Multi-year analysis of solvency capital in life insurance

Abstract

With the commencement of the Solvency II directive, insurers in the European Union need to provide a projection of their solvency figures into the future (as part of the Own Risk and Solvency Assessment, ORSA). This is a highly complex task since future solvency figures depend on the development of numerous (stochastic) risk factors. The required evaluations are numerically challenging, which in practice forces companies to limit their analyses to only a few selected deterministic scenarios. These deterministic scenarios clearly cannot describe the full probability distribution of a company’s future solvency situation. The focus of this paper is on financial guarantees in participating life insurance products. In particular, we study two major types of interest rate guarantees in life insurance, a maturity guarantee and a (path-dependent) cliquet-style guarantee. In order to derive entire probability distributions of future solvency ratios, we limit the model framework to two sources of risk (a Hull–White model for interest rates and a geometric Brownian motion for stocks). This partly leads to closed-form solutions of the market-consistent valuation of the liabilities, ensures higher accuracy in computations and less numerical effort. Furthermore, the model allows for a detailed analysis of the impact of the different types of interest rate guarantees on the future solvency situation. Our results suggest that the type of guarantee has a significant impact on the long-term solvency of the company.