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Modeling Mortality With Jumps: Applications to Mortality Securitization

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  • Hua Chen
  • Samuel H. Cox

Abstract

In this article, we incorporate a jump process into the original Lee-Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality-linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. Cox, Lin, and Wang (2006) employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths. Copyright (c) The Journal of Risk and Insurance, 2009.

Suggested Citation

  • Hua Chen & Samuel H. Cox, 2009. "Modeling Mortality With Jumps: Applications to Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 727-751.
  • Handle: RePEc:bla:jrinsu:v:76:y:2009:i:3:p:727-751
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    References listed on IDEAS

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    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. Rui Zhou & Johnny Siu-Hang Li & Ken Seng Tan, 2013. "Pricing Standardized Mortality Securitizations: A Two-Population Model With Transitory Jump Effects," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 733-774, September.
    3. Pelsser, Antoon & Salahnejhad Ghalehjooghi, Ahmad, 2016. "Time-consistent actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 97-112.
    4. Wang, Zihe & Li, Johnny Siu-Hang, 2016. "A DCC-GARCH multi-population mortality model and its applications to pricing catastrophic mortality bonds," Finance Research Letters, Elsevier, vol. 16(C), pages 103-111.
    5. 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.
    6. Ai, Jing & Brockett, Patrick L. & Jacobson, Allen F., 2015. "A new defined benefit pension risk measurement methodology," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 40-51.
    7. Daniel Rösch & Harald Scheule, 2014. "Forecasting Mortgage Securitization Risk Under Systematic Risk and Parameter Uncertainty," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(3), pages 563-586, September.
    8. Huang, Yu-Lieh & Tsai, Jeffrey Tzuhao & Yang, Sharon S. & Cheng, Hung-Wen, 2014. "Price bounds of mortality-linked security in incomplete insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 30-39.
    9. repec:bla:jrinsu:v:84:y:2017:i:s1:p:393-415 is not listed on IDEAS
    10. Shen, Yang & Siu, Tak Kuen, 2013. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 114-123.
    11. Chou-Wen Wang & Hong-Chih Huang & I-Chien Liu, 2013. "Mortality Modeling With Non-Gaussian Innovations and Applications to the Valuation of Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 775-798, September.
    12. Hua Chen & Michael Sherris & Tao Sun & Wenge Zhu, 2013. "Living With Ambiguity: Pricing Mortality-Linked Securities With Smooth Ambiguity Preferences," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 705-732, September.
    13. Chen, Hua & Cox, Samuel H. & Wang, Shaun S., 2010. "Is the Home Equity Conversion Mortgage in the United States sustainable? Evidence from pricing mortgage insurance premiums and non-recourse provisions using the conditional Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 371-384, April.
    14. Raj Kumari Bahl & Sotirios Sabanis, 2016. "Model-Independent Price Bounds for Catastrophic Mortality Bonds," Papers 1607.07108, arXiv.org.
    15. Liu, Yanxin & Li, Johnny Siu-Hang, 2015. "The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 135-150.
    16. Chen, Hua & Cummins, J. David, 2010. "Longevity bond premiums: The extreme value approach and risk cubic pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 150-161, February.
    17. Risk, J. & Ludkovski, M., 2016. "Statistical emulators for pricing and hedging longevity risk products," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 45-60.
    18. Chen, Bingzheng & Zhang, Lihong & Zhao, Lin, 2010. "On the robustness of longevity risk pricing," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 358-373, December.
    19. Li, Johnny Siu-Hang, 2010. "Pricing longevity risk with the parametric bootstrap: A maximum entropy approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 176-186, October.
    20. Patrick L. Brockett & Shuo-li Chuang & Yinglu Deng & Richard D. MacMinn, 2013. "Incorporating Longevity Risk and Medical Information Into Life Settlement Pricing," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 799-826, September.
    21. repec:bla:jrinsu:v:83:y:2016:i:4:p:877-912 is not listed on IDEAS
    22. 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.
    23. 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.
    24. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310, arXiv.org, revised Sep 2015.
    25. Wang, Chou-Wen & Huang, Hong-Chih & Hong, De-Chuan, 2013. "A feasible natural hedging strategy for insurance companies," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 532-541.

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