Cairns, Andrew and Dowd, Kevin and Blake, David and Coughlan, Guy (2011): Longevity hedge effectiveness: a decomposition.

PDF
MPRA_paper_34236.pdf Download (368kB)  Preview 
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 buyout of pension liabilities or even to a strategy using customised longevity hedges.
Item Type:  MPRA Paper 

Original Title:  Longevity hedge effectiveness: a decomposition 
Language:  English 
Keywords:  Hedge Effectiveness; Correlation; MarktoModel; Valuation Model; Simulation; Value Hedging; Longevity Risk; Stochastic Mortality; Population Basis Risk; Recalibration Risk 
Subjects:  G  Financial Economics > G2  Financial Institutions and Services > G23  Nonbank Financial Institutions ; Financial Instruments ; Institutional Investors J  Labor and Demographic Economics > J1  Demographic Economics > J11  Demographic Trends, Macroeconomic Effects, and Forecasts 
Item ID:  34236 
Depositing User:  David Blake 
Date Deposited:  10. Nov 2011 15:33 
Last Modified:  01. Sep 2015 18:20 
References:  Blake, D., and Burrows, W. (2001) Survivor bonds: Helping to hedge mortality risk. Journal of Risk and Insurance, 68: 339348. Blake, D., Boardman, T., and Cairns, A.J.G. (2010) Sharing longevity risk: Why governments should issue longevity bonds. Pensions Institute Discussion Paper PI1002 (accessed on 14/4/2011 at http://www.pensionsinstitute.org/workingpapers/wp1002.pdf ). Blake, D., Cairns, A.J.G., and Dowd, K. (2006) Living with mortality: Longevity bonds and other mortalitylinked securities. British Actuarial Journal, 12: 153197. Brouhns, N., Denuit, M., and Vermunt J.K. (2002) A Poisson logbilinear regression approach to the construction of projected life tables. Insurance: Mathematics and Economics, 31: 373393. Cairns, A.J.G., Blake, D., and Dowd, K. (2006) A twofactor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73: 687718. Cairns, A.J.G., Blake, D., and Dowd, K. (2008) Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal, 2008(23): 79113. Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A., and Balevich, I. (2009) A quantitative comparison of stochastic mortality models using data from England & Wales and the United States. North American Actuarial Journal, 13: 135. Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., and Khalaf Allah, M. (2011a) Mortality density forecasts: an analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48: 355367. Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., and KhalafAllah, M. (2011b)Bayesian stochastic mortality modelling for two populations, To appear in ASTIN Bulletin. Coughlan, G.D., Emery, S. and Kolb, J. (2004) HEAT (Hedge E®ectiveness Analysis Toolkit): A consistent framework for assessing hedge e®ectiveness under IAS 39 and FAS 133, Journal of Derivatives Accounting, 1(2): 221272. 30 Coughlan, G., Epstein, D., Sinha, A., and Honig, P. (2007) qForwards: Derivatives for transferring longevity and mortality risk. Available at www.lifemetrics.com. Coughlan, G.D. (2009). Longevity risk transfer: Indices and capital market solutions. In Barrieu, P.M. and Albertini, L. (eds), The Handbook of Insurance Linked Securities, Wiley, London. Coughlan, G.D., KhalafAllah, M., Ye, Y., Kumar, S., Cairns, A.J.G., Blake, D. and Dowd, K., (2011) Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness. To appear in North American Actuarial Journal. Czado, C., Delwarde, A., and Denuit, M. (2005) Bayesian Poisson logbilinear mortality projections. Insurance: Mathematics and Economics, 36: 260284. Dahl, M., Melchior, M., and M¿ller, T. (2008) On systematic mortality risk and risk minimisation with survivor swaps. Scandinavian Actuarial Journal, 2008(23):114146. Dahl, M., Glar, S., and M¿ller, T. (2009) Mixed dynamic and static risk minimization with an application to survivor swaps. 19th International AFIR Colloquium, Munich, September 2009. Denuit, M., Haberman, S., and Renshaw, A.E. (2010) Comonotonic approximations to quantiles of life annuity conditional expected present values: Extensions to general ARIMA models and comparison with the bootstrap. ASTIN Bulletin, 40: 331349. Detlefsen, K., and HÄardle, W.K. (2007) Calibration risk for exotic options, Journal of Derivatives, 14: 4763. Dowd, K., Blake, D., and Cairns, A.J.G. (2010a) Facing up to uncertain life expectancy: The longevity fan charts. Demography, 47: 6778. Dowd, K., Blake, D., Cairns, A.J.G., Coughlan, G.D., Epstein, D., and KhalafAllah, M. (2010b) Evaluating the goodness of ¯t of stochastic mortality models, Insurance: Mathematics and Economics, 47, 255265. Dowd, K., Cairns, A.J.G., Blake, D., Coughlan, G.D., and KhalafAllah, M. (2011a)A gravity model of mortality rates for two related populations. To appear in North American Actuarial Journal. Dowd, K., Blake, D., and Cairns, A.J.G. (2011b) A computationally e±cient algorithm for estimating the distribution of future annuity values under interestrate and longevity risks. To appear in North American Actuarial Journal. Jarner, S.F., and Kryger, E.M. (2011) Modelling adult mortality in small populations: The SAINT model. To appear in ASTIN Bulletin. Kogure, A., Kurachi, Y., and Kitsukawa, K. (2009) A Bayesian evaluation of longevity risk: Model comparison, measuring and pricing. Working paper, Keio University. Kogure, A., and Kurachi, Y. (2010) A Bayesian approach to pricing longevity risk based on riskneutral predictive distributions. Insurance: Mathematics and Eco nomics, 46: 162172. Lee, R.D., and Carter, L.R. (1992) Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87: 659675. Li, J.S.H., and Hardy, M.R. (2009) Measuring basis risk involved in longevity hedges. Working paper, University of Waterloo. To appear in North American Actuarial Journal. Li, J.S.H., Hardy, M.R., and Tan, K.S. (2009) Uncertainty in model forecasting: An extension to the classic LeeCarter approach. ASTIN Bulletin, 39: 137164. Li, N., and Lee, R. (2005) Coherent mortality forecasts for a group of populations: An extension of the LeeCarter method. Demography, 42(3): 575594. Nielsen, L.H. (2010) Assessment of the VaR(99.5%) for longevity risk, Working paper, Sampension, Denmark. (accessed on 3/8/2010 at http://www.cea.eu/index.php?page=nonceapublications) Olivieri, A. and Pitacco, E. (2009) Stochastic mortality: The impact on target capital. ASTIN Bulletin, 39: 541563. Pedroza, C. (2006) A Bayesian forecasting model: Predicting U.S. male mortality. Biostatistics, 7: 530550. Plat, R. (2009) Stochastic portfolio speci¯c mortality and the quanti¯cation of mortality basis risk. Insurance: Mathematics and Economics, 45: 123132. Reichmuth, W. and Sarferaz, S. (2008) Bayesian demographic modelling and forecasting: An application to US mortality. SFB 649 Discussion paper 2008052. Wills, S. and Sherris, M. (2010) Securitization, structuring and pricing of longevity risk. Insurance: Mathematics and Economics, 46: 173185. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/34236 