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Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization

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  • Samuel H. Cox
  • Yijia Lin
  • Shaun Wang
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    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.

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    Bibliographic Info

    Article provided by The American Risk and Insurance Association in its journal Journal of Risk & Insurance.

    Volume (Year): 73 (2006)
    Issue (Month): 4 ()
    Pages: 719-736

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    Handle: RePEc:bla:jrinsu:v:73:y:2006:i:4:p:719-736

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    Cited by:
    1. Erhan Bayraktar & Moshe Milevsky & David Promislow & Virginia Young, 2008. "Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities," Papers 0802.3250, arXiv.org.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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.

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