Optimal Longevity Hedging Framework for Insurance Companies Considering Basis and Mispricing Risks

Abstract

This article studies the optimal hedging strategy to deal with longevity risk for the life insurer considering basis risk. We build up a longevity hedging framework that incorporates not only the internal natural hedging but also the external hedging by using the q‐forwards. The optimal hedging strategy is obtained by a minimizing‐variance approach that can minimize the impact of longevity risk on the insurer`s profit function. To investigate the basis risk, instead of using population mortality, we adopt a unique mortality data set of annuity and life insurance policies that enable us to calibrate the multi‐population mortality dynamics for different lines of insurance policies. We consider three different hedging strategies: the natural hedging strategy, the external hedging strategy, and combining both natural hedging, and external hedging strategies. The hedge effectiveness for different hedging strategies is evaluated. In addition, the mortality forecast model based on VECM and ARIMA are used to examine the impact of basis risk on hedge effectiveness. As a result, combining both internal and external hedging strategies is the most effective way to manage longevity risk. Ignoring the basis risk will decrease the hedge effectiveness.