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Autor: Damiano Brigo
ISBN-13: 9780470971437
Einband: E-Book
Seiten: 176
Sprache: Englisch
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Credit Models and the Crisis

A Journey into CDOs, Copulas, Correlations and Dynamic Models
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1
The recent financial crisis has highlighted the need for bettervaluation models and risk management procedures, betterunderstanding of structured products, and has called into questionthe actions of many financial institutions. It has becomecommonplace to blame the inadequacy of credit risk models, claimingthat the crisis was due to sophisticated and obscure products beingtraded, but practitioners have for a long time been aware of thedangers and limitations of credit models. It would seem that a lackof understanding of these models is the root cause of theirfailures but until now little analysis had been published on thesubject and, when published, it had gained very limited attention.
Credit Models and the Crisis is a succinct but technicalanalysis of the key aspects of the credit derivatives modelingproblems, tracing the development (and flaws) of new quantitativemethods for credit derivatives and CDOs up to and through thecredit crisis. Responding to the immediate need for clarity in themarket and academic research environments, this book follows thedevelopment of credit derivatives and CDOs at a technical level,analyzing the impact, strengths and weaknesses of methods rangingfrom the introduction of the Gaussian Copula model and the relatedimplied correlations to the introduction of arbitrage-free dynamicloss models capable of calibrating all the tranches for all thematurities at the same time. It also illustrates the impliedcopula, a method that can consistently account for CDOs withdifferent attachment and detachment points but not for differentmaturities, and explains why the Gaussian Copula model is stillused in its base correlation formulation.

The book reports both alarming pre-crisis research and marketexamples, as well as commentary through history, using data up tothe end of 2009, making it an important addition to modernderivatives literature. With banks and regulators struggling tofully analyze at a technical level, many of the flaws in modernfinancial models, it will be indispensable for quantitativepractitioners and academics who want to develop stable andfunctional models in the future.
4
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 Copulamodel.

3.1.2 Finite pool heterogeneous one-factor Gaussian Copulamodel.

3.1.3 Large pool homogeneous one-factor Gaussian Copulamodel.

3.2 Double-t Copula Model.

3.3 Compound correlation and base correlation.

3.4 Existence and non-monotonicity of market spread as afunction 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 compoundcorrelation?

3.8 Can the Double-t Copula flatten the Gaussian basecorrelation skew?

3.9 Summary on implied correlation.

4 Consistency across Capital Structure: ImpliedCopula.

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-PoissonLoss 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.

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Autor: Damiano Brigo
ISBN-13 :: 9780470971437
ISBN: 0470971436
Verlag: John Wiley & Sons
Seiten: 176
Sprache: Englisch
Auflage 1. Auflage
Sonstiges: Ebook