Long-term insurance products and volatility under the Solvency II Framework

Abstract

Solvency II will become the new regulatory framework for insurance companies in Europe. It sets the capital requirements in function of the insurer’s risk exposure at a one-year time horizon. The objective of the paper is to quantify the cost of the volatility in the required capital induced by the Solvency II liability valuation methodology. First, we show that Solvency II will induce large variation in the required capital for illiquid long-term products with guarantees. The volatility of the required capital is larger for policies with a larger maturity. We then introduce a different liability valuation technique specifically for illiquid liabilities. The volatility of the required capital in this model is lower since it only depends on the default component of the credit spread of the backing assets. We prove that this model is market consistent. We conclude by estimating the cost of the option, which an insurer could buy to eliminate the extra induced capital volatility. Such option will generate the cash flow necessary to supply the extra required capital resulting from a change in illiquidity spread.