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Modeling multi-country mortality dependence and its application in pricing survivor index swaps—A dynamic copula approach

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  • Wang, Chou-Wen
  • Yang, Sharon S.
  • Huang, Hong-Chih

Abstract

This paper introduces mortality dependence in multi-country mortality modeling using a dynamic copula approach. Specifically, we use time-varying copula models to capture the mortality dependence structure across countries, examining both symmetric and asymmetric dependence structures. In addition, to capture the phenomenon of a heavy tail for the multi-country mortality index, we consider not only the setting of Gaussian innovations but also non-Gaussian innovations under the Lee–Carter framework model. As tests of the goodness of fit of different dynamic copula models, the pattern of mortality dependence, and the distribution of the innovations, we used empirical mortality data from Finland, France, the Netherlands, and Sweden. To understand the effect of mortality dependence on longevity derivatives, we also built a valuation framework for pricing a survivor index swap, then investigated the fair swap rates of a survivor swap numerically. We demonstrate that failing to consider the dynamic copula mortality model and non-Gaussian innovations would lead to serious underestimations of the swap rates and loss reserves.

Suggested Citation

  • Wang, Chou-Wen & Yang, Sharon S. & Huang, Hong-Chih, 2015. "Modeling multi-country mortality dependence and its application in pricing survivor index swaps—A dynamic copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 30-39.
  • Handle: RePEc:eee:insuma:v:63:y:2015:i:c:p:30-39
    DOI: 10.1016/j.insmatheco.2015.03.019
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    3. David Blake & Marco Morales & Jing Ai & Patrick L. Brockett & Linda L. Golden & Wei Zhu, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 319-343, April.
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    5. Uditha Balasooriya & Johnny Siu-Hang Li & Jackie Li, 2020. "The Impact of Model Uncertainty on Index-Based Longevity Hedging and Measurement of Longevity Basis Risk," Risks, MDPI, vol. 8(3), pages 1-27, August.
    6. Chen, Fen-Ying & Yang, Sharon S. & Huang, Hong-Chih, 2022. "Modeling pandemic mortality risk and its application to mortality-linked security pricing," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 341-363.
    7. Wang, Zihe & Li, Johnny Siu-Hang, 2016. "A DCC-GARCH multi-population mortality model and its applications to pricing catastrophic mortality bonds," Finance Research Letters, Elsevier, vol. 16(C), pages 103-111.
    8. Wang, Rui & Liao, Xin & Peng, Zuoxiang, 2017. "Second-order expansions for maxima of dynamic bivariate normal copulas," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 275-283.
    9. Zhou, Rui & Ji, Min, 2021. "Modelling mortality dependence: An application of dynamic vine copula," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 241-255.
    10. Tsai, Cary Chi-Liang & Wu, Adelaide Di, 2020. "Incorporating hierarchical credibility theory into modelling of multi-country mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 37-54.
    11. Chen, An & Li, Hong & Schultze, Mark, 2022. "Collective longevity swap: A novel longevity risk transfer solution and its economic pricing," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 227-249.

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