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Misspecified Copulas in Credit Risk Models - How Good Is Gaussian

by Alfred Hamerle of the University of Regensburg, and
Daniel Rösch of the University of Regensburg

October 2005

Abstract: In addition to "classical" approaches, such as the Gaussian CreditMetrics or Basel II model, recently the use of other copulas has been proposed in the area of credit risk for modeling loss distributions, particularly T copulas which lead to fatter tails ceteris paribus. As an amendment to recent research this paper shows some estimation results when the copula in a default-mode framework using a latent variable distribution is misspecified. It turns out that parameter estimates may be biased, but that the resulting forecast for the loss distribution may still be adequate. We also compare the performance of the true and misspecified models with respect to estimation risk. Finally, we demonstrate the ideas using rating agencies data and show a simple way how to deal with estimation risk in practice. Overall, our findings on the robustness of the Gaussian copula considerably reduce model risk in practical applications.

Published in: Journal of Risk, Vol. 8, No. 1, (Fall 2005), pp. 41-58.

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