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http://ssrn.com/abstract=1529498
 
 

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Credit Models and the Crisis, or: How I Learned to Stop Worrying and Love the CDOs


Damiano Brigo


Imperial College London - Department of Mathematics; Capco

Andrea Pallavicini


Banca IMI; Imperial College London - Department of Mathematics

Roberto Torresetti


Banco Popolare

December 29, 2009


Abstract:     
We follow a long path for Credit Derivatives and Collateralized Debt Obligations (CDOs) in particular, from the introduction of the Gaussian copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time. En passant, we also illustrate the implied copula, a method that can consistently account for CDOs with different attachment and detachment points but not for different maturities. The discussion is abundantly supported by market examples through history. The dangers and critics we present to the use of the Gaussian copula and of implied correlation had all been published by us, among others, in 2006, showing that the quantitative community was aware of the model limitations before the crisis. We also explain why the Gaussian copula model is still used in its base correlation formulation, although under some possible extensions such as random recovery. Overall we conclude that the modeling effort in this area of the derivatives market is unfinished, partly for the lack of an operationally attractive single-name consistent dynamic loss model, and partly because of the diminished investment in this research area.

Number of Pages in PDF File: 66

Keywords: Credit Crisis, Credit Derivatives, Gaussian Copula Model, Implied Correlation, Base Correlation, Compound Correlation, Implied Copula, Dynamic Loss Model, GPL Model, Arbitrage Free Models, Collateralized Debt Obligations, DJi-Traxx and CDX Tranches, CDO Tranche Calibration

JEL Classification: C15, C31, C46, C61, G12, G13

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Date posted: December 31, 2009 ; Last revised: February 18, 2010

Suggested Citation

Brigo, Damiano and Pallavicini, Andrea and Torresetti, Roberto, Credit Models and the Crisis, or: How I Learned to Stop Worrying and Love the CDOs (December 29, 2009). Available at SSRN: http://ssrn.com/abstract=1529498 or http://dx.doi.org/10.2139/ssrn.1529498

Contact Information

Damiano Brigo (Contact Author)
Imperial College London - Department of Mathematics ( email )
South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom
HOME PAGE: http://www.damianobrigo.it
Capco ( email )
120 Broadway, 15th Floor
New York, NY 10271
United States
HOME PAGE: http://www.capco.com/capco-insights
Andrea Pallavicini
Banca IMI ( email )
Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)
HOME PAGE: http://apallavicini.it
Imperial College London - Department of Mathematics ( email )
South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom
Roberto Torresetti
Banco Popolare ( email )
Milan
Italy
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