Credit Models and the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Models

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.