Geographical Diversification and Longevity Risk Mitigation in Annuity Portfolios

This paper provides a method to assess the risk relief deriving from a foreign expansion by a life-insurance company. We build a parsimonious continuous-time model for longevity risk, that captures the dependence across different ages in domestic versus foreign populations. We provide three measures of the diversification effects of expanding an annuity portfolio toward a foreign population. The reduction in the risk margin, computed à la Solvency II, provides a regulation-consistent measure of the benefit in the tail risk. The change in the volatility of the average mortality intensity of a portfolio provides an intuitive measure of the change in the longevity risk of a portfolio. The Diversification Index provides a synthetic assessment of the diversification benefit of combining different populations in one portfolio. We calibrate the model to portray the case of a UK annuity portfolio expanding internationally towards Italian policyholders. Our application shows that the longevity risk diversidication benefits of an international expansion are sizable, in particular when interest rates are low