IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v50y2012i1p85-93.html
   My bibliography  Save this article

A comparison of the Lee–Carter model and AR–ARCH model for forecasting mortality rates

Author

Listed:
  • Giacometti, Rosella
  • Bertocchi, Marida
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.

Abstract

With the decline in the mortality level of populations, national social security systems and insurance companies of most developed countries are reconsidering their mortality tables taking into account the longevity risk. The Lee and Carter model is the first discrete-time stochastic model to consider the increased life expectancy trends in mortality rates and is still broadly used today. In this paper, we propose an alternative to the Lee–Carter model: an AR(1)–ARCH(1) model. More specifically, we compare the performance of these two models with respect to forecasting age-specific mortality in Italy. We fit the two models, with Gaussian and t-student innovations, for the matrix of Italian death rates from 1960 to 2003. We compare the forecast ability of the two approaches in out-of-sample analysis for the period 2004–2006 and find that the AR(1)–ARCH(1) model with t-student innovations provides the best fit among the models studied in this paper.

Suggested Citation

  • Giacometti, Rosella & Bertocchi, Marida & Rachev, Svetlozar T. & Fabozzi, Frank J., 2012. "A comparison of the Lee–Carter model and AR–ARCH model for forecasting mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 85-93.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:85-93
    DOI: 10.1016/j.insmatheco.2011.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711001016
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2011.10.002?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. Alho, Juha M., 1990. "Stochastic methods in population forecasting," International Journal of Forecasting, Elsevier, vol. 6(4), pages 521-530, December.
    2. Angus S. Deaton & Christina Paxson, 2004. "Mortality, Income, and Income Inequality over Time in Britain and the United States," NBER Chapters, in: Perspectives on the Economics of Aging, pages 247-286, National Bureau of Economic Research, Inc.
    3. 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.
    4. 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.
    5. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    6. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    7. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
    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. Chen, Hua & MacMinn, Richard & Sun, Tao, 2015. "Multi-population mortality models: A factor copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 135-146.
    2. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    3. Suryo Adi Rakhmawan & Tahir Mahmood & Nasir Abbas & Muhammad Riaz, 2024. "Unifying mortality forecasting model: an investigation of the COM–Poisson distribution in the GAS model for improved projections," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 800-826, October.
    4. Lingbing Feng & Yanlin Shi, 2018. "Forecasting mortality rates: multivariate or univariate models?," Journal of Population Research, Springer, vol. 35(3), pages 289-318, September.
    5. Li, Hong & Shi, Yanlin, 2021. "Forecasting mortality with international linkages: A global vector-autoregression approach," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 59-75.
    6. Doukhan, P. & Pommeret, D. & Rynkiewicz, J. & Salhi, Y., 2017. "A class of random field memory models for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 97-110.

    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. Virginia R. Young, 2007. "Pricing Life Insurance under Stochastic Mortality via the Instantaneous Sharpe Ratio: Theorems and Proofs," Papers 0705.1297, arXiv.org.
    3. Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Papers 0908.3196, arXiv.org.
    4. 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.
    5. Lee, Yung-Tsung & Wang, Chou-Wen & Huang, Hong-Chih, 2012. "On the valuation of reverse mortgages with regular tenure payments," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 430-441.
    6. Jackie Li, 2014. "An application of MCMC simulation in mortality projection for populations with limited data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(1), pages 1-48.
    7. Li, Jing & Szimayer, Alexander, 2011. "The uncertain mortality intensity framework: Pricing and hedging unit-linked life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 471-486.
    8. Post, Thomas & Hanewald, Katja, 2013. "Longevity risk, subjective survival expectations, and individual saving behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 200-220.
    9. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    10. Jorge Miguel Ventura Bravo, 2011. "Pricing Longevity Bonds Using Affine-Jump Diffusion Models," CEFAGE-UE Working Papers 2011_29, University of Evora, CEFAGE-UE (Portugal).
    11. Pieter van Baal & Frederik Peters & Johan Mackenbach & Wilma Nusselder, 2016. "Forecasting differences in life expectancy by education," Population Studies, Taylor & Francis Journals, vol. 70(2), pages 201-216, May.
    12. Han Lin Shang, 2012. "Point and interval forecasts of age-specific life expectancies," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(21), pages 593-644.
    13. R. Giacometti & S. Ortobelli & M. Bertocchi, 2011. "A Stochastic Model for Mortality Rate on Italian Data," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 216-228, April.
    14. 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.
    15. Li, Jing & Szimayer, Alexander, 2010. "The Uncertain Mortality Intensity Framework: Pricing and Hedging Unit-Linked Life Insurance Contracts," Bonn Econ Discussion Papers 13/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    16. Cox, Samuel H. & Lin, Yijia & Pedersen, Hal, 2010. "Mortality risk modeling: Applications to insurance securitization," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 242-253, February.
    17. Young, Virginia R., 2008. "Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 691-703, April.
    18. Lanza Queiroz, Bernardo & Lobo Alves Ferreira, Matheus, 2021. "The evolution of labor force participation and the expected length of retirement in Brazil," The Journal of the Economics of Ageing, Elsevier, vol. 18(C).
    19. 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.
    20. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Estimating the term structure of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 492-504, April.

    More about this item

    Keywords

    Mortality rates; Lee–Carter model; Autoregression–autoregressive conditional heteroskedasticity model; AR(1)–ARCH(1) model;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:eee:insuma:v:50:y:2012:i:1:p:85-93. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.