The Crash-NIG copula model: Risk measurement and management of credit portfolios

Abstract

The one-factor copula models became very popular for modelling dependence in credit portfolios and collateralised debt obligation (CDO) valuation owing to their simplicity. Still, 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 possible to describe historical correlation behaviour realistically. Such an extension of the one-factor copula model, called the Crash-NIG copula model, is proposed by the authors with the following characteristics: (i) more tail dependence than in the Gaussian case, (ii) consistent term structure dimension, (iii) different rating buckets, relaxing the assumption of a large homogeneous portfolio, and (iv) different correlation regimes. Here the authors demonstrate how to apply this model for generating rating transition and default scenarios of a credit portfolio together with the other relevant risk factors. Repricing of instruments on the simulated scenario paths, that is the most difficult problem for such complex instruments as CDO tranches, can also be done efficiently fast using the same model. Finally, portfolio optimisation can be performed on the derived profit and loss distributions that are shown to be very different from normal.