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 e¤ects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. Dependence is modelled through copula functions. We consider Archimedean single and multi-parameter copulas. We …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-…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 quanti…able mispricing of reversionary annuities. The misspeci…cation of the copula produces di¤erent mispricing e¤ects on di¤erent generations. The research is conducted using a well-known dataset of double life contracts. JEL classi…cation: C12, C18, G22, J12.