(37) 3.4.1 Basics of Single-Tranche CDOs 250(3) 3.4.2 CDS Indices as Reference Pool for STCDOs 253(6) 3.4.3 ITraxx Europe Untranched 259(12) 3.4.4 ITraxx Europe Index Tranches: Pricing, Delta Hedging, and Implied Correlations 271(16) 3.5 Tranche Risk Measures 287(24) 3.5.1 Expected Shortfall Contributions 288(4) 3.5.2 Tranche Hit Contributions of Single Names 292(2) 3.5.3 Applications: Asset Selection, Cost-to-Securitize 294(5) 3.5.4 Remarks on Portfolios of CDOs 299(4) 4 Some Practical Remarks 303(4) 5 Suggestions for Further Reading 307(4) 6 Appendix 311(28) 6.1 The Gamma Distribution 311(1) 6.2 The Chi-Square Distribution 312(1) 6.3 The Student-t Distribution 312(2) 6.4 A Natural Clayton-Like Copula Example 314(1) 6.5 Entropy-Based Rationale for Gaussian and Exponential Distributions as Natural Standard Choices 315(3) 6.6 Tail Orientation in Typical Latent Variable Credit Risk Models 318(2) 6.7 The Vasicek Limit Distribution 320(2) 6.8 One-Factor Versus Multi-Factor Models 322(7) 6.9 Description of the Sample Portfolio 329(3) 6.10 CDS Names in CDX.NA.IG and iTraxx Europe 332(7) References 339(10) Index 349