Credit risk stress testing and copulas: Is the Gaussian copula better than its reputation? - Philipp Koziol; Carmen Schell; Meik Eckhardt (Deutsche Bundesbank, 2015)
In the last decade, stress tests have become indispensable in bank risk management which has led to significantly increased requirements for stress tests for banks and regulators. Although the complexity of stress testing frameworks has been enhanced considerably over the course of the last few years, the majority of credit risk models (e.g. Merton (1974), CreditMetrics, KMV) still rely on Gaussian copulas. This paper complements the finance literature providing new insights into the impact of different copulas in stress test applications using supervisory data of 17 large German banks. Our findings imply that the use of a Gaussian copula in credit risk stress testing should not by default be dismissed in favor of a heavy-tailed copula which is widely recommended in the finance literature. Gaussian copula would be the appropriate choice for estimating high stress effects under extreme scenarios. Heavy-tailed copulas like the Clayton or the t copula are recommended in the case of less severe scenarios. Furthermore, the paper provides clear advice for designing a credit risk stress test.
Keywords: G21; G33; C13; C15; 330; credit risk; top-down stress tests; copulas; macroeconomic scenario