IRTG1792DP2018 037
Default probabilities and default correlations under stress
Natalie Packham
Michael Kalkbrener
Ludger Overbeck
Abstract
We investigate default probabilities and default correlations of Merton-type credit portfolio
models in stress scenarios where a common risk factor is truncated. The analysis is
performed in the class of elliptical distributions, a family of light-tailed to heavy-tailed distributions
encompassing many distributions commonly found in nancial modelling. It turns
out that the asymptotic limit of default probabilities and default correlations depend on the
max-domain of the elliptical distribution's mixing variable. In case the mixing variable is
regularly varying, default probabilities are strictly smaller than 1 and default correlations
are in (0; 1). Both can be expressed in terms of the Student t-distribution function. In the
rapidly varying case, default probabilities are 1 and default correlations are 0. We compare
our results to the tail dependence function and discuss implications for credit portfolio
modelling.
Keywords:
financial risk management, credit portfolio modelling, stress testing, elliptic distribution, max-domain
MSC classification:
60G70, 91G40