Misspecified copulas in credit risk models: how good is Gaussian?

Alfred Hamerle, Daniel Rösch

Abstract

ABSTRACT

In addition to “classical” approaches, such as the Gaussian CreditMetrics or Basel II model, the use of other copulas has recently 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 misspeci fied models with respect to estimation risk. Finally, we demonstrate the ideas using rating agencies data and show a simple way of dealing with estimation risk in practice. Overall, our findings on the robustness of the Gaussian copula considerably reduce model risk in practical applications.