Pricing Survivor Bonds with Affine-Jump Diffusion Stochastic Mortality Models

Abstract

Capital-market-based solutions are an interesting alternative to reinsurance-based options for managing systemic longevity risk in pension funds, insurance companies and annuity providers. The pricing of longevity-linked securities depends both on the stochastic process for the underlying risk factors (age-specific mortality rates, interest rate) and on investor's risk attitude. This paper proposes a pricing approach for survivor bonds using affine-jump diffusion stochastic mortality models. The model structure uses a non-mean reverting square-root jump diffusion Feller process combined with a Poisson process with double asymmetric exponentially distributed jumps to account for both negative and positive jumps. The model offers analytical tractability, fits well data and allows for closed-form expressions for the survival probability. Illustrative empirical results on the pricing of survivor bonds are provided using U. S. mortality data for representative cohorts. The results suggest the cost of hedging longevity risk by issuing survivor bonds would be acceptable for the issuer.