Understanding Patterns of Mortality Homogeneity and Heterogeneity Across Countries and Their Role in Modeling Mortality Dynamics and Hedging Longevity Risk

Abstract

Understanding patterns of mortality homogeneity and heterogeneity across countries can assist in modeling mortality dynamics and in hedging longevity risk. This study proposes a methodology, based on the graduation method, to detect differences in mortality rates across different populations. Using an index ${\widehat{h}}^2$ based on the partial standard mortality ratio, we measure mortality homogeneity and heterogeneity, then conduct an empirical study across countries with emerging and developed markets. The results of model fitting show that it is inappropriate to use a coherent mortality model for the mortality-heterogeneous populations. In an application, we demonstrate that a reinsurer can utilize information concerning mortality homogeneity/heterogeneity for pooling risk in its books of life insurance and annuity businesses and increase overall hedge effectiveness. The coherent mortality model can help reduce the volatility of the reinsurer’s profit and help the reinsurer diversify its longevity risk.

ACKNOWLEDGMENTS

We thank anonymous referees for their helpful comments, which substantially improved this article.

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Notes

1 See "MSCI Emerging Markets Indexes," retrieved 2015-02-02.

2 The data collection efforts focused on The Human Mortality Database (HMD), Department of Statistics, Ministry of Health Sample registration system (for India), World Bank, and other sources. It is freely available on the center’s website (www.irfrc.com).

3 Australia, Bangladesh, China, Hong Kong, India, Indonesia, Japan, Malaysia, Nepal, New Zealand, Pakistan, Philippines, Republic of Korea, Singapore, Sri Lanka, Taiwan, Thailand, and Vietnam. The search was conducted at the end of 2012.

4 We ran the simulation 5,000 times to forecast life expectancy.

5 $R^{*}\left(ij\right)$ is mortality homogeneity’s $R(ij)$ divided by mortality heterogeneity’s $R(ij).$ Therefore, if $R^{*}\left(ij\right)$ is higher than 1 then the performance of mortality homogeneity is better than for mortality heterogeneity, and vice versa.

6 For each model, we run 5,000 simulations to forecast the future mortality rate. See Appendix B for the mortality forecast.

7 We also calculate profit functions for men aged 60 and 70 years; the results are similar to those for 50 years. In the following numerical analysis, we only demonstrate for men aged 50 years.

Additional information

Funding

Sharon S. Yang is supported in part by the MOST 102-2410-H-008-011-MY3.