Default Probabilities and Default Correlations Under Stress

17 Pages Posted: 2 Apr 2014

See all articles by Natalie Packham

Natalie Packham

Berlin School of Economics and Law; Humboldt University Berlin

Michael Kalkbrener

Deutsche Bank AG - Risk Management

Ludger Overbeck

University of Giessen

Date Written: April 1, 2014

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 financial 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

JEL Classification: C00, G21, C52

Suggested Citation

Packham, Natalie and Kalkbrener, Michael and Overbeck, Ludger, Default Probabilities and Default Correlations Under Stress (April 1, 2014). Available at SSRN: https://ssrn.com/abstract=2419017 or http://dx.doi.org/10.2139/ssrn.2419017

Natalie Packham (Contact Author)

Berlin School of Economics and Law ( email )

Badensche Strasse 50-51
Berlin, D-10825
Germany

HOME PAGE: http://www.packham.net

Humboldt University Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

Michael Kalkbrener

Deutsche Bank AG - Risk Management ( email )

31 West 52nd Street, 12th Floor
New York, NY 10019

Ludger Overbeck

University of Giessen ( email )

Institut of Mathematics
Giessen, 35394
Germany

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
80
Abstract Views
471
rank
335,545
PlumX Metrics