A Value Based Cohort Index for Longevity Risk Management

Abstract

Existing longevity indices commonly use age-based mortality rates or period life expectancy. We propose an alternative cohort-based value index for insurers and pension funds to manage longevity risk. This index is an expected present value of a longevity linked cash flow valued using a specified cohort mortality model and a commonly used interest rate model. Since interest rate and longevity risk are inherent with any longevity linked obligation and interest rate risk can be effectively hedged, this index will provide a better measure of the longevity risk than current indices. Current mortality models are largely age-period based, so we develop a cohort based stochastic mortality model with age-dependent model parameters that provides realistic cohort correlation structures as an underlying basis for the value index. We show how the model improves fitting performance compared to other cohort models, particularly for very old ages, and has a familiar model formulation for financial market participants. We also demonstrate the hedge effectiveness of the index.

Keywords: Cohort mortality, Value index, Mortality risk, Interest rate risk, Hedge efficiency

JEL Classification: C63, G22, G12