Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Longevity risk in portfolios of pension annuities," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 505-519, April.
- 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.
- Hyndman, Rob J. & Shahid Ullah, Md., 2007.
"Robust forecasting of mortality and fertility rates: A functional data approach,"
Computational Statistics & Data Analysis,
Elsevier, vol. 51(10), pages 4942-4956, June.
- Rob J. Hyndman & Md. Shahid Ullah, 2005. "Robust forecasting of mortality and fertility rates: a functional data approach," Monash Econometrics and Business Statistics Working Papers 2/05, Monash University, Department of Econometrics and Business Statistics.
- Pablo Antolin, 2007. "Longevity Risk and Private Pensions," Financial Market Trends, OECD Publishing, vol. 2007(1), pages 107-128.
- Pablo Antolín, 2007. "Longevity Risk and Private Pensions," OECD Working Papers on Insurance and Private Pensions 3, OECD Publishing.
- Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
- 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.
- 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.
- 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.
- 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, vol. 31(3), pages 373-393, December. Full references (including those not matched with items on IDEAS)