Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T14:15:40.617Z Has data issue: false hasContentIssue false
  • English
  • Français

MODELING LONGEVITY RISK WITH GENERALIZED DYNAMIC FACTOR MODELS AND VINE-COPULAE

Published online by Cambridge University Press:  11 November 2015

Helena Chuliá ,
Montserrat Guillén  and
Jorge M. Uribe
Helena Chuliá
Affiliation:
Universitat de Barcelona, Department of Econometrics and Riskcenter-IREA, Spain E-Mail: hchulia@ub.edu
Montserrat Guillén
Affiliation:
Department of Econometrics and Riskcenter-IREA, Universitat de Barcelona, Spain E-Mail: mgillen@ub.edu
Jorge M. Uribe*
Affiliation:
Department of Economics, Universidad del Valle, Colombia
*
E-Mail: jorge.uribe@correounivalle.edu.co
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a methodology to forecast mortality rates and estimate longevity and mortality risks. The methodology uses generalized dynamic factor models fitted to the differences in the log-mortality rates. We compare their prediction performance with that of models previously described in the literature, including the traditional static factor model fitted to log-mortality rates. We also construct risk measures using vine-copula simulations, which take into account the dependence between the idiosyncratic components of the mortality rates. The methodology is applied to forecast mortality rates for a population portfolio for the UK and to estimate longevity and mortality risks.

Keywords

Longevitymortality forecastingfactor modelsvine-copulaevalue-at-risk
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 1 , January 2016 , pp. 165 - 190
Copyright
Copyright © Astin Bulletin 2015 

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

Aas, K., Czado, C., Frigessi, A. and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44 (2), 182–198.Google Scholar
Alai, D.H. and Sherris, M. (2014) Rethinking age-period-cohort mortality trend models. Scandinavian Actuarial Journal, 2014 (3), 208–227.CrossRefGoogle Scholar
Alonso, A.M. (2008) Predicción de Tablas de Mortalidad Dinámicas Mediante un Procedimiento Bootstrap. Madrid: Fundación MAPFRE.Google Scholar
Bai, J. and Ng, S. (2002) Determining the number of factors in approximate factor models. Econometrica, 70 (1), 191–221.CrossRefGoogle Scholar
Bai, J. and Ng, S. (2004) A panic attack on unit roots and cointegration. Econometrica, 72 (4), 1127–1177.CrossRefGoogle Scholar
Bai, J. and Ng, S. (2007) Determining the number of primitive shocks in factor models. Journal of Business and Economic Statistics, 25 (1), 52–60.CrossRefGoogle Scholar
Bai, J. and Ng, S. (2008) Large dimensional factor analysis. Foundations and Trends in Econometrics, 3 (2), 89–163.CrossRefGoogle Scholar
Bai, J. and Wang, P. (2012) Identification and estimation of dynamic factor models. MPRA Paper, 38434. Available at: https://mpra.ub.uni-muenchen.de/38434/2/MPRA_paper_38434.pdfGoogle Scholar
Bates, B.J., Plagborg-Møller, M., Stock, J.H. and Watson, M.W. (2013) Consistent factor estimation in dynamic factor models with structural instability. Journal of Econometrics, 177 (2), 289–304.CrossRefGoogle Scholar
Bedford, T. and Cooke, R.M. (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence, 32 (1–4), 245–268.CrossRefGoogle Scholar
Bedford, T. and Cooke, R.M. (2002) Vines - A new graphical model for dependent random variables. Annals of Statistics, 30 (4), 1031–1068.CrossRefGoogle Scholar
Belles-Sampera, J., Guillén, M. and Santolino, M. (2014) Beyond value-at-risk: GlueVaR distortion risk measures. Risk Analysis, 34 (1), 121–134.CrossRefGoogle ScholarPubMed
Bisetti, E. and Favero, C.A. (2014) Measuring the impact of longevity risk on pension systems: The case of Italy. North American Actuarial Journal, 18 (1), 87–103.CrossRefGoogle Scholar
Blake, D., Boardman, T. and Cairns, A. (2014) Sharing longevity risk: Why governments should issue longevity bonds. North American Actuarial Journal, 18 (1), 258–277.CrossRefGoogle Scholar
Brouhns, N. and Denuit, M. (2002) Risque de longévité et rentes viagères II. Tables de mortalité prospectives pour la population belge. Belgian Actuarial Bulletin, 2 (1), 49–63.Google Scholar
Cairns, A.J. (2011) Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging. Insurance: Mathematics and Economics, 49 (3), 438–453.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. The Journal of Risk and Insurance, 73 (4), 687–718.CrossRefGoogle Scholar
Cairns, A., Blake, D., Dowd, K., Coughlan, 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.CrossRefGoogle Scholar
Cairns, A., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D. and Khalaf-Allah, M. (2011) Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48 (3), 355–367.Google Scholar
Continuous Mortality Investigation. (2004) Projecting future mortality: A discussion paper. Working paper, 3. Available at: http://www.actuaries.org.uk/research-and-resources/documents/cmi-working-paper-3-projecting-future-mortality-discussion-paperGoogle Scholar
Continuous Mortality Investigation. (2005) Projecting future mortality: Towards a proposal for a stochastic methodology. Working paper, 15. Available at: http://www.actuaries.org.uk/research-and-resources/documents/cmi-working-paper-15-projecting-future-mortality-towards-proposal-sGoogle Scholar
Continuous Mortality Investigation. (2013) The CMI mortality projections model, CMI_2012. Working paper, 63. Available at: http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-paper-63Google Scholar
Cossette, H., Delwarde, A., Denuit, M., Guillot, F. and Marceau, É. (2007) Pension plan valuation and mortality projection: A case study with mortality data. North American Actuarial Journal, 11 (2), 1–34.CrossRefGoogle Scholar
Currie, I. (2006) Smoothing and Forecasting Mortality Rates with P-splines. Presented at the Institute of Actuaries, London. Available at: http://www.macs.hw.ac.uk/~iain/research/talks/Mortality.pdfGoogle Scholar
Currie, I.D., Durban, M. and Eilers, P.H. (2004) Smoothing and forecasting mortality rates. Statistical Modelling, 4 (4), 279–298.CrossRefGoogle Scholar
D'amato, V., Haberman, S., Piscopo, G. and Russolillo, M. (2012) Modelling dependent data for longevity projections. Insurance: Mathematics and Economics, 51 (3), 694–701.Google Scholar
D'amato, V., Haberman, S., Piscopo, G., Russolillo, M. and Trapani, L. (2014) Detecting common longevity trends by a multiple population approach. North American Actuarial Journal, 18 (1), 139–149.CrossRefGoogle Scholar
Dahl, M., Melchior, M. and Møller, T. (2008) On systematic mortality risk and risk-minimization with survivor swaps. Scandinavian Actuarial Journal, 2008 (2–3), 114–146.CrossRefGoogle Scholar
Delwarde, A., Denuit, M., Guillén, M. and Vidiella-I-Anguera, A. (2007) Application of the poisson log-bilinear projection model to the G5 mortality experience. Belgian Actuarial Bulletin, 6 (1), 54–68.Google Scholar
Denton, F.T., Feaver, C.H. and Spencer, B.G. (2005) Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy. Journal of Population Economics, 18 (2), 203–227.CrossRefGoogle Scholar
Dushi, I., Friedberg, L. and Webb, T. (2010) The impact of aggregate mortality risk on defined benefit pension plans. Journal of Pension Economics and Finance, 9 (4), 481–503.CrossRefGoogle Scholar
Engle, R.F. and Granger, C.W.J. (1987) Co-Integration and error correction: Representation, estimation and testing. Econometrica, 55 (2), 251–276.CrossRefGoogle Scholar
Escribano, Á. and Peña, D. (1994) Cointegration and common factors. Journal of Time Series Analysis, 15 (6), 577–586.CrossRefGoogle Scholar
Forni, M. and Reichlin, L. (1998) Let's get real: Factor to analytical cycle approach dynamics disaggregated business. The Review of Economic Studies, 65 (3), 453–473.CrossRefGoogle Scholar
Forni, M., Hallin, M., Lippi, M. and Reichlin, L. (2000) The generalized dynamic-factor model: Identification and estimation. The Review of Economics and Statistics, 82 (4), 540–554.CrossRefGoogle Scholar
Forni, M., Hallin, M., Lippi, M. and Reichlin, L. (2004) The generalized dynamic factor model consistency and rates. Journal of Econometrics, 119 (2), 231–255.CrossRefGoogle Scholar
Forni, M., Hallin, M., Lippi, M. and Reichlin, L. (2005) The generalized dynamic factor model: One-sided estimation and forecasting. Journal of the American Statistical Association, 100 (471), 830–840.CrossRefGoogle Scholar
Gaille, S. and Sherris, M. (2011) Modelling mortality with common stochastic long-run trends. The Geneva Papers on Risk and Insurance-Issues and Practice, 36 (4), 595–621.CrossRefGoogle Scholar
Granger, C.W.J. and Newbold, P. (1974) Spurious regressions in econometrics. Journal of Econometrics, 2 (2), 111–120.CrossRefGoogle Scholar
Haberman, S. and Renshaw, A. (2012) Parametric mortality improvement rate modelling and projecting. Insurance: Mathematics and Economics, 50 (3), 309–333.Google Scholar
Haberman, S. and Renshaw, A. (2013) Modelling and projecting mortality improvement rates using a cohort perspective. Insurance: Mathematics and Economics, 53 (1), 150–168.Google Scholar
Hamilton, J.D. (1994) Time Series Analysis. Princeton: Princeton University Press.CrossRefGoogle Scholar
Hanewald, K., Post, T. and Gründl, H. (2011) Stochastic mortality, macroeconomic risks and life insurer solvency. The Geneva Papers on Risk and Insurance-Issues and Practice, 36 (3), 458–475.CrossRefGoogle Scholar
Hári, N., De Waegenaere, A., Melenberg, B. and Nijman, T.E. (2008) Longevity risk in portfolios of pension annuities. Insurance: Mathematics and Economics, 42 (2), 505–519.Google Scholar
Harvey, A.C. (1990) Forecasting, Structural Time Series Models and the Kalman Filter. New York: Cambridge University Press.CrossRefGoogle Scholar
Hollmann, F.W., Mulder, T.J. and Kallan, J.E. (2000) Methodology and assumptions for the population projections of the United States: 1999 to 2100. Population Division U.S. Census Bureau. Working paper, 38. Available at: http://census.gov/population/www/documentation/twps0038/twps0038.htmlGoogle Scholar
Holmes, E.E., Ward, E.J. and Scheuerell, M.D. (2014) Analysis of Multivariate Time-Series using the MARSS Package. Seattle: Northwest Fisheries Science Center, NOAA.Google Scholar
Jevtić, P., Luciano, E. and Vigna, E. (2013) Mortality surface by means of continuous time cohort models. Insurance: Mathematics and Economics, 53 (1), 122–133.Google Scholar
Joe, H. (1996) Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. Lecture Notes-Monograph Series, 28, 120–141.CrossRefGoogle Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12 (2–3), 231–254.CrossRefGoogle Scholar
Kurowicka, D. and Cooke, R.M. (2005) Distribution-free continuous bayesian belief nets. In Wilson, A., Keller-McNulty, S., Armijo, Y., Limnios, N., Modern Statistical and Mathematical Methods in Reliability, pp. 309–323. World Scientific Publishing Company, Singapore.CrossRefGoogle 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
Lemoine, K. (2014) Mortality regimes and longevity risk in a life annuity portfolio. Scandinavian Actuarial Journal (Published Online), 1–36. Available at: http://www.tandfonline/com/doi/abs/10.1080/03461238.2014.882860?journalCode=sact20Google Scholar
Lin, T., Wang, C.W. and Tsai, C.C.H. (2015) Age specific copula-AR-GARCH mortality models. Insurance: Mathematics and Economics, 61 (March 2015), 110–124.Google Scholar
Lorson, J. and Wagner, J. (2014) The pricing of hedging longevity risk with the help of annuity securitization: An application to the German market. The Journal of Risk Finance: The Convergence of Financial Products and Insurance, 15 (4), 385–416.CrossRefGoogle Scholar
MacMinn, R., Brockett, P. and Blake, D. (2006) Longevity risk and capital markets. The Journal of Risk and Insurance, 73 (4), 551–557.CrossRefGoogle Scholar
Mcneil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton: Princeton University Press.Google Scholar
Mitchell, D., Brockett, P., Mendoza-Arriaga, R. and Muthuraman, K. (2013) Modeling and forecasting mortality rates. Insurance: Mathematics and Economics, 52 (2), 275–285.Google Scholar
Ngai, A. and Sherris, M. (2011) Longevity risk management for life and variable annuities: Effectiveness of static hedging using longevity bonds and derivatives. Insurance: Mathematics and Economics, 49 (1), 100–114.Google Scholar
Njenga, C.N. and Sherris, M. (2011) Longevity risk and the econometric analysis of mortality trends and volatility. Asia-Pacific Journal of Risk and Insurance, 5 (2), 1–54.CrossRefGoogle Scholar
Olivieri, A. (2011) Stochastic mortality: Experience-based modeling and application issues consistent with Solvency 2. European Actuarial Journal, 1 (1), 101–125.CrossRefGoogle Scholar
Peña, D. and Poncela, P. (2006) Nonstationary dynamic factor analysis. Journal of Statistical Planning and Inference, 136 (4), 1237–1257.CrossRefGoogle Scholar
Plat, R. (2011) One-year value-at-risk for longevity and mortality. Insurance: Mathematics and Economics 49 (3), 462–470.Google Scholar
Renshaw, A.E. 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
Richards, S. and Jones, G. (2004) Financial Aspects of Longevity Risk. Working paper presented in the Staple Inn Actuarial Society. Available at: http://sias.org.uk/resources/papers/f4c264d7c93007ff32ea515801f77973.pdfGoogle Scholar
Sklar, A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut de Statistique de l'Université de Paris VIII, 229–231.Google Scholar
Stallard, E. (2006) Demographic issues in longevity risk analysis. The Journal of Risk and Insurance, 73 (4), 575–609.CrossRefGoogle Scholar
Stock, J.H. and Watson, M.W. (1988) Testing for common trends. Journal of the American Statistical Association, 83 (404), 1097–1107.CrossRefGoogle Scholar
Stock, J.H. and Watson, M.W. (2002) Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97 (460), 1167–1179.CrossRefGoogle Scholar
Stock, J.H. and Watson, M.W. (2006) Forecasting with many predictors. In Elliot, G., Granger, C.W.J., Timmermann, A., Handbook of Economic Forecasting, vol. 1, pp. 515–554. Elsevier, Tampa (FL).CrossRefGoogle Scholar
Stock, J.H. and Watson, M.W. (2010) Dynamic factor models. In Clements, M.P., Henry, D.F., Oxford Handbook of Economic Forecasting. pp. 35–59. Oxford University Press, Oxford.Google Scholar
Torri, T. (2011) Building blocks for a mortality index: An international context. European Actuarial Journal, 1 (1), 127–141.CrossRefGoogle Scholar
Wills, S. and Sherris, M. (2008) Integrating financial and demographic longevity risk models: An Australian model for financial applications. Australian School of Business Research. Working paper, 2008ACTL05. Available at: http://www/actuaries.asn.au/Library/Events/FSF/2008/FSF08_6d_Paper_Wills_Mortality.pdfGoogle Scholar
Wong, T.W., Chiu, M.C. and Wong, H.Y. (2014) Time-consistent mean-variance hedging of longevity risk: Effect of cointegration. Insurance: Mathematics and Economics, 56 (May 2014), 56–67.Google Scholar
Yang, S.S., Yue, J.C. and Huang, H.-C. (2010) Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models. Insurance: Mathematics and Economics, 46 (1), 254–270.Google Scholar
Zuur, A.F., Fryer, R.J., Jolliffe, I.T., Dekker, R. and Beukema, J.J. (2003) Estimating common trends in multivariate time series using dynamic factor analysis. Environmetrics, 14 (7), 665–685.CrossRefGoogle Scholar