Cohort and Value-Based Multi-Country Longevity Risk Management

Michael Sherris, Yajing Xu and Jonathan Ziveyi

Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson-Siegel model for the dynamics of interest rates. Index based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer’s portfolio and hedging strategies. We illustrate the effectiveness of using a value–based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks.