Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 037

Default probabilities and default correlations under stress

Natalie Packham
Michael Kalkbrener
Ludger Overbeck

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

financial risk management, credit portfolio modelling, stress testing, elliptic distribution, max-domain

MSC classification:
60G70, 91G40