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Pricing extreme mortality risk in the wake of the COVID-19 pandemic

Author

Listed:
  • Li, Han
  • Liu, Haibo
  • Tang, Qihe
  • Yuan, Zhongyi

Abstract

In pricing extreme mortality risk, it is commonly assumed that interest rate and mortality rate are independent. However, the COVID-19 pandemic calls this assumption into question. In this paper, we employ a bivariate affine jump-diffusion model to describe the joint dynamics of interest rate and excess mortality, allowing for both correlated diffusions and joint jumps. Utilizing the latest U.S. mortality and interest rate data, we find a significant negative correlation between interest rate and excess mortality, and a much higher jump intensity when the pandemic experience is considered. Moreover, we construct a risk-neutral pricing measure that accounts for both diffusion and jump risk premia, and we solve for the market prices of risk based on mortality bond prices. Our results show that the pandemic experience can drastically change investors' perception of the mortality risk market in the post-pandemic era.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:108:y:2023:i:c:p:84-106
    DOI: 10.1016/j.insmatheco.2022.11.002
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    1. 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.
    2. 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.
    3. Daniel Bauer & Florian Kramer, 2016. "The Risk of a Mortality Catastrophe," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 391-405, July.
    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. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    6. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    7. Shaun Wang, 2007. "Normalized Exponential Tilting," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 89-99.
    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. Chen, An & Hentschel, Felix & Klein, Jakob K., 2015. "A utility- and CPT-based comparison of life insurance contracts with guarantees," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 327-339.
    10. 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.
    11. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    12. Yijia Lin & Sheen Liu & Jifeng Yu, 2013. "Pricing Mortality Securities With Correlated Mortality Indexes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 921-948, December.
    13. 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.
    14. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    15. Han Li & Qihe Tang, 2022. "Joint Extremes in Temperature and Mortality: A Bivariate POT Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(1), pages 43-63, January.
    16. Tang, Qihe & Yuan, Zhongyi, 2019. "Cat Bond Pricing Under A Product Probability Measure With Pot Risk Characterization," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 457-490, May.
    17. Samuel H. Cox & Yijia Lin & Shaun Wang, 2006. "Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 719-736, December.
    18. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    19. Hainaut, Donatien & Deelstra, Griselda, 2014. "Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 124-146.
    20. Braun, Alexander & Ben Ammar, Semir & Eling, Martin, 2019. "Asset pricing and extreme event risk: Common factors in ILS fund returns," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 59-78.
    21. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    22. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    23. Marcello Galeotti & Marc Gürtler & Christine Winkelvos, 2013. "Accuracy of Premium Calculation Models for CAT Bonds—An Empirical Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 401-421, June.
    24. Bayraktar, Erhan & Milevsky, Moshe A. & David Promislow, S. & Young, Virginia R., 2009. "Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 676-691, March.
    25. Maria Polyakova & Geoffrey Kocks & Victoria Udalova & Amy Finkelstein, 2020. "Initial economic damage from the COVID-19 pandemic in the United States is more widespread across ages and geographies than initial mortality impacts," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 117(45), pages 27934-27934, November.
    26. Lin, Yijia & Cox, Samuel H., 2008. "Securitization of catastrophe mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 628-637, April.
    27. Liu, Haibo & Tang, Qihe & Yuan, Zhongyi, 2021. "Indifference pricing of insurance-linked securities in a multi-period model," European Journal of Operational Research, Elsevier, vol. 289(2), pages 793-805.
    28. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).
    29. Li, Han & Tang, Qihe, 2019. "Analyzing Mortality Bond Indexes Via Hierarchical Forecast Reconciliation," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 823-846, September.
    30. J. David Cummins, 2008. "CAT Bonds and Other Risk‐Linked Securities: State of the Market and Recent Developments," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 11(1), pages 23-47, March.
    31. Lin, Hang & Zhang, Zhengjun, 2022. "Extreme co-movements between infectious disease events and crude oil futures prices: From extreme value analysis perspective," Energy Economics, Elsevier, vol. 110(C).
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    More about this item

    Keywords

    Affine jump-diffusion model; COVID-19; Implied market price of risk; Instantaneous correlation; Mortality-linked security; Pricing;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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