Risk CDT - Copula dependencies under the Solvency II Environment

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This is a project within the multi-disciplinary EPSRC and ESRC Centre for Doctoral Training (CDT) on Quantification and Management of Risk & Uncertainty in Complex Systems & Environments, within the Institute for Risk and Uncertainty. The studentship is granted for 4 years and includes, in the first year, a Master in Decision Making under Risk & Uncertainty. The project includes extensive collaboration with prime industry to build an optimal basis for employability.

In April 2009 the European Parliament adopted a directive “on the taking-up and pursuit of the business of Insurance and Reinsurance” (Solvency II). According to this 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 UK insurance/reinsurance 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 project we will analyse the method of risk aggregation via the proposed application of correlations.

We will point out 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 modelling causes technical difficulties. A possible solution for this dilemma can be seen in the application of copulas.

In 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. UK insurers/reinsurers will be able to design their internal models by using an aggregation method more complex but even more precisely (e. g. copulas) than the solely utilisation of a correlation matrix. It is clear that modelling 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 1 deployment of copulas in risk modelling in general. Finally, other kind of dependencies between the claim amount and the claim frequency will be examined so as to link copula dependencies with partial internal models in the case that no standard formula is used.