Comparing risk measures when aggregating market risk and credit risk using different copulas

Maciag J., Hesse F., Boeve R., Pfingsten A.

Abstract
We simulate realistic total bank return distributions by means of a top-down copula approach for different parameter settings and ask the following questions. How different are various risk measures in their assessment of the risk of these distributions? How sensitive are the risk measures to changes in parameter values? How reliable are the risk measures in terms of estimation errors due to simulations? We find that the risk measures can be divided roughly into two groups according to their risk assessment, one comprising most value-at-risk-related measures.Within each group, the correlations of the risk-rankings of the return distributions are very high, between the groups they are smaller. The sensitivities with respect to parameter variations are quite different even within each group. It is of particular interest that the copula type has a noticeable impact. Moreover, we confirm the intuitive notion that risk measures that are more accurate in picturing the risk of the return distribution’s lower tail are also more exposed to estimation errors.

Keywords
Copula; Estimation error; Lower tail dependence; Risk aggregation; Risk measure; Simulation