Multi-population mortality models : a factor copula approach

Hua CHEN, Richard MACMINN, Tao SUN

Research output: Journal PublicationsJournal Article (refereed)

16 Citations (Scopus)

Abstract

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
Volume63
Early online date15 Apr 2015
DOIs
Publication statusPublished - Jul 2015
Externally publishedYes

Fingerprint

Copula
Mortality
Model
Factors
Copula Models
Two-stage Procedure
Cointegration
Model Specification
Factor Models
Hedging
Time Series Analysis
Maximum Entropy
Risk Management
Long-run
Modeling
Higher Dimensions
Pricing
Filter
Converge

Keywords

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

Cite this

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title = "Multi-population mortality models : a factor copula approach",
abstract = "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 = "Factor copulas, Maximum entropy principle, Mortality/longevity risk hedging, Mortality/longevity risk pricing, Multi-population mortality model",
author = "Hua CHEN and Richard MACMINN and Tao SUN",
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Multi-population mortality models : a factor copula approach. / CHEN, Hua; MACMINN, Richard; SUN, Tao.

In: Insurance: Mathematics and Economics, Vol. 63, 07.2015, p. 135-146.

Research output: Journal PublicationsJournal Article (refereed)

TY - JOUR

T1 - Multi-population mortality models : a factor copula approach

AU - CHEN, Hua

AU - MACMINN, Richard

AU - SUN, Tao

PY - 2015/7

Y1 - 2015/7

N2 - 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.

AB - 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.

KW - Factor copulas

KW - Maximum entropy principle

KW - Mortality/longevity risk hedging

KW - Mortality/longevity risk pricing

KW - Multi-population mortality model

UR - http://commons.ln.edu.hk/sw_master/5944

U2 - 10.1016/j.insmatheco.2015.03.022

DO - 10.1016/j.insmatheco.2015.03.022

M3 - Journal Article (refereed)

VL - 63

SP - 135

EP - 146

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

ER -