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Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization

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  • Samuel H. Cox
  • Yijia Lin
  • Shaun Wang

Abstract

Normalized exponential tilting is an extension of classical theories, including the Capital Asset Pricing Model (CAPM) and the Black-Merton-Scholes model, to price risks with general-shaped distributions. The need for changing multivariate probability measures arises in pricing contingent claims on multiple underlying assets or liabilities. In this article, we apply it to valuation of mortality-based securities written on mortality indices of several countries. We show how to use multivariate exponential tilting to price the first pure mortality security, the Swiss Re bond. The same technique can be applied in other mortality securitization pricing. Copyright The Journal of Risk and Insurance, 2006.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jrinsu:v:73:y:2006:i:4:p:719-736
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    References listed on IDEAS

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    1. Minton, Bernadette & Sanders, Anthony & Strahan, Philip E., 2004. "Securitization by Banks and Finance Companies: Efficient Financial Contracting or Regulatory Arbitrage?," Working Paper Series 2004-25, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    2. Blake, D. & Cairns, A. J. G. & Dowd, K., 2006. "Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities," British Actuarial Journal, Cambridge University Press, vol. 12(01), pages 153-197, March.
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    Cited by:

    1. 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.
    2. Wang, Chou-Wen & Yang, Sharon S. & Huang, Hong-Chih, 2015. "Modeling multi-country mortality dependence and its application in pricing survivor index swaps—A dynamic copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 30-39.
    3. 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.
    4. Yang, Sharon S. & Wang, Chou-Wen, 2013. "Pricing and securitization of multi-country longevity risk with mortality dependence," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 157-169.
    5. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Jennifer L. Wang & H.C. Huang & Sharon S. Yang & Jeffrey T. Tsai, 2010. "An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 473-497.
    11. Raj Kumari Bahl & Sotirios Sabanis, 2016. "Model-Independent Price Bounds for Catastrophic Mortality Bonds," Papers 1607.07108, arXiv.org.
    12. 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.
    13. 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.
    14. 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.
    15. Hwang Yawen & Huang Hong-Chih, 2012. "Modified Logistic Model for Mortality Forecasting and the Application of Mortality-Linked Securities," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(1), pages 1-20, February.
    16. 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.
    17. Chou-Wen Wang & Sharon S. Yang, 2013. "Pricing Survivor Derivatives With Cohort Mortality Dependence Under the Lee–Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 1027-1056, December.
    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. 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.
    20. repec:bla:jrinsu:v:83:y:2016:i:4:p:877-912 is not listed on IDEAS
    21. Lin, Yijia & MacMinn, Richard D. & Tian, Ruilin, 2015. "De-risking defined benefit plans," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 52-65.
    22. Samuel H. Cox & Yijia Lin & Ruilin Tian & Jifeng Yu, 2013. "Managing Capital Market and Longevity Risks in a Defined Benefit Pension Plan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 585-620, September.
    23. Samuel H. Cox & Yijia Lin & Ruilin Tian & Luis F. Zuluaga, 2013. "Mortality Portfolio Risk Management," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 853-890, December.
    24. repec:bla:jrinsu:v:84:y:2017:i:s1:p:345-365 is not listed on IDEAS
    25. 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.

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