On the mortality/longevity risk hedging with mortality immunization

Abstract

In this paper, we define the mortality durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel shift, respectively, in μs (the forces of mortality), ps (the one-year survival probabilities) and qs (the one-year death probabilities), and further derive them as magnitude-free closed-form formulas. Then we propose several duration/convexity matching strategies to determine the weights of two or three products in an insurance portfolio. With the stochastic mortality models, we evaluate the Value-at-Risk (VaR) values and the hedge effectiveness of the surpluses at time zero for the underlying portfolio with these matching strategies. Illustrated numerical examples demonstrate that the duration/convexity matching strategies with respect to an instantaneously proportional change in μs and qs can significantly hedge the mortality/longevity risks.