Mortality-dependent financial risk measures

This paper uses a recently developed two-factor stochastic mortality model to estimate financial risk measures for four illustrative types of mortality-dependent financial position: investments in zero-coupon longevity bonds; investments in longevity bonds that pay annual survivor-dependent coupons; and two examples of an insurer's annuity book that are each hedged by a longevity bond, one based on the annuity book and hedge having the same reference cohort, and the other not. The risk measures estimated are the value-at-risk, the expected shortfall and a spectral risk measure based on an exponential risk-aversion function. Results are reported on a model calibrated on data provided by the UK Government Actuary's Department, both with and without underlying parameter uncertainty.