Credit Models and the Crisis

Abstract

Preface. Acknowledgements. About the Authors. Notation and List of Symbols. 1 Introduction: Credit Modelling Pre- and In-Crisis. 1.1 Bottom-up models. 1.2 Compound correlation. 1.3 Base correlation. 1.4 Implied Copula. 1.5 Expected Tranche Loss Surface. 1.6 Top (down) framework. 1.7 GPL and GPCL models. 1.8 Structure of the book. 2 Market Quotes. 2.1 Credit indices. 2.2 CDO tranches. 3 Gaussian Copula Model and Implied Correlation. 3.1 One-factor Gaussian Copula model. 3.1.1 Finite pool homogeneous one-factor Gaussian Copula model. 3.1.2 Finite pool heterogeneous one-factor Gaussian Copula model. 3.1.3 Large pool homogeneous one-factor Gaussian Copula model. 3.2 Double- t Copula Model. 3.3 Compound correlation and base correlation. 3.4 Existence and non-monotonicity of market spread as a function of compound correlation. 3.5 Invertibility limitations of compound correlation: pre-crisis. 3.6 Base correlation. 3.7 Is base correlation a solution to the problems of compound correlation? 3.8 Can the Double- t Copula flatten the Gaussian base correlation skew? 3.9 Summary on implied correlation. 4 Consistency across Capital Structure: Implied Copula. 4.1 Calibration of Implied Copula. 4.2 Two-stage regularization. 4.3 Summary of considerations around Implied Copula. 5 Consistency across Capital Structure and Maturities: Expected Tranche Loss. 5.1 Index and tranche NPV as a function of ETL. 5.2 Numerical results. 5.3 Summary on Expected (Equity) Tranche Loss. 6 A Fully Consistent Dynamical Model: Generalized-Poisson Loss Model. 6.1 Loss dynamics. 6.2 Model limits. 6.3 Model calibration. 6.4 Detailed calibration procedure. 6.5 Calibration results. 7 Application to More Recent Data and the Crisis. 7.1 Compound correlation in-crisis. 7.2 Base correlation in-crisis. 7.3 Implied Copula in-crisis. 7.4 Expected Tranche Loss surface in-crisis. 7.4.1 Deterministic piecewise constant recovery rates. 7.5 Generalized-Poisson Loss model in-crisis. 8 Final Discussion and Conclusions. 8.1 There are more things in heaven and earth, Horatio... 8.2 ... Than are dreamt of in your philosophy. Bibliography. Index.