Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-14T06:06:00.688Z Has data issue: false hasContentIssue false
  • English
  • Français

A Value-at-Risk framework for longevity trend risk

Published online by Cambridge University Press:  25 January 2013

S. J. Richards ,
I. D. Currie  and
G. P. Ritchie
Get access Rights & Permissions [Opens in a new window]

Abstract

Longevity risk faced by annuity portfolios and defined-benefit pension schemes is typically long-term, i.e. the risk is of an adverse trend which unfolds over a long period of time. However, there are circumstances when it is useful to know by how much expectations of future mortality rates might change over a single year. Such an approach lies at the heart of the one-year, value-at-risk view of reserves, and also for the pending Solvency II regime for insurers in the European Union. This paper describes a framework for determining how much a longevity liability might change based on new information over the course of one year. It is a general framework and can accommodate a wide choice of stochastic projection models, thus allowing the user to explore the importance of model risk. A further benefit of the framework is that it also provides a robustness test for projection models, which is useful in selecting an internal model for management purposes.

Keywords

Longevity riskmortality projectionsvalue-at-riskSolvency IImodel riskLee-CarterAge-Period-CohortCairns-Blake-DowdP-spline
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 19 , Issue 1 , March 2014 , pp. 116 - 139
Copyright
Copyright © Institute and Faculty of Actuaries 2013 

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.)

References

Börger, M. (2010). Deterministic shock vs. stochastic value-at-risk: An analysis of the Solvency II standard model approach to longevity risk. Blätter DGVFM, 31, 225–259.Google Scholar
Booth, H., Tickle, L. (2008). Mortality modelling and forecasting: a review of methods. Annals of Actuarial Science Vol. 3, Parts 1 and 2, page 8.Google Scholar
Brouhns, N., Denuit, M., Vermunt, J.K. (2002). A Poisson log-bilinear approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373–393.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73, 687–718.CrossRefGoogle 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. (2011). Modelling and management of longevity risk: approximations to survival functions and dynamic hedging. Insurance: Mathematics and Economics, 49, 438–453.Google Scholar
Clayton, D., Schifflers, E. (1987). Models for temporal variation in cancer rates. II: age-period-cohort models. Statistics in Medicine, 6, 469–481.Google Scholar
Continuous Mortality Investigation (2009). User Guide for The CMI Mortality Projections Model: ‘CMI 2009’, November 2009.Google Scholar
Continuous Mortality Investigation (2010). The CMI Mortality Projections Model, ‘CMI 2010’, Working Paper 49, November 2010.Google Scholar
Currie, I.D., Durban, M., Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279–298.CrossRefGoogle Scholar
Currie, I.D. (2011). Modelling and forecasting the mortality of the very old. ASTIN Bulletin, 41, 419–427.Google Scholar
Currie, I.D. (2012). Forecasting with the age-period-cohort model?, Proceedings of 27th International Workshop on Statistical Modelling, Prague, 87–92.Google Scholar
De Boor, C. (2001). A practical guide to splines, Applied Mathematical Sciences, 27, Springer-Verlag, New York.Google Scholar
Delwarde, A., Denuit, M., Eilers, P.H.C. (2007). Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: a penalized likelihood approach. Statistical Modelling, 7, 29–48.CrossRefGoogle Scholar
Djeundje, V.A.B., Currie, I.D. (2011). Smoothing dispersed counts with applications to mortality data. Annals of Actuarial Science, 5(I), 33–52.Google Scholar
The Economist (2012). The ferment of finance, Special report on financial innovation, February 25th 2012, p8.Google Scholar
Eilers, P.H.C., Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89–121.Google Scholar
European Commission (2010). QIS5 Technical Specifications, Brussels, p152.Google Scholar
Gompertz, B. (1825). The nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society, 115, 513–585.Google Scholar
Harrell, F.E., Davis, C.E. (1982). A new distribution-free quantile estimator. Biometrika, 69, 635–640.CrossRefGoogle Scholar
Hyndman, R.J., Fan, Y. (1996). Sample Quantiles in Statistical Packages. American Statistician (American Statistical Association), November 1996, 50(4), 361–365.Google Scholar
Lee, R.D., Carter, L. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
Lindley, D.V., Scott, W. F. (1984). New Cambridge Elementary Statistical Tables. Cambridge University Press, p35.Google Scholar
Makin, S.J. (2011a). Reserving and Regulatory Requirements. In: Longevity Risk, E. McWilliam (ed.), Risk Books, 147–174.Google Scholar
Makin, S.J. (2011b). Economic Capital, Modelling and Longevity Risk. In: Longevity Risk, E. McWilliam (ed.), Risk Books, 175–199.Google Scholar
Oeppen, J., Vaupel, J.W. (2004). Broken Limits to Life Expectancy. Science, 296, 1029–1031.CrossRefGoogle Scholar
Plat, R. (2011). One-year Value-at-Risk for longevity and mortality. Insurance: Mathematics and Economics, 49(3), 462–470.Google Scholar
R Development Core Team (2011). R: a language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, http://www.r-project.org. Accessed on 11th October 2012.Google Scholar
Renshaw, A.E., Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556–570.Google Scholar
Richards, S.J., Kirkby, J.G., Currie, I.D. (2006). The Importance of Year of Birth in Two-Dimensional Mortality Data. British Actuarial Journal, 12(I), 5–61.Google Scholar
Richards, S.J., Ellam, J.R., Hubbard, J., Lu, J.L.C., Makin, S.J., Miller, K.A. (2007). Two-dimensional mortality data: patterns and projections. British Actuarial Journal, 13(III), No. 59, 479–555.Google Scholar
Richards, S.J. (2008). Detecting year-of-birth mortality patterns with limited data. Journal of the Royal Statistical Society, Series A (2008), 171, Part 1, 279–298.Google Scholar
Richards, S.J., Currie, I.D. (2009). Longevity risk and annuity pricing with the Lee-Carter model. British Actuarial Journal, 15(II), No. 65, 317–365(with discussion).Google Scholar
Richards, S.J. (2010). Selected Issues in Modelling Mortality by Cause and in Small Populations. British Actuarial Journal, 15 (supplement), 267–283.Google Scholar
Richards, S.J., Currie, I.D. (2011). Extrapolating mortality projections by age. Life and Pensions Risk magazine, June 2011, 34–38.Google Scholar
Svensson, L.E.O. (1994). Estimating and interpreting forward interest rates: Sweden 1992–1994, Working paper of the International Monetary Fund, 94.114.Google Scholar