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MODELLING MORTALITY FOR PENSION SCHEMES

Published online by Cambridge University Press:  16 January 2017

Andrew Hunt  and
David Blake
Andrew Hunt*
Affiliation:
Pacific Life Re, Tower Bridge House, St. Katharine's Way, London, E1W 1BA
David Blake
Affiliation:
Pensions Institute, Cass Business School, City University London, 106 Bunhill Row, London, EC1Y 8TZ E-Mail: D.Blake@city.ac.uk
*
E-Mail: a.o.d.hunt.00@cantab.net
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Abstract

For many pension schemes, a shortage of data limits their ability to use sophisticated stochastic mortality models to assess and manage their exposure to longevity risk. In this study, we develop a mortality model designed for such pension schemes, which compares the evolution of mortality rates in a sub-population with that observed in a larger reference population. We apply this approach to data from the CMI Self-Administered Pension Scheme study, using U.K. population data as a reference. We then use the approach to investigate the potential differences in the evolution of mortality rates between these two populations and find that, in many practical situations, basis risk is much less of a problem than is commonly believed.

Keywords

Mortality modellingage/period/cohort modelslongevity basis risk
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 2 , May 2017 , pp. 601 - 629
Copyright
Copyright © Astin Bulletin 2017 

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Footnotes

An extended version of this paper (Hunt and Blake, 2016a) is available on the Pensions Institute website (http://www.pensions-institute.org/workingpapers/wp1601.pdf), which contains additional results for female data and more technical details on the models used.

References

Blake, D., Cairns, A.J. and Dowd, K. (2006) Living with mortality: Longevity bonds and other mortality-linked securities. British Actuarial Journal, 12 (1), 153–197.CrossRefGoogle Scholar
Cairns, A.J. (2000) A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27 (3), 313–330.Google Scholar
Cairns, A.J., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D. and Khalaf-Allah, M. (2011) Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48 (3), 355–367.Google Scholar
Cairns, A.J., Blake, D., Dowd, K. and Kessler, A. (2015) Phantoms never die: Living with unreliable population data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 179 (4), 975–1005.CrossRefGoogle Scholar
Cairns, A.J., Dowd, K., Blake, D. and Coughlan, G.D. (2013) Longevity hedge effectiveness: A decomposition. Quantitative Finance, 14 (2), 217–235.Google Scholar
Continuous Mortality Investigation (2008) The graduations of the CMI self-administered pension schemes 2000–2006 mortality experience: Final “S1” series of mortality tables, Working Paper n. 35. URL http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-papers-34-and-35.Google Scholar
Continuous Mortality Investigation (2009) A prototype mortality projection model: Part one - an outline of the proposed approach, Working Paper n. 38. URL http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-papers-38-and-39.Google Scholar
Continuous Mortality Investigation (2011) An initial investigation into rates of mortality improvement for pensioners of self-administered pension schemes, Working Paper n. 53. URL http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-paper-53.Google Scholar
Continuous Mortality Investigation (2014a) Graduations of the CMI SAPS 2004-2011 mortality experience based on data collected by 30 June 2012: Final “S2” series of mortality tables, Working Paper n. 71. URL http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-paper-71.Google Scholar
Continuous Mortality Investigation (2014b) Analysis of the mortality experience of pensioners of self-administered pension schemes for the period 2005 to 2012, Working Paper n. 73. URL http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-paper-73.Google Scholar
Continuous Mortality Investigation (2014c) Analysis of the mortality experience of pensioners of self-administered pension schemes for the period 2006 to 2013, Working Paper n. 76. URL http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-paper-76.Google Scholar
Continuous Mortality Investigation (2015) An investigation into the mortality experience by industry classification of pensioners of self-administered pension schemes for the period 2006 to 2013, Working Paper n. 86.Google Scholar
Coughlan, G.D., Khalaf-Allah, M., Ye, Y., Kumar, S., Cairns, A.J., Blake, D. and Dowd, K. (2011) Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness. North American Actuarial Journal, 15 (2), 150–176.Google Scholar
Dowd, K., Cairns, A.J., Blake, D. and Coughlan, G.D. (2011) A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15 (2), 334–356.Google Scholar
Haberman, S., Kaishev, V.K., Millossovich, P., Villegas, A.M., Baxter, S.D., Gaches, A.T., Gunnlaugsson, S. and Sison, M. (2014) Longevity basis risk: A methodology for assessing basis risk. Tech. rep., Cass Business School, City University London and Hymans Robertson LLP.Google Scholar
Human Mortality Database (2014) Human Mortality Database. Tech. rep., University of California, Berkeley and Max Planck Institute for Demographic Research. URL www.mortality.org Google Scholar
Hunt, A. and Blake, D. (2014) A general procedure for constructing mortality models. North American Actuarial Journal, 18 (1), 116–138.Google Scholar
Hunt, A. and Blake, D. (2015a) Identifiability in age/period mortality models. Tech. rep., Pensions Institute PI 15-08, Cass Business School, City University London.Google Scholar
Hunt, A. and Blake, D. (2015b) Identifiability in age/period/cohort mortality models. Tech. rep., Pensions Institute PI 15-09, Cass Business School, City University London.Google Scholar
Hunt, A. and Blake, D. (2015c) Modelling longevity bonds: Analysing the Swiss Re Kortis Bond. Insurance: Mathematics and Economics, 63, 12–29.Google Scholar
Hunt, A. and Blake, D. (2015d) On the structure and classification of mortality models. Tech. rep., Pensions Institute PI 15-06, Cass Business School, City University London.Google Scholar
Hunt, A. and Blake, D. (2016a) Basis risk and pension schemes: A relative modelling approach. Tech. rep., Pensions Institute PI 16-01, Cass Business School, City University London.CrossRefGoogle Scholar
Hunt, A. and Blake, D. (2016b) Transferring mortality and longevity risks in pension schemes via bespoke longevity swaps. Work in Progress.Google Scholar
Jarner, S.F. and Kryger, E.M. (2011) Modelling mortality in small populations: The SAINT model. ASTIN Bulletin, 41 (2), 377–418.Google Scholar
Koissi, M., Shapiro, A. and Hognas, G. (2006) Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics, 38 (1), 1–20.Google Scholar
Li, J. S.-H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15 (2), 177–200.Google Scholar
Li, J. S.-H., Zhou, R. and Hardy, M.R. (2015) A step-by-step guide to building two-population stochastic mortality models. Insurance: Mathematics and Economics, 63, 121–134.Google Scholar
Oppers, S.E., Chikada, K., Eich, F., Imam, P., Kiff, J., Kisser, M., Soto, M. and Kim, Y.S. (2012) The financial impact of longevity risk. Tech. rep., International Monetary Fund.Google Scholar
Plat, R. (2009) Stochastic portfolio specific mortality and the quantification of mortality basis risk. Insurance: Mathematics and Economics, 45 (1), 123–132.Google Scholar
Richards, S.J. (2008) Detecting year-of-birth mortality patterns with limited data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 171 (1), 279–298.Google Scholar
Salhi, Y. and Loisel, S. (2009) Longevity basis risk modeling: A co-integration based approach. Tech. rep., University of Lyon.Google Scholar
Sithole, T., Haberman, S. and Verrall, R. (2012) Second international comparative study of mortality tables for pension fund retirees: A discussion paper. British Actuarial Journal, 7 (3), 650–671.Google Scholar
The Pensions Regulator (2013a) Scheme funding. Tech. rep. URL http://www.thepensionsregulator.gov.uk/codes/code-funding-defined-benefits.aspx Google Scholar
The Pensions Regulator (2013b) The Purple Book. Tech. rep. URL http://www.thepensionsregulator.gov.uk/doc-library/research-analysis.aspx Google Scholar
Villegas, A.M. and Haberman, S. (2014) On the modeling and forecasting of socioeconomic mortality differentials: An application to deprivation and mortality in England. North American Actuarial Journal, 18 (1), 168–193.Google Scholar
Yang, B., Li, J. and Balasooriya, U. (2015) Using bootstrapping to incorporate model error for risk-neutral pricing of longevity risk. Insurance: Mathematics and Economics, 62, 16–27.Google Scholar
Zhou, R., Wang, Y., Kaufhold, K., Li, J. S.-H. and Tan, K.S. (2014) Modeling period effects in multi-population mortality models: Applications to Solvency II. North American Actuarial Journal, 18 (1), 150–167.CrossRefGoogle Scholar
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