Market-consistent valuation of long-term insurance contracts: valuation framework and application to German private health insurance

Abstract

In this paper we derive a market-consistent value for long-term insurance contracts, with a focus on long-term health insurance contracts as found, e.g., in the German private health insurance industry. To this end, we first set up a health insurance company model and, second, conduct a simulation study to calculate the present value of future profits and the time value of financial options and guarantees from a portfolio of private health insurance policies. Our analysis quantifies the impact of investment results and underwriting surpluses on shareholder profits with respect to profit sharing rules and premium adjustment mechanisms. In contrast to the valuation of life insurance contracts with similar calculation techniques the results indicate that the time value of financial options and guarantees of German private health insurance contracts is substantially smaller in typical parameter settings.