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Nonlinear Modeling of Mortality Data and Its Implications for Longevity Bond Pricing

Author

Listed:
  • Huijing Li

    (College of Finance, Nanjing Agricultural University, Nanjing 210095, China)

  • Rui Zhou

    (Department of Economics, The University of Melbourne, Melbourne, VIC 3010, Australia)

  • Min Ji

    (Department of Mathematics, Towson University, Towson, MD 21252, USA)

Abstract

Human mortality has been improving faster than expected over the past few decades. This unprecedented improvement has caused significant financial stress to pension plan sponsors and annuity providers. The widely recognized Lee–Carter model often assumes linearity in its period effect as an integral part of the model. Nevertheless, deviation from linearity has been observed in historical mortality data. In this paper, we investigate the applicability of four nonlinear time-series models: threshold autoregressive model, Markov switching model, structural change model, and generalized autoregressive conditional heteroskedasticity model for mortality data. By analyzing the mortality data from England and Wales and Italy spanning the years 1900 to 2019, we compare the goodness of fit and forecasting performance of the four nonlinear models. We then demonstrate the implications of nonlinearity in mortality modeling on the pricing of longevity bonds as a practical illustration of our findings.

Suggested Citation

  • Huijing Li & Rui Zhou & Min Ji, 2023. "Nonlinear Modeling of Mortality Data and Its Implications for Longevity Bond Pricing," Risks, MDPI, vol. 11(12), pages 1-25, November.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:12:p:207-:d:1289443
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    References listed on IDEAS

    as
    1. Zhou, Rui, 2019. "Modelling Mortality Dependence With Regime-Switching Copulas," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 373-407, May.
    2. Hansen, Bruce E., 1999. "Threshold effects in non-dynamic panels: Estimation, testing, and inference," Journal of Econometrics, Elsevier, vol. 93(2), pages 345-368, December.
    3. Hainaut, Donatien, 2012. "Multidimensional Lee–Carter model with switching mortality processes," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 236-246.
    4. Sweeting, P. J., 2011. "A Trend-Change Extension of the Cairns-Blake-Dowd Model," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 143-162, September.
    5. Frank van Berkum & Katrien Antonio & Michel Vellekoop, 2016. "The impact of multiple structural changes on mortality predictions," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(7), pages 581-603, August.
    6. Andreas Milidonis & Yijia Lin & Samuel Cox, 2011. "Mortality Regimes and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 266-289.
    7. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
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