Risk Aggregation by Using Copulas in Internal Models

Abstract

According to the Solvency II directive the Solvency Capital Requirement (SCR) corresponds to the economic capital needed to limit the probability of ruin to 0.5%. This implies that (re-)insurance undertakings will have to identify their overall loss distributions. The standard approach of the mentioned Solvency II directive proposes the use of a correlation matrix for the aggregation of the single so-called risk modules respectively sub-modules. In our paper we will analyze the method of risk aggregation via the proposed application of correlations. We will find serious weaknesses, particularly concerning the recognition of extreme events, e. g. natural disasters, terrorist attacks etc. Even though the concept of copulas is not explicitly mentioned in the directive, there is still a possibility of applying it. It is clear that modeling dependencies with copulas would incur significant costs for smaller companies that might outbalance the resulting more precise picture of the risk situation of the insurer. However, incentives for those companies who use copulas, e. g. reduced solvency capital requirements compared to those who do not use it, could push the deployment of copulas in risk modeling in general.