IDEAS home Printed from https://ideas.repec.org/a/bpj/apjrin/v5y2011i2n2.html
   My bibliography  Save this article

Longevity Risk and the Econometric Analysis of Mortality Trends and Volatility

Author

Listed:
  • Njenga Carolyn N

    (University of New South Wales)

  • Sherris Michael

    (University of New South Wales)

Abstract

Longevity risk and the modeling of trends and volatility for mortality improvement have attracted increased attention driven by ageing populations around the world and the expected financial implications. The original Lee-Carter model that was used for longevity risk assessment included a single improvement factor with differential impacts by age. Financial models that allow for risk pricing and risk management have attracted increasing attention along with multiple factor models. This paper investigates trends, including common trends through co-integration, and the factors driving the volatility of mortality using principal components analysis for a number of developed countries including Australia, England, Japan, Norway and USA. The results demonstrate the need for multiple factors for modeling mortality rates across all these countries. The basic structure of the Lee-Carter model cannot adequately model the random variation and the full risk structure of mortality changes. Trends by country are found to be stochastic. Common trends and co-integrating relationships are found across ages highlighting the benefits from modeling mortality rates as a system in a Vector-Autoregressive (VAR) model and capturing long run equilibrium relationships in a Vector Error-Correction Model (VECM) framework.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:apjrin:v:5:y:2011:i:2:n:2
    DOI: 10.2202/2153-3792.1115
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/2153-3792.1115
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/2153-3792.1115?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Katja Hanewald, 2009. "Mortality modeling: Lee-Carter and the macroeconomy," SFB 649 Discussion Papers SFB649DP2009-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer;Population Association of America (PAA), vol. 38(4), pages 537-549, November.
    3. Carlos Wong-Fupuy & Steven Haberman, 2004. "Projecting Mortality Trends," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 56-83.
    4. Pagan, A.R. & Pesaran, M. Hashem, 2008. "Econometric analysis of structural systems with permanent and transitory shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3376-3395, October.
    5. Pfaff, Bernhard, 2008. "VAR, SVAR and SVEC Models: Implementation Within R Package vars," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i04).
    6. Shripad Tuljapurkar, 1998. "Forecasting Mortality Change," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(4), pages 127-134.
    7. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    8. Robert McNown & Andrei Rogers, 1989. "Forecasting Mortality: A Parameterized Time Series Approach," Demography, Springer;Population Association of America (PAA), vol. 26(4), pages 645-660, November.
    9. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310.
    10. Ronald Lee, 2000. "The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(1), pages 80-91.
    11. Shripad Tuljapurkar & Carl Boe, "undated". "Mortality Change and Forecasting: How Much and How Little Do We Know?," Pension Research Council Working Papers 98-2, Wharton School Pension Research Council, University of Pennsylvania.
    12. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    13. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    14. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    15. Shripad Tuljapurkar & Carl Boe, 1998. "Mortality Change and Forecasting," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(4), pages 13-47.
    16. Anonymous, 2009. "Abstract of the discussion," British Actuarial Journal, Cambridge University Press, vol. 15(1), pages 202-217, March.
    17. 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.
    18. 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.
    19. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    20. Umberto Triacca, 2002. "Cointegration in VAR(1) process: Characterization and testing," Statistical Papers, Springer, vol. 43(3), pages 435-443, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. David Atance & Alejandro Balbás & Eliseo Navarro, 2020. "Constructing dynamic life tables with a single-factor model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 787-825, December.
    2. 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.
    3. Jarner, Søren F. & Jallbjørn, Snorre, 2020. "Pitfalls and merits of cointegration-based mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 80-93.
    4. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    5. Arnold, Séverine & Glushko, Viktoriya, 2021. "Cause-specific mortality rates: Common trends and differences," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 294-308.
    6. A. Ntamjokouen & S. Haberman & G. Consigli, 2017. "Projecting the long run relationship of Multi-population life expectancy by race," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(2), pages 1-3.
    7. Giuseppe Giordano & Steven Haberman & Maria Russolillo, 2019. "Coherent modeling of mortality patterns for age-specific subgroups," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 189-204, June.
    8. Yajing Xu & Michael Sherris & Jonathan Ziveyi, 2020. "Market Price of Longevity Risk for a Multi‐Cohort Mortality Model With Application to Longevity Bond Option Pricing," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(3), pages 571-595, September.
    9. Yang Chang & Michael Sherris, 2018. "Longevity Risk Management and the Development of a Value-Based Longevity Index," Risks, MDPI, vol. 6(1), pages 1-20, February.
    10. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    2. Niels Haldrup & Carsten P. T. Rosenskjold, 2019. "A Parametric Factor Model of the Term Structure of Mortality," Econometrics, MDPI, vol. 7(1), pages 1-22, March.
    3. Haberman, Steven & Renshaw, Arthur, 2011. "A comparative study of parametric mortality projection models," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 35-55, January.
    4. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    5. Hatzopoulos, P. & Haberman, S., 2009. "A parameterized approach to modeling and forecasting mortality," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 103-123, February.
    6. Hyndman, Rob J. & Booth, Heather, 2008. "Stochastic population forecasts using functional data models for mortality, fertility and migration," International Journal of Forecasting, Elsevier, vol. 24(3), pages 323-342.
    7. Jorge Bravo, 2011. "Pricing Longevity Bonds Using Affine-Jump Diffusion Models," CEFAGE-UE Working Papers 2011_29, University of Evora, CEFAGE-UE (Portugal).
    8. Tickle Leonie & Booth Heather, 2014. "The Longevity Prospects of Australian Seniors: An Evaluation of Forecast Method and Outcome," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 8(2), pages 1-34, July.
    9. Colin O’hare & Youwei Li, 2017. "Modelling mortality: are we heading in the right direction?," Applied Economics, Taylor & Francis Journals, vol. 49(2), pages 170-187, January.
    10. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2022. "Thirty years on: A review of the Lee-Carter method for forecasting mortality," SocArXiv 8u34d, Center for Open Science.
    11. O'Hare, Colin & Li, Youwei, 2014. "Identifying structural breaks in stochastic mortality models," MPRA Paper 62994, University Library of Munich, Germany.
    12. 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.
    13. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    14. Ahbab Mohammad Fazle Rabbi & Stefano Mazzuco, 2021. "Mortality Forecasting with the Lee–Carter Method: Adjusting for Smoothing and Lifespan Disparity," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 97-120, March.
    15. Marie-Pier Bergeron-Boucher & Søren Kjærgaard & James E. Oeppen & James W. Vaupel, 2019. "The impact of the choice of life table statistics when forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(43), pages 1235-1268.
    16. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    17. Hong Li & Johnny Siu-Hang Li, 2017. "Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements," Demography, Springer;Population Association of America (PAA), vol. 54(3), pages 1073-1095, June.
    18. Han Lin Shang & Heather Booth & Rob Hyndman, 2011. "Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 25(5), pages 173-214.
    19. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2010. "Evaluating the goodness of fit of stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 255-265, December.
    20. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:apjrin:v:5:y:2011:i:2:n:2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.