Credit Models and the Crisis
A Journey into CDOs, Copulas, Correlations and Dynamic Models
Published on 13. October 2010
176 pages
978-0-470-97143-7 (ISBN)
Description
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.
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Damiano Brigo | Andrea Pallavicini | Roberto Torresetti
Credit Models and the Crisis
A Journey into CDOs, Copulas, Correlations and Dynamic Models
Book
04/2010
Wiley
€56.00
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Persons
DAMIANO BRIGO is Managing Director and Global Head of theQuantitative team in Fitch Solutions, and Visiting Professor at theDepartment of Mathematics at Imperial College, London.
Damiano has published more than 50 articles in top journals formathematical finance, systems theory, probability and statistics,and a book for Springer Verlag that has become a field reference instochastic interest rate modeling. Damiano is Managing Editor ofthe International Journal of Theoretical and Applied Finance, he isa member of the Fitch Academic Advisory Board and is part ofscientific committees for academic conference occurring at MIT andother academic and industry institutions. Damiano has also been acharter member of Risk's Who's Who since 2007.
Damiano's interests include pricing, risk measurement, credit anddefault modeling, counterparty risk, and stochastic dynamicalmodels for commodities and inflation.
Damiano obtained a Ph.D. in stochastic filtering with differentialgeometry in 1996 from the Free University of Amsterdam, following aBSc in Mathematics with honours from the University of Padua.
ANDREA PALLAVICINI is Head of Financial Engineering atBanca Leonardo in Milan. Previously, he worked as Head of Equityand Hybrid Models in Banca IMI, working also on dynamical lossmodels, interest-rate derivatives, smile modelling and counterpartyrisk.
Over the years he has published several academic andpractitioner-oriented articles in financial modeling, theoreticalphysics and astrophysics. He has taught Master courses in financeat the Universities of Pavia and Milan.
He obtained a Degree in astrophysics, and a Ph.D. in theoreticaland mathematical physics from the University of Pavia.
ROBERTO TORRESETTI is responsible for Structured CreditDerivatives at BBVA. He was previously a senior credit derivativesmodeller at Banca IMI and equity derivatives analyst at LehmanBrothers and a quantitative fund manager at San Paolo IMI AssetManagement. He holds a bachelor's degree in economics fromUniversità Bocconi in Milan and completed his MA in economicsat Università Bocconi and MS in financial mathematics at theUniversity of Chicago.
Content
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.
