A comparative study of two-population models for the assessment of basis risk in longevity hedges. (English) Zbl 1390.91215

Summary: Longevity swaps have been one of the major success stories of pension scheme de-risking in recent years. However, with some few exceptions, all of the transactions to date have been bespoke longevity swaps based upon the mortality experience of a portfolio of named lives. In order for this market to start to meet its true potential, solutions will ultimately be needed that provide protection for all types of members, are cost effective for large and smaller schemes, are tradable, and enable access to the wider capital markets. Index-based solutions have the potential to meet this need; however, concerns remain with these solutions. In particular, the basis risk emerging from the potential mismatch between the underlying forces of mortality for the index reference portfolio and the pension fund/annuity book being hedged is the principal issue that has, to date, prevented many schemes progressing their consideration of index-based solutions. Two-population stochastic mortality models offer an alternative to overcome this obstacle as they allow market participants to compare and project the mortality experience for the reference and target populations and thus assess the amount of demographic basis risk involved in an index-based longevity hedge. In this paper, we systematically assess the suitability of several multi-population stochastic mortality models for assessing basis risks and provide guidelines on how to use these models in practical situations paying particular attention to the data requirements for the appropriate calibration and forecasting of such models.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91D20 Mathematical geography and demography
Full Text: DOI Link


[1] Ahcan, A.; Medved, D.; Olivieri, A.; Pitacco, E., Forecasting mortality for small populations by mixing mortality data, Insurance: Mathematics and Economics, 54, 12-27, (2014)
[2] Ahmadi, S. S.; Li, J. S.-H., Coherent mortality forecasting with generalized linear models: A modified time-transformation approach, Insurance: Mathematics and Economics, 59, 194-221, (2014) · Zbl 1306.91067
[3] Antonio, K.; Bardoutsos, A.; Ouburg, W., Bayesian Poisson log-bilinear models for mortality projections with multiple populations, European Actuarial Journal, 5, 245-281, (2015) · Zbl 1329.91111
[4] Biatat, V.; Currie, I. D., (2010)
[5] Booth, H.; Hyndman, R. J.; Tickle, L.; De Jong, P., Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions, Demography, 15, 289-310, (2006)
[6] Börger, M.; Fleischer, D.; Kuksin, N., Modeling the mortality trend under modern solvency regimes, ASTIN Bulletin, 44, 1-38, (2013)
[7] Brouhns, N.; Denuit, M.; Van Keilegom, I., Bootstrapping the Poisson log-bilinear model for mortality forecasting, Scandinavian Actuarial Journal, 2005, 212-224, (2005) · Zbl 1092.91038
[8] Butt, Z.; Haberman, S., Ilc: A collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms, (2009), Cass Business School
[9] Cairns, A. J.G., Robust hedging of longevity risk, Journal of Risk and Insurance, 80, 621-648, (2013)
[10] 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)
[11] Cairns, A. J.G.; Blake, D.; Dowd, K., Modelling and management of mortality risk: A review, Scandinavian Actuarial Journal, 2008, 79-113, (2008) · Zbl 1224.91048
[12] Cairns, A. J.G.; Blake, D.; Dowd, K.; Coughlan, G. D., Bayesian stochastic mortality modelling for two populations, ASTIN Bulletin, 41, 29-59, (2011)
[13] Cairns, A. J.G.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah, M., Mortality density forecasts: An analysis of six stochastic mortality models, Insurance: Mathematics and Economics, 48, 355-367, (2011)
[14] Cairns, A. J.G.; 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, North American Actuarial Journal, 13, 1-35, (2009)
[15] Cairns, A. J.G.; Dowd, K.; Blake, D.; Coughlan, G. D., Longevity hedge effectiveness: A decomposition, Quantitative Finance, 14, 217-235, (2014) · Zbl 1294.91072
[16] Carter, L. R.; Lee, R. D., Modeling and forecasting US sex differentials in mortality, International Journal of Forecasting, 8, 393-411, (1992)
[17] (2007)
[18] Coughlan, G. D.; Khalaf-Allah, M.; Ye, Y.; Kumar, S.; Cairns, A. J. G.; Blake, D.; Dowd, K., Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness, North American Actuarial Journal, 15, 150-176, (2011)
[19] Currie, I. D.; Durban, M.; Eilers, P. H., Smoothing and forecasting mortality rates, Statistical Modelling, 4, 279-298, (2004) · Zbl 1061.62171
[20] Debón, A.; Martínez-Ruiz, F.; Montes, F., A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities, Insurance: Mathematics and Economics, 47, 327-336, (2010) · Zbl 1231.91173
[21] Debón, A.; Montes, F.; Martínez-Ruiz, F., Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions, European Actuarial Journal, 1, 291-308, (2011)
[22] Delwarde, A.; Denuit, M.; Guillén, M.; Vidiella-I Anguera, A., Application of the Poisson log-bilinear projection model to the G5 mortality experience, Belgian Actuarial Bulletin, 6, 54-68, (2006) · Zbl 1356.91056
[23] Dowd, K.; Cairns, A. J. G.; Blake, D.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah, M., Backtesting stochastic mortality models: An ex-post evaluation of multi-period-ahead density forecasts, North American Actuarial Journal, 14, 281-298, (2010)
[24] Dowd, K.; Cairns, A. J.G.; Blake, D.; Coughlan, G. D.; Khalaf-Allah, M., A gravity model of mortality rates for two related populations, North American Actuarial Journal, 15, 334-356, (2011) · Zbl 1228.91032
[25] Haberman, S.; Kaishev, V. K.; Millossovich, P.; Villegas, A. M.; Baxter, S.; Gaches, A.; Gunnlaugsson, S.; Sison, M., (2014)
[26] Haberman, S.; Renshaw, A., On age-period-cohort parametric mortality rate projections, Insurance: Mathematics and Economics, 45, 255-270, (2009) · Zbl 1231.91195
[27] Haberman, S.; Renshaw, A., A comparative study of parametric mortality projection models, Insurance: Mathematics and Economics, 48, 35-55, (2011)
[28] Hatzopoulos, P.; Haberman, S., Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data, Insurance: Mathematics and Economics, 52, 320-337, (2013) · Zbl 1284.91238
[29] (2013)
[30] Hunt, A.; Blake, D., Modelling longevity bonds: Analysing the Swiss Re Kortis bond, Insurance: Mathematics and Economics, 63, 12-29, (2015) · Zbl 1348.91150
[31] Hunt, A.; Blake, D., (2015)
[32] Hunt, A.; Villegas, A. M., Robustness and convergence in the Lee-Carter model with cohorts, Insurance: Mathematics and Economics, 64, 186-202, (2015) · Zbl 1348.62241
[33] (2015)
[34] Hyndman, R. J.; Booth, H.; Yasmeen, F., Coherent mortality forecasting: The product-ratio method with functional time series models, Demography, 50, 261-283, (2013)
[35] Jarner, S. F.; Kryger, E. M., ASTIN Bulletin, 41, 377-418, (2011)
[36] Kleinow, T., A common age effect model for the mortality of multiple populations, Insurance: Mathematics and Economics, 63, 147-152, (2015) · Zbl 1348.91233
[37] Koissi, M.-C.; Shapiro, A.; Hognas, G., Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval, Insurance: Mathematics and Economics, 38, 1-20, (2006) · Zbl 1098.62138
[38] Lee, R. D.; Carter, L. R., Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 659-671, (1992) · Zbl 1351.62186
[39] Li, J., A Poisson common factor model for projecting mortality and life expectancy jointly for females and males, Population Studies, 67, 111-126, (2012)
[40] Li, J. S.-H.; Hardy, M. R., Measuring basis risk in longevity hedges, North American Actuarial Journal, 15, 177-200, (2011) · Zbl 1228.91042
[41] Li, J. S.-H.; Zhou, R.; Hardy, M., A step-by-step guide to building two-population stochastic mortality models, Insurance: Mathematics and Economics, 63, 121-134, (2015) · Zbl 1348.91164
[42] Li, N.; Lee, R. D., Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography, 42, 575-594, (2005)
[43] Basis risk in longevity hedging: Parallels with the past, Institutional Investor Journals, 2012, 39-45, (2012)
[44] Lu, J. L.C.; Wong, W.; Bajekal, M., Mortality improvement by socio-economic circumstances in England (1982 to 2006), British Actuarial Journal, 19, 1-35, (2014)
[45] Noble, M.; Mclennan, D.; Wilkinson, K.; Whitworth, A.; Exley, S.; Barnes, H.; Dibben, C., The English Indices of Deprivation 2007, (2007), London: Department of Communities and Local Government, London
[46] Plat, R., On stochastic mortality modeling, Insurance: Mathematics and Economics, 45, 393-404, (2009) · Zbl 1231.91227
[47] Plat, R., Stochastic portfolio specific mortality and the quantification of mortality basis risk, Insurance: Mathematics and Economics, 45, 123-132, (2009) · Zbl 1231.91226
[48] Renshaw, A.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570, (2006) · Zbl 1168.91418
[49] Renshaw, A.; Haberman, S., On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling, Insurance: Mathematics and Economics, 42, 797-816, (2008) · Zbl 1152.91598
[50] Russolillo, M.; Giordano, G.; Haberman, S., (2011)
[51] Villegas, A. M.; Haberman, S., On the modeling and forecasting of socioeconomic mortality differentials: An application to deprivation and mortality in England, North American Actuarial Journal, 18, 168-193, (2014)
[52] Villegas, A. M.; Kaishev, V.; Millossovich, P., (2017)
[53] Wan, C.; Bertschi, L., Swiss coherent mortality model as a basis for developing longevity de-risking solutions for Swiss pension funds: A practical approach, Insurance: Mathematics and Economics, 63, 66-75, (2015) · Zbl 1348.62248
[54] Willets, R., The cohort effect: Insights and explanations, British Actuarial Journal, 10, 833-877, (2004)
[55] Wilmoth, J.; Valkonen, T., (2001)
[56] Wood, S., (2015)
[57] Yang, B.; Li, J.; Balasooriya, U., Cohort extensions of the Poisson common factor model for modelling both genders jointly, Scandinavian Actuarial Journal, 2016, 93-112, (2016) · Zbl 1401.91203
[58] Yang, S. S.; Wang, C.-W., Pricing and securitization of multi-country longevity risk with mortality dependence, Insurance: Mathematics and Economics, 52, 157-169, (2013) · Zbl 1284.91556
[59] 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, North American Actuarial Journal, 18, 150-167, (2014)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.