Spouses’ Dependence across Generations and Pricing Impact on Reversionary Annuities

Elisa Luciano,Jaap Spreeuw,Elena Vigna

doi:10.3390/risks4020016

Elisa Luciano, Jaap Spreeuw + Show 1 more

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https://doi.org/10.3390/risks4020016

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Journal: Risks	Publication Date: May 25, 2016
Citations: 33	License type: CC BY 4.0

Affiliation: City, University of London, Collegio Carlo Alberto

Abstract

This paper studies the dependence between coupled lives, i.e., the spouses’ dependence, across different generations, and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. We find that a generation-based model is important, since spouses’ dependence decreases when passing from older generations to younger generations. The independence assumption produces quantifiable mispricing of reversionary annuities, with different effects on different generations. The research is conducted using a well-known dataset of double life contracts.

Highlights

Longevity risk, i.e., the risk that individuals live longer than expected, has become a relevant issue for the sustainability of public and private pension systems
This paper models the mortality of couples using a copula approach: the joint survival probability is written in terms of the marginal survival probabilities and a function—the survival copula—which represents spouses’ dependence
Each figure reports the analytical survival function Sz (t) for initial age z and the empirical survival function obtained with the Kaplan–Meier methodology

Summary

Introduction

I.e., the risk that individuals live longer than expected, has become a relevant issue for the sustainability of public and private pension systems. The recent surge in these contracts, together or as a substitute of reinsurance treaties, proves that the burden of longevity is important, and its quantification is key (see [2]). Within these arrangements and the assessments they require, attention should be paid to annuities or pensions payable to couples. Both in the first and in the second pillar of pension provision, the offer of insurance products includes last survivor and reversionary annuities. An accurate pricing scheme of joint survivorship, which goes beyond the elementary assumption of independence between the lifetimes of members of a couple, Risks 2016, 4, 16; doi:10.3390/risks4020016 www.mdpi.com/journal/risks

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