Multi-Population Mortality Models: A Factor Copula Approach

42 Pages Posted: 31 Dec 2014 Last revised: 16 Dec 2016

See all articles by Hua Chen

Hua Chen

University of Hawaii at Manoa

Richard D. MacMinn

National Chengchi University; The University of Texas

Tao Sun


Date Written: November 30, 2014


Modeling mortality co-movements for multiple populations have significant implications for mortality/longevity risk management. A few two-population mortality models have been proposed to date. They are typically based on the assumption that the forecasted mortality experiences of two or more related populations converge in the long run. This assumption might be justified by the long-term mortality co-integration and thus be applicable to longevity risk modeling. However, it seems too strong to model the short term mortality dependence. In this paper, we propose a two-stage procedure based on the time series analysis and a factor copula approach to model mortality dependence for multiple populations. In the first stage, we filter the mortality dynamics of each population using an ARMA-GARCH process with heavy-tailed innovations. In the second stage, we model the residual risk using a one-factor copula model that is widely applicable to high dimension data and very flexible in terms of model specification. We then illustrate how to use our mortality model and the maximum entropy approach for mortality risk pricing and hedging. Our model generates par spreads that are very close to the actual spreads of the Vita III mortality bond. We also propose a longevity trend bond and demonstrate how to use this bond to hedge residual longevity risk of an insurer with both annuity and life books of business.

Keywords: Multi-population mortality model, factor copulas, maximum entropy principle, mortality/longevity risk pricing and hedging

Suggested Citation

Chen, Hua and MacMinn, Richard D. and Sun, Tao, Multi-Population Mortality Models: A Factor Copula Approach (November 30, 2014). Insurance: Mathematics and Economics, Forthcoming, Fox School of Business Research Paper No. 15-052, Available at SSRN: or

Hua Chen (Contact Author)

University of Hawaii at Manoa ( email )

2404 Maile Way, E-602e
Honolulu, HI 96822
United States
(808) 956-8063 (Phone)
(808) 956-9887 (Fax)

Richard D. MacMinn

National Chengchi University ( email )


The University of Texas ( email )

2317 Speedway
Austin, TX 78712
United States

Tao Sun


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