Estimation of the diversification effect in Solvency II under dependence uncertainty

The paper focuses on the problem of the accurate estimation of the diversification effect in the process of determining Solvency Capital Requirements (SCRs) in Solvency II. First, the method of determining SCRs in Solvency II is briefly characterised, the role of dependences for the correct specification of the diversification effect is presented, and a diversification ratio is defined. This is followed by an analysis of the use of this ratio of the diversification effect sensitivity to the dependence structure based on an example of life and health underwriting risk. The cases of lacking knowledge, partial knowledge (of a correlation coefficient only) and full knowledge are considered (it has been assumed that variables are independent and comonotonic). Dependence structures are modelled using copulas. The article shows that without identifying the actual dependence structure, the application of the standard formula in accordance with Commission Delegated Regulation (EU) 2015/35 may lead to the incorrect estimation of the diversification effect, and it indicates (based on a simulation analysis) the size of possible errors.