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

8

Final Discussion and Conclusions

8.1 THERE ARE MORE THINGS IN HEAVEN AND EARTH, HORATIO. . .

We have followed a long path for credit derivatives, and CDOs in particular, from the introduction of the Gaussian Copula consistent at most with a single tranche at a single maturity, to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time.

The critics we presented to the use of the Gaussian Copula and of compound and base correlation had all been published before the beginning of the credit crisis. Thus, the notion that quantitative analysts and academics had no idea of the limits and dangers underlying the copula model is simply false. There is even a book titled Credit Correlation: Life After Copulas, edited by Lipton and Rennie (2007) that is the summary of talks given at a conference of the same name in 2006 in London.

Despite these warnings, the Gaussian Copula model is still used in its base correlation formulation, although under some possible extensions such as random recovery. The reasons for this are complex. First, the difficulty of all the loss models, improving the consistency issues, in accounting for single-name data and to allow for single-name sensitivities. While the aggregate loss is modelled in order to calibrate, satisfactorily, indices and tranches, the model does not see the single-name defaults but just the loss dynamics as an aggregate object. Therefore, partial hedges with ...