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Asymptotic behaviour of multivariate default probabilities and default correlations under stress

Published online by Cambridge University Press:  24 March 2016

N. Packham ,
M. Kalkbrener  and
L. Overbeck
M. Kalkbrener
Affiliation:
Deutsche Bank AG, Taunusanlage 12, 60325 Frankfurt am Main, Germany. Email address: michael.kalkbrener@db.com
L. Overbeck
Affiliation:
Institute of Mathematics, University of Giessen, Arndtstrasse 2, 35392 Giessen, Germany. Email address: ludger.overbeck@math.uni-giessen.de
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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.

Keywords

Financial risk managementcredit portfolio modellingstress testingelliptic distributionmax-domain of attraction
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 71 - 81
Copyright
Copyright © Applied Probability Trust 2016 

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