Skip to main content
    • Aa
    • Aa


  • Andrés M. Villegas (a1), Steven Haberman (a2), Vladimir K. Kaishev (a3) and Pietro Millossovich (a4) (a5)

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.

Corresponding author
Hide All
AhcanA., MedvedD., OlivieriA. and PitaccoE. (2014) Forecasting mortality for small populations by mixing mortality data. Insurance: Mathematics and Economics, 54, 1227.
AhmadiS.S. and LiJ.S.-H. (2014) Coherent mortality forecasting with generalized linear models: A modified time-transformation approach. Insurance: Mathematics and Economics, 59, 194221.
AntonioK., BardoutsosA. and OuburgW. (2015) Bayesian Poisson log-bilinear models for mortality projections with multiple populations. European Actuarial Journal, 5 (2), 245281.
BiatatV. and CurrieI.D. (2010) Joint models for classification and comparison of mortality in different countries. Proceedings of 25rd International Workshop on Statistical Modelling, Glasgow, pp. 89–94.
BoothH., HyndmanR.J., TickleL. and de JongP. (2006) Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions. Demography, 15, 289310.
BörgerM., FleischerD. and KuksinN. (2013) Modeling the mortality trend under modern solvency regimes. ASTIN Bulletin, 44 (1), 138.
BrouhnsN., DenuitM. and Van KeilegomI. (2005) Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 2005 (3), 212224.
ButtZ. and HabermanS. (2009) Ilc: A collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms. Actuarial Research Paper, Cass Business School.
CairnsA.J.G. (2013) Robust hedging of longevity risk. Journal of Risk and Insurance, 80, 621648.
CairnsA.J.G., BlakeD. and DowdK. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73 (4), 687718.
CairnsA.J.G., BlakeD. and DowdK. (2008) Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal, 2008 (2), 79113.
CairnsA.J.G., BlakeD., DowdK. and CoughlanG.D. (2011a) Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41, 2959.
CairnsA.J.G., BlakeD., DowdK., CoughlanG.D., EpsteinD. and Khalaf-AllahM. (2011b) Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48 (3), 355367.
CairnsA.J.G., BlakeD., DowdK., CoughlanG.D., EpsteinD., OngA. and BalevichI. (2009) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13 (1), 135.
CairnsA.J.G., DowdK., BlakeD. and CoughlanG.D. (2014) Longevity hedge effectiveness: A decomposition. Quantitative Finance, 14 (2), 217235.
CarterL.R. and LeeR.D. (1992) Modeling and forecasting US sex differentials in mortality. International Journal of Forecasting, 8 (3), 393411.
Continuous Mortality Investigation (2007) Stochastic projection methodologies: Lee–Carter model features, example results and implications. Working Paper n. 25.
CoughlanG.D., Khalaf-AllahM., YeY., KumarS., CairnsA. J.G., BlakeD. and DowdK. (2011) Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness. North American Actuarial Journal, 15 (2), 150176.
CurrieI.D., DurbanM. and EilersP.H. (2004) Smoothing and forecasting mortality rates. Statistical Modelling, 4 (4), 279298.
DebónA., Martínez-RuizF. and MontesF. (2010) A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47 (3), 327336.
DebónA., MontesF. and Martínez-RuizF. (2011) Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions. European Actuarial Journal, 1 (2), 291308.
DelwardeA., DenuitM., GuillénM. and Vidiella-i AngueraA. (2006) Application of the Poisson log-bilinear projection model to the G5 mortality experience. Belgian Actuarial Bulletin, 6 (1), 5468.
DowdK., CairnsA. J.G., BlakeD., CoughlanG.D., EpsteinD. and Khalaf-AllahM. (2010) Backtesting stochastic mortality models: An ex-post evaluation of multi-period-ahead density forecasts. North American Actuarial Journal, 14 (3), 281298.
DowdK., CairnsA.J.G., BlakeD., CoughlanG.D. and Khalaf-AllahM. (2011) A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15 (2), 334356.
HabermanS., KaishevV.K., MillossovichP., VillegasA.M., BaxterS., GachesA., GunnlaugssonS. and SisonM. (2014) Longevity basis risk: A methodology for assessing basis risk. Institute and Faculty of Actuaries Sessional Research Paper.
HabermanS. and RenshawA. (2009) On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics, 45 (2), 255270.
HabermanS. and RenshawA. (2011) A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48 (1), 3555.
HatzopoulosP. and HabermanS. (2013) Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data. Insurance: Mathematics and Economics, 52 (2), 320337.
Human Mortality Database (2013) University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany).
HuntA. and BlakeD. (2015a) Modelling longevity bonds: Analysing the Swiss Re Kortis bond. Insurance: Mathematics and Economics, 63, 1229.
HuntA. and BlakeD. (2015b) On the structure and classification of mortality models mortality models. Pension Institute Working Paper PI-1506.
HuntA. and VillegasA.M. (2015) Robustness and convergence in the Lee-Carter model with cohorts. Insurance: Mathematics and Economics, 64, 186202.
Hymans Robertson LLP (2015) Buy-outs, buy-ins and longevity hedging, Q4 2014.
HyndmanR.J., BoothH. and YasmeenF. (2013) Coherent mortality forecasting: The product-ratio method with functional time series models. Demography, 50 (1), 261283.
JarnerS.F. and KrygerE.M. (2011) Modelling adult mortality in small populations: The saint model. ASTIN Bulletin, 41 (2), 377418.
KleinowT. (2015) A common age effect model for the mortality of multiple populations. Insurance: Mathematics and Economics, 63, 147152.
KoissiM.-C., ShapiroA. and HognasG. (2006) Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics, 38 (1), 120.
LeeR.D. and CarterL.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87 (419), 659671.
LiJ. (2012) A Poisson common factor model for projecting mortality and life expectancy jointly for females and males. Population Studies, 67 (1), 111126.
LiJ.S.-H. and HardyM.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15 (2), 177200.
LiJ.S.-H., ZhouR. and HardyM. (2015) A step-by-step guide to building two-population stochastic mortality models. Insurance: Mathematics and Economics, 63, 121134.
LiN. and LeeR.D. (2005) Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42 (3), 575594.
LLMA (2012) Basis risk in longevity hedging: Parallels with the past. Institutional Investor Journals, 2012 (1), 3945.
LuJ.L.C., WongW. and BajekalM. (2014) Mortality improvement by socio-economic circumstances in England (1982 to 2006). British Actuarial Journal, 19 (1), 135.
NobleM., MclennanD., WilkinsonK., WhitworthA., ExleyS., BarnesH. and DibbenC. (2007) The English Indices of Deprivation 2007. London: Department of Communities and Local Government.
PlatR. (2009a) On stochastic mortality modeling. Insurance: Mathematics and Economics, 45 (3), 393404.
PlatR. (2009b) Stochastic portfolio specific mortality and the quantification of mortality basis risk. Insurance: Mathematics and Economics, 45 (1), 123132.
RenshawA. and HabermanS. (2006) A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38 (3), 556570.
RenshawA. and HabermanS. (2008) On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling. Insurance: Mathematics and Economics, 42 (2), 797816.
RussolilloM., GiordanoG. and HabermanS. (2011) Extending the Lee-Carter model: A three-way decomposition. Scandinavian Actuarial Journal, (2), 96–117.
VillegasA.M. and HabermanS. (2014) On the modeling and forecasting of socioeconomic mortality differentials: An application to deprivation and mortality in England. North American Actuarial Journal, 18 (1), 168193.
VillegasA.M., KaishevV. and MillossovichP. (2017) StMoMo: An R Package for Stochastic Mortality Modelling. Journal of Statistical Software, preprint.
WanC. and BertschiL. (2015) 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, 6675.
WilletsR. (2004) The cohort effect: Insights and explanations. British Actuarial Journal, 10 (4), 833877.
WilmothJ. and ValkonenT. (2001) A parametric representation of mortality differentials over age and time. Fifth Seminar of EAPS Working Group on Differential in Health, Morbidity and Mortality in Europe.
YangB., LiJ. and BalasooriyaU. (2016) Cohort extensions of the Poisson common factor model for modelling both genders jointly. Scandinavian Actuarial Journal, 2016 (2), 93112.
YangS.S. and WangC.-W. (2013) Pricing and securitization of multi-country longevity risk with mortality dependence. Insurance: Mathematics and Economics, 52 (2), 157169.
ZhouR., WangY., KaufholdK., LiJ.S.-H. and TanK.S. (2014) Modeling period effects in multi-population mortality models: Applications to Solvency II. North American Actuarial Journal, 18 (1), 150167.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 53 *
Loading metrics...

Abstract views

Total abstract views: 157 *
Loading metrics...

* Views captured on Cambridge Core between 29th August 2017 - 23rd October 2017. This data will be updated every 24 hours.