Modeling Life Expectancy at Birth for Multi-Population: A Cointegration Approach

Abstract

The continuous improvements in mortality rates and life expectancy from the last century have been giving particular attention from academics, life insurers, financial engineers and pension planners, particularly in developped countries. Mortality-linked securities such as longevity bonds (EIB & BNP as well as Swiss Re bonds), survivor swaps or mortality forward (q-forward) have appeared recently in the industry to help operators hegding such risks. A classical survivor bond has been proposed in literature with coupons payment linked to life time of the last survivor in insurance reference portfolio. It appears therefore to be crucial to improve the accuracy of future life expectancy. In this paper, we investigate time varying dependency associated with common trends which drive regional life expectancy within Canada. We aim to compare the three main models appeared recently in literature such as Autoregressive Integrated Moving Average (ARIMA), Vector Autoregressive model (VAR) and Vector Error Correction Model (VECM), to analyse the common factors that have determined a progressive shift of life expectancy in six Canadian regions. The latter shows better performance over VAR and ARIMA in terms of backtesting and its ability to capture the dynamics of common life expectancy. Findings from these analysis are useful for local insurers and demographers in their goal to project life expectancy improvements and also to forecast future trends.