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Longevity hedge effectiveness: a decomposition

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  • Cairns, Andrew
  • Dowd, Kevin
  • Blake, David
  • Coughlan, Guy

Abstract

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 factor. 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, parameter uncertainty and Poisson risk have only a marginal impact on hedge effectiveness. Our case study shows that longevity risk can be substantially hedged using index hedges as an alternative to customised longevity hedges and that, as a consequence, 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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 34236.

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Date of creation: May 2011
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Handle: RePEc:pra:mprapa:34236

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Keywords: Hedge Effectiveness; Correlation; Mark-to-Model; Valuation Model; Simulation; Value Hedging; Longevity Risk; Stochastic Mortality; Population Basis Risk; Recalibration Risk;

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  1. 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.
  2. 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, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
  3. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
  4. Dowd, Kevin & Cairns, Andrew & Blake, David & Coughlan, Guy & Khalaf-Allah, Marwa, 2011. "A gravity model of mortality rates for two related populations," MPRA Paper 35738, University Library of Munich, Germany.
  5. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2010. "Evaluating the goodness of fit of stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 255-265, December.
  6. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer, Springer, vol. 42(3), pages 575-594, August.
  7. Wolfgang Reichmuth & Samad Sarferaz, 2008. "Bayesian Demographic Modeling and Forecasting: An Application to U.S. Mortality," SFB 649 Discussion Papers SFB649DP2008-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Wills, Samuel & Sherris, Michael, 2010. "Securitization, structuring and pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 173-185, February.
  9. Blake, David & Boardman, Tom & Cairns, Andrew, 2010. "Sharing longevity risk: Why governments should issue longevity bonds," MPRA Paper 34184, University Library of Munich, Germany.
  10. Kogure, Atsuyuki & Kurachi, Yoshiyuki, 2010. "A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 162-172, February.
  11. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
  12. Czado, Claudia & Delwarde, Antoine & Denuit, Michel, 2005. "Bayesian Poisson log-bilinear mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 260-284, June.
  13. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, Elsevier, vol. 8(3), pages 393-411, November.
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