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Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models

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  • Yang, Sharon S.
  • Yue, Jack C.
  • Huang, Hong-Chih

Abstract

This research proposes a mortality model with an age shift to project future mortality using principal component analysis (PCA). Comparisons of the proposed PCA model with the well-known models--the Lee-Carter model, the age-period-cohort model (Renshaw and Haberman, 2006), and the Cairns, Blake, and Dowd model--employ empirical studies of mortality data from six countries, two each from Asia, Europe, and North America. The mortality data come from the human mortality database and span the period 1970-2005. The proposed PCA model produces smaller prediction errors for almost all illustrated countries in its mean absolute percentage error. To demonstrate longevity risk in annuity pricing, we use the proposed PCA model to project future mortality rates and analyze the underestimated ratio of annuity price for whole life annuity and deferred whole life annuity product respectively. The effect of model risk on annuity pricing is also investigated by comparing the results from the proposed PCA model with those from the LC model. The findings can benefit actuaries in their efforts to deal with longevity risk in pricing and valuation.

Suggested Citation

  • Yang, Sharon S. & Yue, Jack C. & Huang, Hong-Chih, 2010. "Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 254-270, February.
  • Handle: RePEc:eee:insuma:v:46:y:2010:i:1:p:254-270
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    References listed on IDEAS

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    1. Pablo Antolín, 2007. "Longevity Risk and Private Pensions," OECD Working Papers on Insurance and Private Pensions 3, OECD Publishing.
    2. Wilkie, A. D. & Waters, H. R. & Yang, S., 2003. "Reserving, Pricing and Hedging For Policies with Guaranteed Annuity Options," British Actuarial Journal, Cambridge University Press, vol. 9(02), pages 263-391, June.
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    4. Bauer, Daniel & Weber, Frederik, 2007. "Assessing Investment and Longevity Risks within Immediate Annuities," Discussion Papers in Business Administration 1982, University of Munich, Munich School of Management.
    5. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, pages 4942-4956.
    6. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, pages 195-214.
    7. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, pages 4942-4956.
    8. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
    9. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
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    11. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, pages 373-393.
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    Citations

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    Cited by:

    1. David Blake & Christophe Courbage & Richard MacMinn & Michael Sherris, 2011. "Longevity Risk and Capital Markets: The 2010–2011 Update," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(4), pages 489-500, October.
    2. Lee, Yung-Tsung & Wang, Chou-Wen & Huang, Hong-Chih, 2012. "On the valuation of reverse mortgages with regular tenure payments," Insurance: Mathematics and Economics, Elsevier, pages 430-441.
    3. Mitchell, Daniel & Brockett, Patrick & Mendoza-Arriaga, Rafael & Muthuraman, Kumar, 2013. "Modeling and forecasting mortality rates," Insurance: Mathematics and Economics, Elsevier, pages 275-285.
    4. repec:eee:insuma:v:75:y:2017:i:c:p:151-165 is not listed on IDEAS
    5. Blake, David & Brockett, Patrick & Cox, Samuel & MacMinn, Richard, 2011. "Longevity risk and capital markets: The 2009-2010 update," MPRA Paper 28868, University Library of Munich, Germany.
    6. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2017. "Cohort effects in mortality modelling: a Bayesian state-space approach," Papers 1703.08282, arXiv.org.
    7. Shang, Han Lin & Smith, Peter W.F. & Bijak, Jakub & Wiśniowski, Arkadiusz, 2016. "A multilevel functional data method for forecasting population, with an application to the United Kingdom," International Journal of Forecasting, Elsevier, vol. 32(3), pages 629-649.
    8. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.
    9. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2010. "Evaluating the goodness of fit of stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 255-265, December.

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