Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-23T07:15:53.641Z Has data issue: false hasContentIssue false
  • English
  • Français

A COMPARATIVE STUDY OF TWO-POPULATION MODELS FOR THE ASSESSMENT OF BASIS RISK IN LONGEVITY HEDGES

Published online by Cambridge University Press:  29 August 2017

Andrés M. Villegas ,
Steven Haberman ,
Vladimir K. Kaishev  and
Pietro Millossovich
Andrés M. Villegas
Affiliation:
School of Risk and Actuarial Studies and ARC Centre of Excellence in Population Ageing Research (CEPAR), UNSW Business School, University of New South Wales, Sydney, Australia, E-Mail: a.villegas@unsw.edu.au
Steven Haberman
Affiliation:
Cass Business School, Faculty of Actuarial Science and Insurance, City, University of London, London, UK, E-Mail: s.haberman@city.ac.uk
Vladimir K. Kaishev
Affiliation:
Cass Business School, Faculty of Actuarial Science and Insurance, City, University of London, London, UK, E-Mail: v.kaishev@city.ac.uk
Pietro Millossovich*
Affiliation:
Cass Business School, Faculty of Actuarial Science and Insurance, City, University of London, London, UK Department of Economics, Business Mathematics and Statistics ‘B. de Finetti’, University of Trieste, Italy
*
E-Mail: Pietro.Millossovich.1@city.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

Stochastic moralitylongevity basis risktwo-population mortality modelshedge effectivenessindex-based hedges
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 631 - 679
Copyright
Copyright © Astin Bulletin 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahcan, A., Medved, D., Olivieri, A. and Pitacco, E. (2014) Forecasting mortality for small populations by mixing mortality data. Insurance: Mathematics and Economics, 54, 12–27.Google Scholar
Ahmadi, S.S. and Li, J.S.-H. (2014) Coherent mortality forecasting with generalized linear models: A modified time-transformation approach. Insurance: Mathematics and Economics, 59, 194–221.Google Scholar
Antonio, K., Bardoutsos, A. and Ouburg, W. (2015) Bayesian Poisson log-bilinear models for mortality projections with multiple populations. European Actuarial Journal, 5 (2), 245–281.CrossRefGoogle Scholar
Biatat, V. and Currie, I.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.Google Scholar
Booth, H., Hyndman, R.J., Tickle, L. and de Jong, P. (2006) Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions. Demography, 15, 289–310.Google Scholar
Börger, M., Fleischer, D. and Kuksin, N. (2013) Modeling the mortality trend under modern solvency regimes. ASTIN Bulletin, 44 (1), 1–38.CrossRefGoogle Scholar
Brouhns, N., Denuit, M. and Van Keilegom, I. (2005) Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 2005 (3), 212–224.Google Scholar
Butt, Z. and Haberman, S. (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.Google Scholar
Cairns, A.J.G. (2013) Robust hedging of longevity risk. Journal of Risk and Insurance, 80, 621–648.Google Scholar
Cairns, A.J.G., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73 (4), 687–718.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D. and Dowd, K. (2008) Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal, 2008 (2), 79–113.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K. and Coughlan, G.D. (2011a) Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41, 29–59.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D. and Khalaf-Allah, M. (2011b) Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48 (3), 355–367.Google Scholar
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 and Wales and the United States. North American Actuarial Journal, 13 (1), 1–35.Google Scholar
Cairns, A.J.G., Dowd, K., Blake, D. and Coughlan, G.D. (2014) Longevity hedge effectiveness: A decomposition. Quantitative Finance, 14 (2), 217–235.Google Scholar
Carter, L.R. and Lee, R.D. (1992) Modeling and forecasting US sex differentials in mortality. International Journal of Forecasting, 8 (3), 393–411.Google Scholar
Continuous Mortality Investigation (2007) Stochastic projection methodologies: Lee–Carter model features, example results and implications. Working Paper n. 25.Google Scholar
Coughlan, G.D., Khalaf-Allah, 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. North American Actuarial Journal, 15 (2), 150–176.Google Scholar
Currie, I.D., Durban, M. and Eilers, P.H. (2004) Smoothing and forecasting mortality rates. Statistical Modelling, 4 (4), 279–298.Google Scholar
Debón, A., Martínez-Ruiz, F. and Montes, F. (2010) A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47 (3), 327–336.Google Scholar
Debón, A., Montes, F. and Martínez-Ruiz, F. (2011) Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions. European Actuarial Journal, 1 (2), 291–308.CrossRefGoogle Scholar
Delwarde, A., Denuit, M., Guillén, M. and Vidiella-i Anguera, A. (2006) Application of the Poisson log-bilinear projection model to the G5 mortality experience. Belgian Actuarial Bulletin, 6 (1), 54–68.Google Scholar
Dowd, K., Cairns, A. J.G., Blake, D., Coughlan, G.D., Epstein, D. and Khalaf-Allah, M. (2010) Backtesting stochastic mortality models: An ex-post evaluation of multi-period-ahead density forecasts. North American Actuarial Journal, 14 (3), 281–298.Google Scholar
Dowd, K., Cairns, A.J.G., Blake, D., Coughlan, G.D. and Khalaf-Allah, M. (2011) A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15 (2), 334–356.Google Scholar
Haberman, S., Kaishev, V.K., Millossovich, P., Villegas, A.M., Baxter, S., Gaches, A., Gunnlaugsson, S. and Sison, M. (2014) Longevity basis risk: A methodology for assessing basis risk. Institute and Faculty of Actuaries Sessional Research Paper. http://www.actuaries.org.uk/documents/longevity-basis-risk-methodology-assessing-basis-risk Google Scholar
Haberman, S. and Renshaw, A. (2009) On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics, 45 (2), 255–270.Google Scholar
Haberman, S. and Renshaw, A. (2011) A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48 (1), 35–55.Google Scholar
Hatzopoulos, P. and Haberman, S. (2013) Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data. Insurance: Mathematics and Economics, 52 (2), 320–337.Google Scholar
Human Mortality Database (2013) University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). www.mortality.org Google Scholar
Hunt, A. and Blake, D. (2015a) Modelling longevity bonds: Analysing the Swiss Re Kortis bond. Insurance: Mathematics and Economics, 63, 12–29.Google Scholar
Hunt, A. and Blake, D. (2015b) On the structure and classification of mortality models mortality models. Pension Institute Working Paper PI-1506. http://www.pensions-institute.org/workingpapers/wp1506.pdf Google Scholar
Hunt, A. and Villegas, A.M. (2015) Robustness and convergence in the Lee-Carter model with cohorts. Insurance: Mathematics and Economics, 64, 186–202.Google Scholar
Hymans Robertson LLP (2015) Buy-outs, buy-ins and longevity hedging, Q4 2014. http://www.hymans.co.uk/media/591924/150317-managing-pension-scheme-risk-q4-2014.pdf Google Scholar
Hyndman, R.J., Booth, H. and Yasmeen, F. (2013) Coherent mortality forecasting: The product-ratio method with functional time series models. Demography, 50 (1), 261–283.Google Scholar
Jarner, S.F. and Kryger, E.M. (2011) Modelling adult mortality in small populations: The saint model. ASTIN Bulletin, 41 (2), 377–418.Google Scholar
Kleinow, T. (2015) A common age effect model for the mortality of multiple populations. Insurance: Mathematics and Economics, 63, 147–152.Google Scholar
Koissi, M.-C., Shapiro, A. and Hognas, G. (2006) Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics, 38 (1), 1–20.Google Scholar
Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87 (419), 659–671.Google Scholar
Li, J. (2012) A Poisson common factor model for projecting mortality and life expectancy jointly for females and males. Population Studies, 67 (1), 111–126.CrossRefGoogle ScholarPubMed
Li, J.S.-H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15 (2), 177–200.Google Scholar
Li, J.S.-H., Zhou, R. and Hardy, M. (2015) A step-by-step guide to building two-population stochastic mortality models. Insurance: Mathematics and Economics, 63, 121–134.Google Scholar
Li, N. and Lee, R.D. (2005) Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42 (3), 575–594.Google Scholar
LLMA (2012) Basis risk in longevity hedging: Parallels with the past. Institutional Investor Journals, 2012 (1), 39–45.Google Scholar
Lu, J.L.C., Wong, W. and Bajekal, M. (2014) Mortality improvement by socio-economic circumstances in England (1982 to 2006). British Actuarial Journal, 19 (1), 1–35.CrossRefGoogle Scholar
Noble, M., Mclennan, D., Wilkinson, K., Whitworth, A., Exley, S., Barnes, H. and Dibben, C. (2007) The English Indices of Deprivation 2007. London: Department of Communities and Local Government.Google Scholar
Plat, R. (2009a) On stochastic mortality modeling. Insurance: Mathematics and Economics, 45 (3), 393–404.Google Scholar
Plat, R. (2009b) Stochastic portfolio specific mortality and the quantification of mortality basis risk. Insurance: Mathematics and Economics, 45 (1), 123–132.Google Scholar
Renshaw, A. and Haberman, S. (2006) A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38 (3), 556–570.Google Scholar
Renshaw, A. and Haberman, S. (2008) On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling. Insurance: Mathematics and Economics, 42 (2), 797–816.Google Scholar
Russolillo, M., Giordano, G. and Haberman, S. (2011) Extending the Lee-Carter model: A three-way decomposition. Scandinavian Actuarial Journal, (2), 96–117.CrossRefGoogle Scholar
Villegas, A.M. and Haberman, S. (2014) On the modeling and forecasting of socioeconomic mortality differentials: An application to deprivation and mortality in England. North American Actuarial Journal, 18 (1), 168–193.Google Scholar
Villegas, A.M., Kaishev, V. and Millossovich, P. (2017) StMoMo: An R Package for Stochastic Mortality Modelling. Journal of Statistical Software, preprint. http://openaccess.city.ac.uk/17378/ Google Scholar
Wan, C. and Bertschi, L. (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, 66–75.Google Scholar
Willets, R. (2004) The cohort effect: Insights and explanations. British Actuarial Journal, 10 (4), 833–877.CrossRefGoogle Scholar
Wilmoth, J. and Valkonen, T. (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.Google Scholar
Wood, S. (2015) Package mgcv. http://cran.r-project.org/web/packages/mgcv/index.html Google Scholar
Yang, B., Li, J. and Balasooriya, U. (2016) Cohort extensions of the Poisson common factor model for modelling both genders jointly. Scandinavian Actuarial Journal, 2016 (2), 93–112.CrossRefGoogle Scholar
Yang, S.S. and Wang, C.-W. (2013) Pricing and securitization of multi-country longevity risk with mortality dependence. Insurance: Mathematics and Economics, 52 (2), 157–169.Google Scholar
Zhou, R., Wang, Y., Kaufhold, K., Li, J.S.-H. and Tan, K.S. (2014) Modeling period effects in multi-population mortality models: Applications to Solvency II. North American Actuarial Journal, 18 (1), 150–167.Google Scholar