An Efficient Method for Mitigating Longevity Value-at-Risk

Abstract

Many of the existing index-based longevity hedging strategies focus on the reduction in variance. However, solvency capital requirements are typically based on the τ-year-ahead Value-at-Risk, with τ = 1 under Solvency II. Optimizing a longevity hedge using variance minimization is particularly inadequate when the cost of hedging is nonzero and mortality improvements are driven by a skewed and/or heavy-tailed distribution. In this article, we contribute a method to formulate a value hedge that aims to minimize the Value-at-Risk of the hedged position over a horizon of τ years. The proposed method works with all stochastic mortality models that can be formulated in a state-space form, even when a non normal distributional assumption is made. We further develop a technique to expedite the evaluation of a value longevity hedge. By utilizing the generic assumption that the innovations in the stochastic processes for the period and cohort effects are not serially correlated, the proposed technique spares us from the need for nested simulations that are generally required when evaluating a value hedge.