The Crash-NIG-Factor Copula Model: Risk Management of Credit Portfolios

The one-factor copula models became very popular for modeling dependence in credit portfolios and CDO valuation due to their simplicity. However, it is also well known that they are too simple for an exact pricing. Nevertheless, it is possible to extend the model in various ways so that it is able to describe historical correlation behavior realistically. Such an extension of the one-factor copula model, called Crach-NIG copula model, was proposed by [1] and has the following characteristics: (i) more tail dependence than in the Gaussian case ([2]), (ii) consistent term structure dimension, (iii) di erent rating buckets, relaxing the assumption of a large homogeneous portfolio, and (iv) di erent correlation regimes. Here we demonstrate how to apply this model for generating rating transition and default scenarios of a credit portfolio together with the other relevant risk factors. Computation of the instrument returns on the simulated paths, that is the most di cult problem for such complex instruments as CDO tranches, can also be done e ciently fast using the same model. Finally, a portfolio optimization can be performed on the derived P&L distributions that are shown to be very di erent from normal.