Valuation of long-term care options embedded in life annuities

An Chen,Thorsten Sehner,Joël Wagner,Michel Fuino

doi:10.1017/s1748499521000063

Abstract

AbstractIn most industrialised countries, one of the major societal challenges is the demographic change coming along with the ageing of the population. The increasing life expectancy observed over the last decades underlines the importance to find ways to appropriately cover the financial needs of the elderly. A particular issue arises in the area of health, where sufficient care must be provided to a growing number of dependent elderly in need of long-term care (LTC) services. In many markets, the offering of life insurance products incorporating care options and LTC insurance products is generally scarce. In our research, we therefore examine a life annuity product with an embedded care option potentially providing additional financial support to dependent persons. To evaluate the care option, we determine the minimum price that the annuity provider requires and the policyholder’s willingness to pay for the care option. For the latter, we employ individual utility functions taking account of the policyholder’s condition. We base our numerical study on recently developed transition probability data from Switzerland. Our findings give new and realistic insights into the nature and the utility of life annuity products proposing an embedded care option for tackling the financing of LTC needs.

Highlights

Nowadays, ageing is set to become one of the main concerns in most developed economies
We find that κa∗ and κa∗ increase in γ, i.e. the more risk averse the policyholder is, the smaller, in case of γ ∈ [0, 1), respectively, the greater, in case of γ > 1, the utility impact of the care dependency must be in order for the trade of the care option to occur
We examine an long-term care (LTC) option embedded in a life annuity which, if contracted for a fee, entails an increase of the annuity payments in case of care dependency

Summary

Introduction

Nowadays, ageing is set to become one of the main concerns in most developed economies. From an individual’s perspective, becoming care-dependent has both health and financial consequences (Guillén & Comas-Herrera, 2012; Scheil-Adlung & Bonan, 2013). For the latter, it is especially alarming that the households’ care expenses have recently disproportionately increased (ZhouRichter et al, 2010). Assuring proper funding is cornerstone (Costa-Font et al, 2015; Costa-Font et al, 2017)

Objectives

Results

Conclusion