Evolution of Coupled Lives' Dependency Across Generations and Pricing Impact

Abstract

This paper studies the dependence between coupled lives - both within and across generations - and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. Dependence is modeled through copula functions. We consider Archimedean single and multi-parameter copulas. We fi…nd that dependence decreases when passing from older generations to younger generations. Not only the level of dependence but also its features - as measured by the copula - change across generations: the best-fi…t Archimedean copula is not the same across generations. Moreover, for all the generations under exam the single-parameter copula is dominated by the two-parameter one. The independence assumption produces quantifi…able mispricing of reversionary annuities. The misspeci…cation of the copula produces different mispricing effects on different generations. The research is conducted using a well-known dataset of double life contracts.

Keywords: copula, goodness-of-fi…t, signifi…cance test, stochastic mortality, generation effect, reversionary annuity

JEL Classification: C12, C18, G22, J12