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Copulas from Infinitely Divisible Distributions: Applications to Credit Value at Risk

by Thomas Moosbrucker of the University of Cologne

June 2006

Abstract: This article proposes infinitely divisible distributions for credit portfolio modelling. First, we show that these distributions are well suited to fit into a one factor copula approach. We compare four different specifications (Normal Inverse Gaussian, Variance Gamma, Merton Jump Diffusion and Kou Jump Diffusion), where the last two distributions are new to credit portfolio modelling. The comparison in this article is done with respect to Value at Risk (VaR) measures. When we apply three different methods (identical correlations of default triggering variables, identical default correlations and an estimation-based method), we find that the more extreme tail behaviour of the infinitively divisible distributions leads to significantly different VaR measures. Therefore, our conclusion is that the identification of the correct dependence structure is of major importance for the estimation of VaR.

JEL Classification: G13.

Keywords: Credit Value at Risk, Credit Portfolio Models, LHP approximation, Infinitely Divisible Distributions, LÚvy Processes.

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