The Determinants of Mortality Heterogeneity and Implications for Pricing Underwritten Annuities
36 Pages Posted: 28 Feb 2013
Date Written: February 21, 2013
It is widely accepted that mortality risk varies across individuals within age-sex bands of a population. This heterogeneity exposes insurers to adverse selection if only the healthiest lives purchase annuities, so standard annuities are priced with a mortality table that assumes above-average longevity. This makes standard annuities expensive for many individuals. To address this issue there has been a shift to underwriting annuities in order to offer lower prices to individuals with below-average longevity. While underwriting reduces heterogeneity, mortality risk still varies within each risk class due to unobservable individual-specific factors, referred to as frailty. This paper quantifies the financial impact of frailty on underwritten annuities. The heterogeneity implied by underwriting factors and frailty is quantified by fitting Generalized Linear Mixed Models to longitudinal data for a large sample of US males. The results show that heterogeneity remains after underwriting, creating significant variation in the fair value of underwritten annuities. We develop a method to adjust annuity prices to allow for frailty.
Keywords: mortality heterogeneity, frailty modeling, annuity pricing, longitudinal data, generalized linear mixed models
JEL Classification: G22, G23, C23
Suggested Citation: Suggested Citation