Annuity Valuation with Dependent Mortality

Abstract

Annuities are contractual guarantees that promise to provide periodic income over the lifetime(s) of individuals. Standard insurance industry practice assumes independence of lives when valuing annuities where the promise is based on more than one life. This article investigates the use of dependent mortality models to value this type of annuity. We discuss a broad class of parametric models using a bivariate survivorship function called a copula. Using data from a large insurance company, we calculate maximum likelihood estimates to calibrate the model. The estimation results show strong positive dependence between joint lives with real economic significance. Annuity values are reduced by approximately 5 percent when dependent mortality models are used compared to the standard models that assume independence.