Expected Shortfall voor toezicht op verzekeraars: is het relevant?

Solvency II is in force as the European regulatory framework for insurance companies since 2016. The Solvency II regulation calibrates the capital requirements based on the risk measure Value-at-Risk, whereas Basel III and the Swiss Solvency Test both use the risk measure Expected Shortfall. This paper illustrates the conceptual differences between both risk measures, and shows that the differences vanish if it is assumed that the risk drivers have Gaussian distributions – as long as an appropriate parameter for Expected Shortfall is chosen. Moreover, we calibrate the stress scenario’s as proposed by EIOPA, but then also with the Expected Shortfall. We focus on the Solvency Capital Requirements (SCR) for three important risk modules: equity, interest rate, and longevity risk. For a representative life annuity insurer, we study the effects of a hypothetical change of risk measure in the Solvency II regulation from Value-at-Risk to Expected Shortfall. We find that the effects are small when the 99.5%-Value-at-Risk (as used in Solvency II) is replaced by the 98.8%-Expected Shortfall. We show that this finding is robust, also when we use historical simulations to determine the stress scenarios.