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Longevity hedge effectiveness: a decomposition. (English) Zbl 1294.91072

Summary: We use a case study of a pension plan wishing to hedge the longevity risk in its pension liabilities at a future date. The plan has the choice of using either a customised hedge or an index hedge, with the degree of hedge effectiveness being closely related to the correlation between the value of the hedge and the value of the pension liability. The key contribution of this paper is to show how correlation and, therefore, hedge effectiveness can be broken down into contributions from a number of distinct types of risk factors. Our decomposition of the correlation indicates that population basis risk has a significant influence on the correlation. But recalibration risk as well as the length of the recalibration window are also important, as is cohort effect uncertainty. Having accounted for recalibration risk, additional parameter uncertainty has only a marginal impact on hedge effectiveness. Finally, the inclusion of Poisson risk only starts to become significant when the smaller population falls below about 10,000 members over age 50. Our case study shows that, at least for medium and large pension plans, longevity risk can be substantially hedged using index hedges as an alternative to customised longevity hedges. As a consequence, when the hedger’s population involves more than about 10,000 members over age 50, index longevity hedges (in conjunction with the other components of an ALM strategy) can provide an effective and lower cost alternative to both a full buy-out of pension liabilities or even to a strategy using customised longevity hedges.

MSC:

91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography

References:

[1] Balistreri, E.J. and Hillberry, R.H., Estibration: an illustration of structural estimation as calibration. 2005, Working Paper, Colorado School of Mines and University of Melbourne.
[2] Bauer, D., Benth, F.E. and Kiesel, R., Modeling the forward surface of mortality. 2010, Working Paper, University of Ulm (accessed 30 May 2012). · Zbl 1255.91443
[3] DOI: 10.1080/03461230903331634 · Zbl 1226.91022 · doi:10.1080/03461230903331634
[4] DOI: 10.2307/2678106 · doi:10.2307/2678106
[5] DOI: 10.1017/S1357321700004736 · doi:10.1017/S1357321700004736
[6] Börger, M., Fleischer, D., and Kuksin, N., Modeling mortality trend under modern solvency regimes. 2012, Working Paper, University of Ulm.
[7] Brouhns, N., Denuit, M. and Vermunt, J.K., A Poisson log-bilinear regression approach to the construction of projected life tables.Insurance. Math. Econ., 2002,31, 373–393. · Zbl 1074.62524 · doi:10.1016/S0167-6687(02)00185-3
[8] Cairns, A.J.G., Modelling and management of longevity risk: approximations to survival functions and dynamic hedging.Insurance:Math. Econ., 2011a,49, 438–453. · Zbl 1230.91068
[9] Cairns, A.J.G., Robust hedging of longevity risk. Paper presented at Longevity 7: the Seventh International Longevity Risk and Capital Markets Solutions Conference, Frankfurt, September 2011b (Working Paper, Heriot-Watt University).
[10] DOI: 10.1111/j.1539-6975.2006.00195.x · doi:10.1111/j.1539-6975.2006.00195.x
[11] DOI: 10.1080/03461230802173608 · Zbl 1224.91048 · doi:10.1080/03461230802173608
[12] DOI: 10.1080/10920277.2009.10597538 · doi:10.1080/10920277.2009.10597538
[13] Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D. and Khalaf-Allah, M., Mortality density forecasts: an analysis of six stochastic mortality models.Insurance. Math. Econ., 2011a,48, 355–367. · doi:10.1016/j.insmatheco.2010.12.005
[14] Cairns A.J.G., ASTIN Bull. 41 pp 29– (2011)
[15] Coughlan, G.D., Longevity risk transfer: indices and capital market solutions. InThe Handbook of Insurance Linked Securities, edited by P.M. Barrieu and L. Albertini, 2009 (Wiley: Chichester).
[16] DOI: 10.1142/S0219868104000178 · doi:10.1142/S0219868104000178
[17] DOI: 10.1080/10920277.2011.10597615 · doi:10.1080/10920277.2011.10597615
[18] Czado, C., Delwarde, A. and Denuit, M., Bayesian Poisson log-bilinear mortality projections.Insurance: Math. Econ., 2005,36, 260–284. · Zbl 1110.62142 · doi:10.1016/j.insmatheco.2005.01.001
[19] Dahl, M., Melchior, M. and Møller, T., On systematic mortality risk and risk minimisation with survivor swaps. Scand. Actuar. J., 2008,2/3, 114–146. · Zbl 1224.91054 · doi:10.1080/03461230701795873
[20] Dahl, M., Glar, S. and Møller, T., Mixed dynamic and static risk minimization with an application to survivor swaps. Paper presented at the 19th International AFIR Colloquium, Munich, September 2009.
[21] DOI: 10.2143/AST.40.1.2049232 · Zbl 1189.62162 · doi:10.2143/AST.40.1.2049232
[22] DOI: 10.3905/jod.2007.686422 · doi:10.3905/jod.2007.686422
[23] DOI: 10.1353/dem.0.0083 · doi:10.1353/dem.0.0083
[24] Dowd, K., Blake, D., Cairns, A.J.G., Coughlan, G.D., Epstein, D. and Khalaf-Allah, M., Evaluating the goodness of fit of stochastic mortality models.Insurance:Math. Econ., 2010b,47, 255–265. · Zbl 1231.91179 · doi:10.1016/j.insmatheco.2010.06.006
[25] DOI: 10.1080/10920277.2011.10597624 · Zbl 1228.91032 · doi:10.1080/10920277.2011.10597624
[26] DOI: 10.1080/10920277.2011.10597619 · Zbl 1228.91031 · doi:10.1080/10920277.2011.10597619
[27] Jarner S.F., ASTIN Bull. 41 pp 377– (2011)
[28] Kogure, A., Kurachi, Y. and Kitsukawa, K., A Bayesian evaluation of longevity risk: model comparison, measuring and pricing. 2009, Working Paper, Keio University.
[29] Kogure, A. and Kurachi, Y., A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions.Insurance:Math. Econ., 2010,46, 162–172. · Zbl 1231.91438 · doi:10.1016/j.insmatheco.2009.10.005
[30] DOI: 10.1080/01621459.1992.10475265 · Zbl 1351.62186 · doi:10.1080/01621459.1992.10475265
[31] DOI: 10.1080/10920277.2011.10597616 · Zbl 1228.91042 · doi:10.1080/10920277.2011.10597616
[32] DOI: 10.2143/AST.39.1.2038060 · Zbl 1203.91113 · doi:10.2143/AST.39.1.2038060
[33] Li J.S.-H., ASTIN Bull. 42 pp 413– (2012)
[34] DOI: 10.1353/dem.2005.0021 · doi:10.1353/dem.2005.0021
[35] DOI: 10.2143/AST.39.2.2044647 · Zbl 1179.91108 · doi:10.2143/AST.39.2.2044647
[36] DOI: 10.1093/biostatistics/kxj024 · Zbl 1170.62397 · doi:10.1093/biostatistics/kxj024
[37] Plat, R., Stochastic portfolio specific mortality and the quantification of mortality basis risk.Insurance. Math. Econ., 2009,45, 123–132. · Zbl 1231.91226 · doi:10.1016/j.insmatheco.2009.05.002
[38] Reichmuth, W. and Sarferaz, S., Bayesian demographic modelling and forecasting: an application to US mortality. 2008, SFB 649 Discussion Paper 2008–052.
[39] Wills, S. and Sherris, M., Securitization, structuring and pricing of longevity risk.Insurance. Math. Econ., 2010,46, 173–185. · Zbl 1231.91251 · doi:10.1016/j.insmatheco.2009.09.014
[40] DOI: 10.1080/14697680902956695 · Zbl 1194.91199 · doi:10.1080/14697680902956695
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