IDEAS home Printed from https://ideas.repec.org/a/spr/fininn/v10y2024i1d10.1186_s40854-023-00515-0.html
   My bibliography  Save this article

A simplified model for measuring longevity risk for life insurance products

Author

Listed:
  • David Atance

    (University of Alcalá)

  • Eliseo Navarro

    (University of Alcalá)

Abstract

In this paper, we propose a simple dynamic mortality model to fit and forecast mortality rates for measuring longevity and mortality risks. This proposal is based on a methodology for modelling interest rates, which assumes that changes in spot interest rates depend linearly on a small number of factors. These factors are identified as interest rates with a given maturity. Similarly, we assume that changes in mortality rates depend linearly on changes in a specific mortality rate, which we call the key mortality rate. One of the main advantages of this model is that it allows the development of an easy to implement methodology to measure longevity and mortality risks using simulation techniques. Particularly, we employ the model to calculate the Value-at-Risk and Conditional-Value-at-Risk of an insurance product testing the accuracy and robustness of our proposal using out-of-sample data from six different populations.

Suggested Citation

  • David Atance & Eliseo Navarro, 2024. "A simplified model for measuring longevity risk for life insurance products," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-30, December.
    • Handle: RePEc:spr:fininn:v:10:y:2024:i:1:d:10.1186_s40854-023-00515-0
    DOI: 10.1186/s40854-023-00515-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40854-023-00515-0
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40854-023-00515-0?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
    ---><---

    References listed on IDEAS

    as
    1. Yajing Xu & Michael Sherris & Jonathan Ziveyi, 2020. "Continuous-time multi-cohort mortality modelling with affine processes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(6), pages 526-552, July.
    2. Sweeting, Paul & Christie, Alexandre & Gladwyn, Edward, 2015. "The missing link: economic exposure and pension plan risk," Annals of Actuarial Science, Cambridge University Press, vol. 9(2), pages 290-303, September.
    3. 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.
    4. Richards, S. J. & Currie, I. D. & Ritchie, G. P., 2014. "A Value-at-Risk framework for longevity trend risk," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 116-139, March.
    5. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    6. Debón, A. & Montes, F. & Puig, F., 2008. "Modelling and forecasting mortality in Spain," European Journal of Operational Research, Elsevier, vol. 189(3), pages 624-637, September.
    7. Eliseo Navarro & Juan M. Nave, 2001. "The structure of spot rates and immunization: Some further results," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(4), pages 273-294.
    8. Erengul Dodd & Jonathan J. Forster & Jakub Bijak & Peter W. F. Smith, 2021. "Stochastic modelling and projection of mortality improvements using a hybrid parametric/semi-parametric age–period–cohort model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(2), pages 134-155, February.
    9. Elton, Edwin J & Gruber, Martin J & Michaely, Roni, 1990. "The Structure of Spot Rates and Immunization," Journal of Finance, American Finance Association, vol. 45(2), pages 629-642, June.
    10. Bauer Daniel & Börger Matthias & Ruß Jochen & Zwiesler Hans-Joachim, 2008. "The Volatility of Mortality," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(1), pages 1-29, September.
    11. repec:cup:bracjl:v:26:y:2021:i::p:-_13 is not listed on IDEAS
    12. Dowd, Kevin & Cairns, Andrew J. G. & Blake, David, 2020. "CBDX: a workhorse mortality model from the Cairns–Blake–Dowd family," Annals of Actuarial Science, Cambridge University Press, vol. 14(2), pages 445-460, September.
    13. Chuliá, Helena & Guillén, Montserrat & Uribe, Jorge M., 2016. "Modeling Longevity Risk With Generalized Dynamic Factor Models And Vine-Copulae," ASTIN Bulletin, Cambridge University Press, vol. 46(1), pages 165-190, January.
    14. Vasil Enchev & Torsten Kleinow & Andrew J. G. Cairns, 2017. "Multi-population mortality models: fitting, forecasting and comparisons," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(4), pages 319-342, April.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    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.
    21. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "On the Validity of Value-at-Risk: Comparative Analyses with Expected Shortfall," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 57-85, January.
    22. Börger, Matthias & Fleischer, Daniel & Kuksin, Nikita, 2014. "Modeling The Mortality Trend Under Modern Solvency Regimes," ASTIN Bulletin, Cambridge University Press, vol. 44(1), pages 1-38, January.
    23. Macdonald,Angus S. & Richards,Stephen J. & Currie,Iain D., 2018. "Modelling Mortality with Actuarial Applications," Cambridge Books, Cambridge University Press, number 9781107045415, Enero.
    24. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    25. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    26. 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.
    27. Neves, César & Fernandes, Cristiano & Hoeltgebaum, Henrique, 2017. "Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 48-57.
    28. David Atance & Ana Debón & Eliseo Navarro, 2020. "A Comparison of Forecasting Mortality Models Using Resampling Methods," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    29. Li, Johnny Siu-Hang & Hardy, Mary R. & Tan, Ken Seng, 2009. "Uncertainty in Mortality Forecasting: An Extension to the Classical Lee-Carter Approach," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 137-164, May.
    30. Plat, Richard, 2011. "One-year Value-at-Risk for longevity and mortality," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 462-470.
    31. 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.
    32. Nan Li & Ronald Lee & Patrick Gerland, 2013. "Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections," Demography, Springer;Population Association of America (PAA), vol. 50(6), pages 2037-2051, December.
    33. Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    4. repec:osf:socarx:8u34d_v1 is not listed on IDEAS
    5. 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.
    6. David Atance & Ana Debón & Eliseo Navarro, 2020. "A Comparison of Forecasting Mortality Models Using Resampling Methods," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    7. 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.
    8. Rachel WINGENBACH & Jong-Min KIM & Hojin JUNG, 2020. "Living Longer in High Longevity Risk," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 86(1), pages 47-86, March.
    9. Guibert, Quentin & Lopez, Olivier & Piette, Pierrick, 2019. "Forecasting mortality rate improvements with a high-dimensional VAR," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 255-272.
    10. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    11. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    12. 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.
    13. Han Lin Shang & Steven Haberman, 2020. "Retiree Mortality Forecasting: A Partial Age-Range or a Full Age-Range Model?," Risks, MDPI, vol. 8(3), pages 1-11, July.
    14. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    15. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    16. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
    17. Marie-Pier Bergeron-Boucher & James E. Oeppen & James W. Vaupel & Søren Kjærgaard, 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.
    18. Li, Hong & De Waegenaere, Anja & Melenberg, Bertrand, 2015. "The choice of sample size for mortality forecasting: A Bayesian learning approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 153-168.
    19. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2017. "Cohort effects in mortality modelling: a Bayesian state-space approach," Papers 1703.08282, arXiv.org.
    20. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2023. "Intergenerational actuarial fairness when longevity increases: Amending the retirement age," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 161-184.
    21. David Atance & Josep Lledó & Eliseo Navarro, 2025. "Modelling and Forecasting Mortality Rates for a Life Insurance Portfolio," Risk Management, Palgrave Macmillan, vol. 27(1), pages 1-25, February.

    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:spr:fininn:v:10:y:2024:i:1:d:10.1186_s40854-023-00515-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.