Modeling multi-population life expectancy: a cointegration approach

The continuous improvements in mortality rates and life expectancy of the last century have been given a great deal of attention by academics, life insurers, financial engineers, and pension planners, particularly in developed countries. Mortality-linked securities such as longevity bonds (EIB & BNP as well as the Swiss Re bond), survivor swaps, and mortality forward (q-forward) have appeared recently in the industry to help operators hedge such risks. A classic survivor bond has been proposed in the literature with coupon payment linked to the life time of the last survivor in an insurance reference portfolio. It appears therefore to be crucial to improve the accuracy of future life expectancy forecasts. In this paper, the authors investigate time-varying dependency associated with common trends that drive regional life expectancy within Canada. The aim is to compare three major models that have recently appeared in the literature, the autoregressive integrated moving average (ARIMA), the vector autoregressive model (VAR) and the vector error correction model (VECM), to analyze the common factors that have determined a progressive shift of life expectancy in specific Canadian regions. Results show that VECM performs better than VAR and ARIMA in terms of backtesting and its ability to capture the dynamics of common life expectancy. Findings from these analyses are useful for local insurers and demographers in their goal to project life expectancy improvements and also to forecast future trends.