Solvency II – Considering Risk Dependencies
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In November 2009 the European Parliament adopted a directive "on the taking-up and pursuit of the business of Insurance and Reinsurance" (SolvencyII). According to this SolvencyII directive the Solvency Capital Requirement (SCR) corresponds to the economic capital needed to limit the probability of ruin to 0.5This implies that (re-)insurance undertakings will have to identify their overall loss distributions. The standard approach of the mentioned SolvencyII 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. The reason for this is that correlations compress information about dependencies into a single ratio. Therefore important information concerning the tail of a distribution may possibly not be considered. In contrast, multivariate distribution functions provide full information with respect to dependencies between the relevant risks. However, aggregation of risks through "traditional"multivariate modeling causes technical difficulties. A possible solution for this dilemma can be seen in the application of copulas. We come to the conclusion that it would have been desirable to fix the concept of copulas in the new solvency directive. Even though the concept of copulas is not explicitly mentioned in the directive, there is still a possibility of applying it. (Re-)insurers will be able to design their internal models by using an aggregation method more complex but even more precisely (e.copulas) than the solely utilization of a correlation matrix. 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.reduced solvency capital requirements compared to those who do not use it, could push the deployment of copulas in risk modeling in general.
Abstract
In November 2009 the European Parliament adopted a directive "on the taking-up and pursuit of the business of Insurance and Reinsurance" (SolvencyII). According to this SolvencyII directive the Solvency Capital Requirement (SCR) corresponds to the economic capital needed to limit the probability of ruin to 0.5This implies that (re-)insurance undertakings will have to identify their overall loss distributions. The standard approach of the mentioned SolvencyII 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. The reason for this is that correlations compress information about dependencies into a single ratio. Therefore important information concerning the tail of a distribution may possibly not be considered. In contrast, multivariate distribution functions provide full information with respect to dependencies between the relevant risks. However, aggregation of risks through "traditional"multivariate modeling causes technical difficulties. A possible solution for this dilemma can be seen in the application of copulas. We come to the conclusion that it would have been desirable to fix the concept of copulas in the new solvency directive. Even though the concept of copulas is not explicitly mentioned in the directive, there is still a possibility of applying it. (Re-)insurers will be able to design their internal models by using an aggregation method more complex but even more precisely (e.copulas) than the solely utilization of a correlation matrix. 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.reduced solvency capital requirements compared to those who do not use it, could push the deployment of copulas in risk modeling in general.
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