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Packham, Natalie
Kalkbrener, Michael
Overbeck, Ludger
Year of Publication: 
Series/Report no.: 
IRTG 1792 Discussion Paper No. 2018-037
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.
financial risk management
credit portfolio modelling
stress testing
elliptic distribution
Document Type: 
Working Paper

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