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Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions

Author

Listed:
  • Helena Chuliá

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • Montserrat Guillén

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • Jorge M. Uribe

    (Facultad de Ciencias Sociales y Economicas, Universidad del Valle)

Abstract

We present a methodology to forecast mortality rates and estimate longevity and mortality risks. The methodology uses Generalized Dynamic Factor Models fitted over the differences of the log-mortality rates. We compare prediction performance with models previously proposed in the literature, such as the traditional Static Factor Model fitted over the level of log-mortality rates. We also construct risk measures by the means of vinecopulae simulations, taking into account the dependence between the idiosyncratic components of the mortality rates. The methodology is implemented to project the mortality rates of the United Kingdom, for which we consider a portfolio and study longevity and mortality risks.

Suggested Citation

  • Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.
    • Handle: RePEc:bak:wpaper:201503
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    as
    1. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    2. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
    3. Felipe, Angie & Guillen, Montserrat & Nielsen, Jens Perch, 2001. "Longevity studies based on kernel hazard estimation," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 191-204, April.
    4. Bates, Brandon J. & Plagborg-Møller, Mikkel & Stock, James H. & Watson, Mark W., 2013. "Consistent factor estimation in dynamic factor models with structural instability," Journal of Econometrics, Elsevier, vol. 177(2), pages 289-304.
    5. Jonas Lorson & Joël Wagner, 2014. "The pricing of hedging longevity risk with the help of annuity securitizations: An application to the German market," Journal of Risk Finance, Emerald Group Publishing, vol. 15(4), pages 385-416, August.
    6. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
    7. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    8. Ngai, Andrew & Sherris, Michael, 2011. "Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 100-114, July.
    9. Njenga Carolyn N & Sherris Michael, 2011. "Longevity Risk and the Econometric Analysis of Mortality Trends and Volatility," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 5(2), pages 1-54, July.
    10. David Blake & Tom Boardman & Andrew Cairns, 2014. "Sharing Longevity Risk: Why Governments Should Issue Longevity Bonds," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 258-277.
    11. Bai, Jushan & Wang, Peng, 2012. "Identification and estimation of dynamic factor models," MPRA Paper 38434, University Library of Munich, Germany.
    12. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    13. Dushi, Irena & Friedberg, Leora & Webb, Tony, 2010. "The impact of aggregate mortality risk on defined benefit pension plans," Journal of Pension Economics and Finance, Cambridge University Press, vol. 9(4), pages 481-503, October.
    14. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    15. Adair Turner, 2006. "Pensions, Risks, and Capital Markets," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 559-574, December.
    16. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, October.
    17. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 10, pages 515-554, Elsevier.
    18. Haberman, Steven & Renshaw, Arthur, 2013. "Modelling and projecting mortality improvement rates using a cohort perspective," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 150-168.
    19. Hélène Cossette & Antoine Delwarde & Michel Denuit & Frédérick Guillot & Étienne Marceau, 2007. "Pension Plan Valuation and Mortality Projection," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 1-34.
    20. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    21. Alvaro Escribano & Daniel Peña, 1994. "Cointegration And Common Factors," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 577-586, November.
    22. Mario Forni & Lucrezia Reichlin, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 453-473.
    23. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    24. Katja Hanewald & Thomas Post & Helmut Gründl, 2011. "Stochastic Mortality, Macroeconomic Risks and Life Insurer Solvency," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(3), pages 458-475, July.
    25. Eric Stallard, 2006. "Demographic Issues in Longevity Risk Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 575-609, December.
    26. Haberman, Steven & Renshaw, Arthur, 2012. "Parametric mortality improvement rate modelling and projecting," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 309-333.
    27. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    28. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    29. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    30. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
    31. Cairns, Andrew J.G., 2011. "Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 438-453.
    32. D’Amato, Valeria & Haberman, Steven & Piscopo, Gabriella & Russolillo, Maria, 2012. "Modelling dependent data for longevity projections," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 694-701.
    33. Wong, Tat Wing & Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Time-consistent mean–variance hedging of longevity risk: Effect of cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 56-67.
    34. Lin, Tzuling & Wang, Chou-Wen & Tsai, Cary Chi-Liang, 2015. "Age-specific copula-AR-GARCH mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 110-124.
    35. Felipe, A. & Guillen, M. & Perez-Marin, A. M., 2002. "Recent Mortality Trends in the Spanish Population," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 757-786, October.
    36. Valeria D’Amato & Steven Haberman & Gabriella Piscopo & Maria Russolillo & Lorenzo Trapani, 2014. "Detecting Common Longevity Trends by a Multiple Population Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 139-149.
    37. David Blake & Pat Brockett & Samuel Cox & Richard MacMinn, 2011. "Longevity Risk and Capital Markets," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 141-149.
    38. Mitchell, Daniel & Brockett, Patrick & Mendoza-Arriaga, Rafael & Muthuraman, Kumar, 2013. "Modeling and forecasting mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 275-285.
    39. Guillen, M. & Nielsen, J. P. & Perez-Marin, A. M., 2006. "Multiplicative Hazard Models for Studying the Evolution of Mortality," Annals of Actuarial Science, Cambridge University Press, vol. 1(1), pages 165-177, March.
    40. Jevtić, Petar & Luciano, Elisa & Vigna, Elena, 2013. "Mortality surface by means of continuous time cohort models," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 122-133.
    41. Yang, Sharon S. & Yue, Jack C. & Huang, Hong-Chih, 2010. "Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 254-270, February.
    42. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2013. "Exchanging uncertain mortality for a cost," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 65-76.
    43. Emilio Bisetti & Carlo Favero, 2014. "Measuring the Impact of Longevity Risk on Pension Systems: The Case of Italy," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 87-103.
    44. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Longevity risk in portfolios of pension annuities," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 505-519, April.
    45. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    46. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    47. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    48. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    49. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    50. Frank Denton & Christine Feaver & Byron Spencer, 2005. "Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy," Journal of Population Economics, Springer;European Society for Population Economics, vol. 18(2), pages 203-227, June.
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    2. Manuela Alcañiz & Aïda Solé-Auró, 2018. "Ageing and health-related quality of life: evidence from Catalonia (Spain)," Working Papers 2018-01, Universitat de Barcelona, UB Riskcenter.

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    Keywords

    Longevity; mortality forecasting; factor models; vine-copulae; Value at Risk.;
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