Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk

Abstract

This article provides natural hedging strategies for life insurance and annuity businesses written on a single generation or on different generations in the presence of both longevity and interest-rate risks. We obtain closed-form solutions for delta and gamma hedges against cohort-based longevity risk. We exploit the correlation between the mortality intensities of different generations and hedge the longevity risk of one cohort with products on other cohorts. An application with UK data on survivorship and bond dynamics shows that hedging is effective, even when rebalancing is infrequent.