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A Trend-Change Extension of the Cairns-Blake-Dowd Model

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  • Sweeting, P. J.

Abstract

This paper builds on the two-factor mortality model known as the Cairns-Blake-Dowd (CBD) model, which is used to project future mortality. It is shown that these two factors do not follow a random walk, as proposed in the original model, but that each should instead be modelled as a random fluctuation around a trend, the trend changing periodically. The paper uses statistical techniques to determine the points at which there are statistically significant changes in each trend. The frequency of change in each trend is then used to project the frequency of future changes, and the sizes of historical changes are used to project the sizes of future changes. The results are then presented as fan charts, and used to estimate the range of possible future outcomes for period life expectancies. These projections show that modelling mortality rates in this way leaves much greater uncertainty over future life expectancy in the long term.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:anacsi:v:5:y:2011:i:02:p:143-162_00
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    Cited by:

    1. Simon Schnürch & Torsten Kleinow & Ralf Korn, 2021. "Clustering-Based Extensions of the Common Age Effect Multi-Population Mortality Model," Risks, MDPI, vol. 9(3), pages 1-32, March.
    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. 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.
    4. 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.
    5. Börger, Matthias & Schupp, Johannes, 2018. "Modeling trend processes in parametric mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 369-380.
    6. Ralph Stevens, 2017. "Managing Longevity Risk by Implementing Sustainable Full Retirement Age Policies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1203-1230, December.
    7. Marie-Pier Bergeron-Boucher & Søren Kjærgaard & James E. Oeppen & James W. Vaupel, 2019. "The impact of the choice of life table statistics when forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(43), pages 1235-1268.
    8. Li, Johnny Siu-Hang & Liu, Yanxin, 2021. "Recent declines in life expectancy: Implication on longevity risk hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 376-394.
    9. 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.
    10. Börger, Matthias & Russ, Jochen & Schupp, Johannes, 2021. "It takes two: Why mortality trend modeling is more than modeling one mortality trend," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 222-232.
    11. Hong Li & Johnny Siu-Hang Li, 2017. "Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements," Demography, Springer;Population Association of America (PAA), vol. 54(3), pages 1073-1095, June.
    12. Li, Johnny Siu-Hang & Liu, Yanxin, 2020. "The heat wave model for constructing two-dimensional mortality improvement scales with measures of uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 1-26.

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