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Market Price of Longevity Risk for a Multi‐Cohort Mortality Model With Application to Longevity Bond Option Pricing

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  • Yajing Xu
  • Michael Sherris
  • Jonathan Ziveyi

Abstract

We introduce a multi‐cohort continuous time affine mortality model and, along with an affine arbitrage‐free term structure model, determine implied market prices of longevity risk in the BlackRock CoRI Retirement Indexes. These indexes provide a daily level of estimated cost of lifetime retirement income for 20 cohorts in the United States. Individuals can invest in BlackRock funds that track the indexes that are quoted on the NYSE. We use our model to derive closed‐form expressions for prices of European options on longevity zero‐coupon bonds and show the impact of stochastic mortality on long‐term longevity bond option prices.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jrinsu:v:87:y:2020:i:3:p:571-595
    DOI: 10.1111/jori.12273
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    References listed on IDEAS

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    1. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    2. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    3. 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.
    4. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    5. Bisetti, Emilio & Favero, Carlo A. & Nocera, Giacomo & Tebaldi, Claudio, 2017. "A Multivariate Model of Strategic Asset Allocation with Longevity Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(5), pages 2251-2275, October.
    6. Leung, Melvern & Fung, Man Chung & O’Hare, Colin, 2018. "A comparative study of pricing approaches for longevity instruments," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 95-116.
    7. 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.
    8. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    9. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    10. Blackburn, Craig & Sherris, Michael, 2013. "Consistent dynamic affine mortality models for longevity risk applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 64-73.
    11. 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.
    12. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    13. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    14. 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.
    15. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252, June.
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    Cited by:

    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. Zhiping Huang & Michael Sherris & Andrés M. Villegas & Jonathan Ziveyi, 2022. "Modelling USA Age-Cohort Mortality: A Comparison of Multi-Factor Affine Mortality Models," Risks, MDPI, vol. 10(9), pages 1-28, September.
    3. Li, Han & Liu, Haibo & Tang, Qihe & Yuan, Zhongyi, 2023. "Pricing extreme mortality risk in the wake of the COVID-19 pandemic," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 84-106.
    4. Hung-Tsung Hsiao & Chou-Wen Wang & I.-Chien Liu & Ko-Lun Kung, 2024. "Mortality improvement neural-network models with autoregressive effects," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 363-383, April.

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