Solvency II and diversification effect for non-life premium and reserves risk: new results based on non-parametric copulas

To increase the safety of the insured, the Solvency II regulation of 2016 introduces the obligation to determine the Solvency Capital Requirement. The standard approach consists in aggregating the capital requirements for individual risk types, based on the dependence structure described by the correlation matrix established in the Directive. A pan-European comparative study was launched in October 2020 with one aim to better understand the dependence between, on the one side, the interdependencies modeling approaches and risk aggregation and, on the other, the resulting diversification benefits. In the present article, we will present a new method of non-parametric estimation of the quantile of the sum of the dependent insurer's risk types. The diversification effect obtained from the dependencies with the use of these non-parametric copulas is higher than the diversification effect obtained by using the dependence based on vine copulas. This method makes it possible to determine the structure of dependencies more flexibly in the absence of prior knowledge about the stochastic properties of risk-modeling variables and for a limited number of observations.