Modelling Mortality Risk with Extreme Value Theory

Abstract

Financial losses due to unanticipated movements of mortality rates (either catastrophic mortality risk or longevity risk) have become a major concern for pension annuities. To transfer these risks to the capital market, a new risk management tool - mortality-linked securities - has been developed. Proper mortality models are therefore required to value the securities. To capture rare extreme events that cause either mortality or longevity risk, I propose a mixed model for the mortality factor kappa_t. Small random fluctuations of kappa_t are modeled with a random walk with drift, while the generalized Pareto distribution in the left and/or right tail is used to incorporate extreme events. The advantage of this procedure is its unifi ed modeling framework and its ability to extrapolate more extreme out-of-sample mortality events. Furthermore, it integrates both types of mortality risk.