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Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II

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  • Rui Zhou
  • Yujiao Wang
  • Kai Kaufhold
  • Johnny Li
  • Ken Tan

Abstract

Recently Cairns et al. introduced a general framework for modeling the dynamics of mortality rates of two related populations simultaneously. Their method ensures that the resulting forecasts do not diverge over the long run by modeling the difference in the stochastic factors between the two populations with a mean-reverting autoregressive process. In this article, we investigate how the modeling of the stochastic factors may be improved by using a vector error correction model. This extension is highly intuitive, allowing us to visualize the cross-correlations and the long-term equilibrium relation between the two populations. Another key benefit is that this extension does not require the user to assume which one of the two populations is dominant. This benefit is important because, as we demonstrate, it is not always easy to identify the dominant population, even if one population is much larger than the other. We illustrate our proposed extension with data from a pair of populations and apply it to the calculation of Solvency II risk capital.

Suggested Citation

  • Rui Zhou & Yujiao Wang & Kai Kaufhold & Johnny Li & Ken Tan, 2014. "Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 150-167.
    • Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:150-167
    DOI: 10.1080/10920277.2013.872553
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    Cited by:

    1. Snorre Jallbjørn & Søren Fiig Jarner, 2022. "Sex Differential Dynamics in Coherent Mortality Models," Forecasting, MDPI, vol. 4(4), pages 1-26, September.
    2. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    3. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    4. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    5. Liu, Yanxin & Li, Johnny Siu-Hang, 2016. "It’s all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 301-319.
    6. Arnold, Séverine & Glushko, Viktoriya, 2021. "Cause-specific mortality rates: Common trends and differences," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 294-308.
    7. Cuixia Liu & Yanlin Shi, 2023. "Extensions of the Lee–Carter model to project the data‐driven rotation of age‐specific mortality decline and forecast coherent mortality rates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(4), pages 813-834, July.
    8. Thilini Dulanjali Kularatne & Jackie Li & Yanlin Shi, 2022. "Forecasting Mortality Rates with a Two-Step LASSO Based Vector Autoregressive Model," Risks, MDPI, vol. 10(11), pages 1-23, November.
    9. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2020. "A more meaningful parameterization of the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 1-8.
    10. Li, Hong & Lu, Yang, 2017. "Coherent Forecasting Of Mortality Rates: A Sparse Vector-Autoregression Approach," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 563-600, May.
    11. Hunt, Andrew & Blake, David, 2018. "Identifiability, cointegration and the gravity model," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 360-368.
    12. Jarner, Søren F. & Jallbjørn, Snorre, 2020. "Pitfalls and merits of cointegration-based mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 80-93.
    13. Shang, Han Lin & Haberman, Steven & Xu, Ruofan, 2022. "Multi-population modelling and forecasting life-table death counts," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 239-253.
    14. 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.
    15. Li, Johnny Siu-Hang & Zhou, Rui & Hardy, Mary, 2015. "A step-by-step guide to building two-population stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 121-134.
    16. Selin Ozen & c{S}ule c{S}ahin, 2021. "A Two-Population Mortality Model to Assess Longevity Basis Risk," Papers 2101.06690, arXiv.org.
    17. Ahmadi, Seyed Saeed & Li, Johnny Siu-Hang, 2014. "Coherent mortality forecasting with generalized linear models: A modified time-transformation approach," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 194-221.
    18. Selin Özen & Şule Şahin, 2021. "A Two-Population Mortality Model to Assess Longevity Basis Risk," Risks, MDPI, vol. 9(2), pages 1-19, February.
    19. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    20. Rui Zhou & Guangyu Xing & Min Ji, 2019. "Changes of Relation in Multi-Population Mortality Dependence: An Application of Threshold VECM," Risks, MDPI, vol. 7(1), pages 1-18, February.
    21. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2016. "Coherent modeling of male and female mortality using Lee–Carter in a complex number framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 130-137.

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