A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions. (English) Zbl 1231.91438

Summary: We present a Bayesian approach to pricing longevity risk under the framework of the Lee-Carter methodology. Specifically, we propose a Bayesian method for pricing the survivor bond and the related survivor swap designed by Denuit et al. (2007). Our method is based on the risk neutralization of the predictive distribution of future survival rates using the entropy maximization principle discussed by Stutzer (1996). The method is illustrated by applying it to Japanese mortality rates.


91G20 Derivative securities (option pricing, hedging, etc.)
91G80 Financial applications of other theories
Full Text: DOI


[1] Bauer, D., Boerger, M., Russ, J., 2008. On the pricing of longevity-linked securities. Working paper presented at the 4th International Longevity Risk and Capital Markets Solutions Conference
[2] Blake, D.; Dowd, K.; Cairns, A.J.G., Longevity risk and the grim reaper’s toxic tail: the survivor Fan charts, Insurance: mathematics and economics, 42, 1062-1068, (2008) · Zbl 1141.91485
[3] Bray, I., Application of Markov chain Monte Carlo methods to projecting cancer incidence and mortality, Applied statistics, 51, 151-164, (2002) · Zbl 1111.62331
[4] Brouhns, N.; Denuit, M.; Vermunt, J.K., A Poisson log-bilinear regression approach to the construction of projected life tables, Insurance: mathematics and economics, 31, 373-393, (2002) · Zbl 1074.62524
[5] Brouhns, N.; Denuit, M.; Vermunt, J.K., Measuring the longevity risk in mortality projections, Bulletin of the swiss association of actuaries, 2, 105-130, (2002) · Zbl 1187.62158
[6] Buchen, P.W.; Kelly, M., The maximum entropy distribution of an asset inferred from option prices, Journal of financial and quantitative analysis, 31, 143-159, (1996)
[7] Cairns, A.J.G.; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration, Journal of risk and insurance, 73, 687-718, (2006)
[8] Cowles, M.K.; Carlin, B.P, Markov chain Monte Carlo convergence diagnostics: A comparative review, Journal of the American statistical association, 91, 883-904, (1996) · Zbl 0869.62066
[9] Cowley, A.; Cummins, D.J., Securitization of life insurance assets and liabilities, Journal of risk and insurance, 72, 193-226, (2005)
[10] Czado, C.; Delwarde, A.; Denuit, M., Bayesian Poisson log-bilinear mortality projections, Insurance: mathematics and economics, 36, 260-284, (2005) · Zbl 1110.62142
[11] Denuit, M.; Devolder, P.; Goderniaux, A., Securitization of longevity risk: pricing survivor bonds with Wang transform in the lee – carter framework, Journal of risk and insurance, 74, 87-113, (2007)
[12] Dowd, K.; Blake, D.; Cairns, A.J.; Dawson, P., Survivor swaps, Journal of risk and insurance, 73, 1-17, (2006)
[13] Foster, F.D.; Whiteman, C.H., Bayesian prediction, entropy, and option pricing, Australian journal of management, 31, 181-206, (2006)
[14] Gerber, H.U.; Shiu, E.S.W., Option pricing by esscher transforms, Transactions of the society of actuaries, 46, 99-191, (1994)
[15] Kapur, J.N.; Kesavan, H.K., Entropy optimization principle with applications, (1992), Academic Press San Diego · Zbl 0718.62007
[16] Kogure, A.; Kitsukawa, K.; Kurachi, Y., A Bayesian comparison of models for changing mortalities toward evaluating the longevity risk in Japan, Asia-Pacific journal of risk and insurance, 3, 1-22, (2009)
[17] Kull, A., 2002. A unifying approach to pricing insurance and financial Risk. CAS Forum Winter 2003, Data Management, Quality, and Technology Call Papers and Ratemaking Discussion Papers, 317-350 available at http://www.casact.org/pubs/forum/03wforum/
[18] Lee, R.D.; Carter, L.R., Modeling and forecasting US mortality, Journal of the American statistical association, 87, 659-675, (1992) · Zbl 1351.62186
[19] Lin, Y.; Cox, S.H., Securitization of mortality risks in life annuities, Journal of risk and insurance, 72, 227-252, (2005)
[20] Milevsky, M.A.; Promislow, S.D., Mortality derivatives and the option to annuities, Insurance: mathematics and economics, 29, 299-318, (2001) · Zbl 1074.62530
[21] Pedroza, C., A Bayesian forecasting model: predicting US male mortality, Biostatistics, 7, 530-550, (2006) · Zbl 1170.62397
[22] Reichmuth, W., Sarferaz, S., 2008. Bayesian demographic modeling and forecasting: An application to U.S. mortality. SFB 649 Discussion Paper 2008-052
[23] Stutzer, M., A simple nonparametric approach to derivative security valuation, Journal of finance, 51, 1633-1652, (1996)
[24] Wang, S., A class of distortion operators for pricing financial and insurance risks, Journal of risk and insurance, 67, 15-36, (2000)
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