Multi-population mortality models : a factor copula approach

Hua CHEN, Richard MACMINN, Tao SUN

Research output: Journal PublicationsJournal Article (refereed)peer-review

48 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)135-146
Number of pages12
JournalInsurance: Mathematics and Economics
Early online date15 Apr 2015
Publication statusPublished - Jul 2015
Externally publishedYes


  • Factor copulas
  • Maximum entropy principle
  • Mortality/longevity risk hedging
  • Mortality/longevity risk pricing
  • Multi-population mortality model


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