Hostname: page-component-89b8bd64d-9prln Total loading time: 0 Render date: 2026-05-11T22:51:12.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Demographic risk in deep-deferred annuity valuation

Published online by Cambridge University Press:  03 April 2017

Min Ji  and
Rui Zhou
Min Ji
Affiliation:
Department of Mathematics, Towson University, Towson, MD, USA
Rui Zhou*
Affiliation:
Warren Centre for Actuarial Studies and Research, University of Manitoba, Winnipeg, MB, Canada R3T 5V4
*
*Correspondence to: Rui Zhou, Warren Centre for Actuarial Studies and Research, University of Manitoba, 181 Freedman Crescent, Winnipeg, MB, Canada R3T 5V4. Tel: (1)204-474-9783; E-mail: rui.zhou@umanitoba.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

A deep-deferred annuity is a deferred annuity where payments start very late in life, i.e. well after the normal retirement age. This annuity has received much attention lately as it was made accessible to 401(k) plans in the United States in 2014. By transferring the risk of outliving retirement savings at high ages to annuity providers, deep-deferred annuities provide annuitants with enhanced later-life financial security. However, the valuation of this annuity suffers from high uncertainty because the mortality data at high ages are sparse and possibly unreliable. In this paper, we use risk ratio to measure demographic risk in the valuation. Demographic risk is decomposed into the following four components: (1) mortality tail curve risk, (2) mortality improvement model risk, (3) parameter risk in mortality tail curves, and (4) parameter risk in mortality improvement rate models. Our quantitative analysis aims to provide insights into the development and risk management of deep-deferred annuities.

Keywords

High age mortalityMortality improvement rate modelDeep-deferred annuityModel riskParameter risk

Information

Type
Papers
Information
Annals of Actuarial Science , Volume 11 , Issue 2 , September 2017 , pp. 286 - 314
Copyright
© Institute and Faculty of Actuaries 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Arai, Y., Inagaki, H., Takayama, M., Abe, Y., Saito, Y., Takebayashi, T. & Hirose, N. (2014). Physical independence and mortality at the extreme limit of life span: supercentenarians study in Japan. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 69(4), 486–494.Google Scholar
Beard, R.E. (1963). A theory of mortality based on actuarial, biological, and medical considerations. Proceedings of International Population Conference, New York, 1, 611–625.Google Scholar
Beard, R.E. (1971). Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes. In W. Brass, Ed. Biological aspects of demography (pp. 57–68). Taylor & Francis, London.Google Scholar
Blake, D. & Turner, J.A. (2014). Longevity insurance annuities: lessons from the United Kingdom. Benefits Quarterly, 30(1), 39–47.Google Scholar
Brouhns, N., Denuit, M. & Van Keilegom, I. (2005). Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 2005(3), 212–224.Google Scholar
Brouhns, N., Denuit, M. & Vermunt, J.K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(2002), 373–393.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1–35.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D. & Khalaf-Allah, M. (2011). Bayesian stochastic mortality modelling for two populations. Astin Bulletin, 41(1), 29–59.Google Scholar
Danielsson, J., James, K.R., Valenzuela, M. & Zer, I. (2015). Model risk of risk models. Journal of Financial Stability, forthcoming, https://doi.org/10.2139/ssrn.2425689.Google Scholar
Dowd, K., Cairns, A.J.G., Blake, D., Coughlan, G.D. & Khalaf-Allah, M. (2011). A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15(2), 334–356.Google Scholar
Draper, D. (1995). Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society. Series B (Methodological) , 57(1), 45–97.Google Scholar
Gavrilov, L.A. & Gavrilova, N.S. (2011). Mortality measurement at advanced ages: a study of the social security administration death master file. North American Actuarial Journal, 15(3), 432–447.Google Scholar
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115(1825), 513–583.Google Scholar
Gong, G. & Webb, A. (2010). Evaluating the advanced life deferred annuity – an annuity people might actually buy. Insurance: Mathematics and Economics, 46(1), 210–221.Google Scholar
Greenwood, M. & Irwin, J.O. (1939). The biostatistics of senility. Human Biology, 11(1), 1–23.Google Scholar
Haberman, S. & Renshaw, A. (2012). Parametric mortality improvement rate modelling and projecting. Insurance: Mathematics and Economics, 50(3), 309–333.Google Scholar
Kannisto, V. (1992). Presentation at a Workshop on Old-Age Mortality. Odense University, Odense, Denmark.Google Scholar
Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Li, J.S.H. & Hardy, M.R. (2011). Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177–200.Google Scholar
Li, J.S.H., Chan, W.S. & Zhou, R. (2015 a). Semi-coherent multi-population mortality modeling: the impact on longevity risk securitization. Journal of Risk and Insurance (in press).Google Scholar
Li, J.S.H., Hardy, M.R. & Tan, K.S. (2009). Uncertainty in mortality forecasting: an extension to the classical Lee-Carter approach. Astin Bulletin, 39(1), 137–164.Google Scholar
Li, J.S.H., Zhou, R. & Hardy, M. (2015 b). A step-by-step guide to building two-population stochastic mortality models. Insurance: Mathematics and Economics, 65, 121–134.Google Scholar
Li, N. & Lee, R. (2005). Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method. Demography, 42(3), 575–594.Google Scholar
Milevsky, M. (2005). Real longevity insurance with a deductible: an introduction to advanced-life delayed annuities (ALDA). North American Actuarial Journal, 9(4), 109–122.Google Scholar
Mitchell, D., Brockett, P., Mendoza-Arriaga, R. & Muthuraman, K. (2013). Modeling and forecasting mortality rates. Insurance: Mathematics and Economics, 52(2), 275–285.Google Scholar
Mitchell, O.S. & McCarthy, D. (2002). Estimating international adverse selection in annuities. North American Actuarial Journal, 6(4), 38–54.Google Scholar
Nusbaum, T.J., Mueller, L.D. & Rose, M.R. (1996). Evolutionary patterns among measures of aging. Experimental Gerontology, 31(4), 507–516.Google Scholar
Office for National Statistics (2013). National population projections, 2012-based statistical bulletin. Available online at the address http://www.ons.gov.uk/ons/dcp171778_334975.pdf. Accessed on February 1st, 2016.Google Scholar
Oeppen, J. & Vaupel, J.W. (2002). Broken limits to life expectancy. Science, 296(5570), 1029–1031.Google Scholar
Panjer, H.H. & Russo, G. (1992). Parametric graduation of Canadian individual insurance mortality experience: 1982-1988. Proceedings of the Canadian Institute of Actuaries, 23, 378–449.Google Scholar
Panjer, H.H. & Tan, K.S. (1995). Graduation of Canadian Individual Insurance Mortality Experience: 1986-1992 . Canadian Institute of Actuaries, Retrieved from http://www.cia-ica.ca/docs/default-source/1995/9529e.pdf.Google Scholar
Perks, W. (1932). On some experiments on the graduation of tail curvetatistics. Journal of the Institute of Actuaries, 63, 12–40.Google Scholar
Renshaw, A. & Haberman, S. (2003). Lee-Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections. Applied Statistics, 52(1), 119–137.Google Scholar
Robine, J.M., Cheung, S.L.K., Saito, Y., Jeune, B., Parker, M.G. & Herrmann, F.R. (2010). Centenarians today: new insights on selection from the 5-COOP study. Current Gerontology and Geriatrics Research, 2010, Retrieved from http://dx.doi.org/10.1155/2010/120354.Google Scholar
Robine, J.M. & Saito, Y. (2003). Survival beyond age 100: the case of Japan. Population and Development Review, 29, 208–228.Google Scholar
Weitz, J.S. & Fraser, H.B. (2001). Explaining mortality rate plateaus. Proceedings of the National Academy of Sciences, 98(26), 15383–15386.Google Scholar
Willets, R.C. (2004). The Cohort Effect: Insights and Explanations. British Actuarial Journal, 10(4), 833–877.CrossRefGoogle Scholar
Wilson, C. (2001). On the scale of global demographic convergence 1950-2000. Population and Development Review, 27(1), 593–600.Google Scholar
Zhou, R., Wang, Y., Kaufhold, K., Li, J.S.H. & Tan, K.S. (2014). Modeling mortality of multiple populations with vector error correction models: applications to solvency II. North American Actuarial Journal, 18(1), 150–167.Google Scholar