Calculating Capital Requirements for Longevity Risk in Life Insurance Products Using an Internal Model in Line with Solvency II

Over the last decades, significant improvements in life expectancy have been observed in most Western countries. More importantly, there is considerable uncertainty regarding the future development of life expectancy. This uncertainty imposes significant risk on pension providers and life insurance companies, and is referred to as longevity risk. The new Solvency II regulation requires that insurers and pension funds hold a reserve capital in order to limit the probability of underfunding in a one year horizon to 0.5%, taking into account the impact of longevity risk on funding ratio volatility. In this paper we develop a methodology to determine reserve requirements for longevity risk in life insurance products. We consider the case where, as suggested in Solvency II, the risk premium for longevity risk is determined by the Cost of Capital approach. Because longevity risk arises from uncertainty in future survivor probabilities, the capital reserve depends on the probability distribution of future mortality rates. The literature has devoted considerable attention to the development of statistical models to forecast future mortality improvements. However, using such statistical models to determine solvency requirements can be highly time-consuming. The goal of the paper is twofold. First, we propose a computationally tractable approach that yields an accurate approximation for the required solvency capital for different portfolios of life insurance products, in case mortality rates are forecasted by means of the Lee and Carter (1992) model. Second, we quantify the effects of a number of simplified approaches, as suggested in the Solvency II proposal, on the level of the required solvency capital