Solvency II's Market Risk Standard Formula: How Credible is the Proclaimed Ruin Probability?

In this paper, we address the issue of calculating actual ruin probabilities under the market risk standard formula of Solvency II. Our discussion begins with a short overview of the Solvency II market risk module and a partial internal model, which both can be used to calculate the insurer's capital requirements for market risk. Consistent with the Solvency II guidelines, the internal model relies on the value at risk measure with a ruin probability of 0.5 percent per year. In a next step, we then derive efficient portfolios under budget and short sale constraints as well as the prevailing legal investment limits in Germany in order to determine the capital requirements under both approaches for each individual portfolio. Finally, by inverting our internal model, the actual ruin probabilities of the Solvency II standard formula can be calculated. Our analysis reveals that the latter deviate substantially from the proclaimed one by the regulator. Based on these results and given the fact that a large fraction of European insurance companies may apply the standard formula, Solvency II can be expected to create wrong incentives and cause a high level of hidden risks in the insurance sector.