Credit Models and the Crisis, or: How I learned to stop worrying and love the CDOs
by Damiano Brigo of Imperial College,
February 17, 2010
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 e ort 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.
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.
Published in: Journal of Risk Management in Financial Institutions, Vol. 4, No. 3, (June 2011), pp. 243-253.