Asymptotic behaviour of multivariate default probabilities and default correlations under stress

Abstract

We investigate default probabilities and default correlations of Merton-type credit portfolio models in stress scenarios where a common risk factor is truncated. For elliptically distributed asset variables, the asymptotic limits of default probabilities and default correlations depend on the max-domain of attraction of the asset variables. In the regularly varying case, we derive an integral representation for multivariate default probabilities, which turn out to be strictly smaller than 1. Default correlations are in (0, 1). In the rapidly varying case, asymptotic multivariate default probabilities are 1 and asymptotic default correlations are 0.