Modelling longevity bonds: analysing the Swiss Re Kortis bond. (English) Zbl 1348.91150

Summary: A key contribution to the development of the traded market for longevity risk was the issuance of the Kortis bond, the world’s first longevity trend bond, by Swiss Re in 2010. We analyse the design of the Kortis bond, develop suitable mortality models to analyse its payoff and discuss the key risk factors for the bond. We also investigate how the design of the Kortis bond can be adapted and extended to further develop the market for longevity risk.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91D20 Mathematical geography and demography
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[1] Arnold-Gaille, S.; Sherris, M., Forecasting mortality trends allowing for cause-of-death mortality dependence, N. Am. Actuar. J., 17, 4, 273-282, (2013) · Zbl 1412.91218
[2] Bauer, D.; Kramer, F., Risk and valuation of mortality contingent catastrophe bonds. tech. rep, (2007), University of Ulm
[3] Beelders, O., Colarossi, D., 2004. Modelling mortality risk with extreme value theory: The case of Swiss Re’s mortality-indexed bonds. Global Association of Risk Professionals, pp. 26-30.
[4] Blake, D.; Burrows, W., Survivor bonds: helping to hedge mortality risk, J. Risk Insurance, 68, 2, 339-348, (2001)
[5] Blake, D.; Cairns, A. J.; Coughlan, G. D.; Dowd, K.; MacMinn, R., The new life market, J. Risk Insurance, 80, 3, 501-558, (2013)
[6] Blake, D.; Cairns, A. J.; Dowd, K., Living with mortality: longevity bonds and other mortality-linked securities, Br. Actuar. J., 12, 1, 153-197, (2006)
[7] Cairns, A. J., A discussion of parameter and model uncertainty in insurance, Insurance Math. Econom., 27, 3, 313-330, (2000) · Zbl 0971.62063
[8] Cairns, A. J.; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration, J. Risk Insurance, 73, 4, 687-718, (2006)
[9] Cairns, A. J.; Blake, D.; Dowd, K., Pricing death: frameworks for the valuation and securitization of mortality risk, ASTIN Bull., 36, 1, 79-120, (2006) · Zbl 1162.91403
[10] Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah, M., Mortality density forecasts: an analysis of six stochastic mortality models, Insurance Math. Econom., 48, 3, 355-367, (2011)
[11] Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Ong, A.; Balevich, I., A quantitative comparison of stochastic mortality models using data from england and wales and the united states, N. Am. Actuar. J., 13, 1, 1-35, (2009)
[12] Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Khalaf-Allah, M., Bayesian stochastic mortality modelling for two populations, ASTIN Bull., 41, 1, 29-59, (2011)
[13] Cairns, A. J.; Blake, D.; Dowd, K.; Kessler, A., Phantoms never die. tech. rep., (2014), Herriot Watt University Edinburgh
[14] Carter, R.; Lee, D., Modeling and forecasting US sex differentials, Int. J. Forecast., 8, 393-411, (1992)
[15] Chen, H.; Cox, S. H., Modeling mortality with jumps: applications to mortality securitization, J. Risk Insurance, 76, 3, 727-751, (2009)
[16] Continuous Mortality Investigation, 2002. Working Paper 1—An interim basis for adjusting the “92” series mortality projections for cohort effects. URL: http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-paper-1.
[17] Coughlan, G.D., Epstein, D., Sinha, A., Honig, P., 2007. q-forwards: Derivatives for transferring longevity and mortality risks. JPMorgan Pension Advisory Group.
[18] Cowley, A.; Cummins, J., Securitization of life insurance assets and liabilities, J. Risk Insurance, 72, 2, 193-226, (2005)
[19] Cox, S. H.; Lin, Y., Natural hedging of life and annuity mortality risks, N. Am. Actuar. J., 11, 3, 1-15, (2007)
[20] Darkiewicz, G.; Hoedemakers, T., How the co-integration analysis can help in mortality forecasting. tech. rep., (2004), Catholic University of Leuven
[21] Denuit, M. M.; Devolder, P.; Goderniaux, A.-M., Securitization of longevity risk: pricing survivor bonds with Wang transform in the Lee-Carter framework, J. Risk Insurance, 74, 1, 87-113, (2007)
[22] Dowd, K.; Cairns, A. J.; Blake, D., Mortality-dependent financial risk measures, Insurance Math. Econom., 38, 3, 427-440, (2006) · Zbl 1168.91411
[23] Dowd, K.; Cairns, A. J.; Blake, D.; Coughlan, G. D., A gravity model of mortality rates for two related populations, N. Am. Actuar. J., 15, 2, 334-356, (2011) · Zbl 1228.91032
[24] EIOPA, 2014. Technical specification for the preparatory phase (Part I). Tech. Rep., Frankfurt am Main, Germany.
[25] Gaille, S.; Sherris, M., Modelling mortality with common stochastic long-run trends, Geneva Pap. Risk Insur. Issues Pract., 36, 4, 595-621, (2011)
[26] Haberman, S.; Renshaw, A., A comparative study of parametric mortality projection models, Insurance Math. Econom., 48, 1, 35-55, (2011)
[27] Haberman, S.; Renshaw, A., Parametric mortality improvement rate modelling and projecting, Insurance Math. Econom., 50, 3, 309-333, (2012) · Zbl 1237.91129
[28] Human mortality database. tech. rep., (2014), University of California, Berkeley and Max Planck Institute for Demographic Research, URL: www.mortality.org
[29] Hunt, A.; Blake, D., A general procedure for constructing mortality models, N. Am. Actuar. J., 18, 1, 116-138, (2014) · Zbl 1412.91045
[30] Hunt, A., Blake, D., 2015. A Bayesian approach to modelling and projecting cohort effects (in preparation-a).
[31] Hunt, A., Blake, D., 2015. Identifiability, cointegration and the gravity model (in preparation-b).
[32] Hunt, A., Blake, D., 2015. Identifiability in age/period mortality models (in preparation-c).
[33] Hunt, A., Blake, D., 2015. Identifiability in age/period/cohort mortality models (in preparation-d).
[34] Hunt, A., Blake, D., 2015. On the structure and classification of mortality models (in preparation-e).
[35] Hyndman, R.; Booth, H.; Yasmeen, F., Coherent mortality forecasting: the product-ratio method with functional time series models, Demography, 50, 1, 261-283, (2013)
[36] Jarner, S. F.; Kryger, E. M., Modelling mortality in small populations: the SAINT model, ASTIN Bull., 41, 2, 377-418, (2011) · Zbl 1239.91128
[37] Johansen, S., Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models, Econometrica, 59, 6, 1551-1580, (1991) · Zbl 0755.62087
[38] Juselius, K., The cointegrated VAR model: methodology and applications, (2006), Oxford University Press · Zbl 1258.91006
[39] Koissi, M.; Shapiro, A.; Hognas, G., Evaluating and extending the Lee-Carter model for mortality forecasting: bootstrap confidence interval, Insurance Math. Econom., 38, 1, 1-20, (2006) · Zbl 1098.62138
[40] Lane, M. N.; Beckwith, R., Prague spring or louisiana morning? annual review for the four quarters, Q2 2010 to Q1 2011. tech. rep., (2011), Lane Finacial LLC
[41] Lane, M. N.; Beckwith, R., More return; more risk: annual review for the four quarters, Q2 2011 to Q1 2012. tech. rep., (2012), Lane Financial LLC
[42] Lane, M. N.; Beckwith, R., Soft markets ahead!? annual review for the four quarters, Q2 2012 to Q1 2013. tech. rep., (2013), Lane Financial LLC
[43] Lane, M. N.; Beckwith, R., Straw hats in winter: annual review for the four quarters, Q2 2013 to Q1 2014. tech. rep., (2014), Lane Financial LLC
[44] Lazar, D.; Denuit, M. M., A multivariate time series approach to projected life tables, Appl. Stoch. Models Bus. Ind., 25, 6, 806-823, (2009) · Zbl 1224.91069
[45] Lee, R. D.; Carter, L. R., Modeling and forecasting US mortality, J. Amer. Statist. Assoc., 87, 419, 659-671, (1992) · Zbl 1351.62186
[46] Li, J. S.-H.; Hardy, M. R., Measuring basis risk in longevity hedges, N. Am. Actuar. J., 15, 2, 177-200, (2011) · Zbl 1228.91042
[47] Li, J. S.-H.; Hardy, M. R.; Tan, K. S., Uncertainty in mortality forecasting: an extension to the classical Lee-Carter approach, ASTIN Bull., 39, 1, 137-164, (2009) · Zbl 1203.91113
[48] Li, N.; Lee, R. D., Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method, Demography, 42, 3, 575-594, (2005)
[49] Lin, Y.; Cox, S. H., Securitization of mortality risks in life annuities, J. Risk Insurance, 72, 2, 227-252, (2005)
[50] Michaelson, A.; Mulholland, J., Strategy for increasing the global capacity for longevity risk transfer: developing transactions that attract capital markets investors, J. Altern. Invest., 17, 1, 18-27, (2014)
[51] Mitchell, D.; Brockett, P. L.; Mendoza-Arriaga, R.; Muthuraman, K., Modeling and forecasting mortality rates, Insurance Math. Econom., 52, 2, 275-285, (2013) · Zbl 1284.91259
[52] Murphy, M., The “golden generations” in historical context, Br. Actuar. J., 15, S1, 151-184, (2009)
[53] Murphy, M., Re-examining the dominance of birth cohort effects on mortality, Popul. Dev. Rev., 36, 2, 365-390, (2010)
[54] Plat, R., On stochastic mortality modeling, Insurance Math. Econom., 45, 3, 393-404, (2009) · Zbl 1231.91227
[55] Renshaw, A.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance Math. Econom., 38, 3, 556-570, (2006) · Zbl 1168.91418
[56] Richards, S. J., Detecting year-of-birth mortality patterns with limited data, J. Roy. Statist. Soc. Ser. A, 171, 1, 279-298, (2008)
[57] Salhi, Y.; Loisel, S., Longevity basis risk modeling: A co-integration based approach. tech. rep., (2009), University of Lyon
[58] Presale information: kortis capital ltd. tech. rep., (2010), Standard and Poors
[59] Villegas, A. M.; Haberman, S., On the modeling and forecasting of socioeconomic mortality differentials: an application to deprivation and mortality in england, N. Am. Actuar. J., 18, 1, 168-193, (2014) · Zbl 1412.91057
[60] Wang, C.-W.; Huang, H.; Liu, I.-C., A quantitative comparison of the Lee-Carter model under different types of non-Gaussian innovations, Geneva Pap. Risk Insur. Issues Pract., 36, 4, 675-696, (2011)
[61] Wang, J. L.; Huang, H.; Yang, S. S.; Tsai, J. T., An optimal product mix for hedging longevity risk in life insurance companies: the immunization theory approach, J. Risk Insurance, 77, 2, 473-497, (2009)
[62] Willets, R., Mortality in the next millennium, (1999), Staple Inn Actuarial Society
[63] Willets, R., The cohort effect: insights and explanations, Br. Actuar. J., 10, 4, 833-877, (2004)
[64] Yang, S. S.; Wang, C.-W., Pricing and securitization of multi-country longevity risk with mortality dependence, Insurance Math. Econom., 52, 2, 157-169, (2013) · Zbl 1284.91556
[65] Zhou, R.; Wang, Y.; Kaufhold, K.; Li, J. S.-H.; Tan, K. S., Modeling period effects in multi-population mortality models: applications to solvency II, N. Am. Actuar. J., 18, 1, 150-167, (2014) · Zbl 1412.91060
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