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Longevity bond pricing under the threshold CIR model

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  • Dong, Fangyuan
  • Wong, Hoi Ying

Abstract

While mean reversion is a well-documented feature in interest rate and commodity prices, empirical studies show that the long-term mean level and the mean reversion rate are not persistent in time. This paper introduces a threshold Cox–Ingersol–Ross (TCIR) model in which a regime shift is determined endogenously by the underlying financial asset. We derive the joint moment-generating function (MGF) of the terminal TCIR value and an average of it. The MGF enables us to value risk-free bonds and Longevity bonds analytically.

Suggested Citation

  • Dong, Fangyuan & Wong, Hoi Ying, 2015. "Longevity bond pricing under the threshold CIR model," Finance Research Letters, Elsevier, vol. 15(C), pages 195-207.
  • Handle: RePEc:eee:finlet:v:15:y:2015:i:c:p:195-207
    DOI: 10.1016/j.frl.2015.09.010
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    References listed on IDEAS

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    1. David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 647-672.
    2. Qiang Dai & Kenneth J. Singleton & Wei Yang, 2007. "Regime Shifts in a Dynamic Term Structure Model of U.S. Treasury Bond Yields," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1669-1706, 2007 12.
    3. Wong, Tat Wing & Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Time-consistent mean–variance hedging of longevity risk: Effect of cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 56-67.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    5. Ravi Bansal & Hao Zhou, 2002. "Term Structure of Interest Rates with Regime Shifts," Journal of Finance, American Finance Association, vol. 57(5), pages 1997-2043, October.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. 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.
    8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    9. Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
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    Cited by:

    1. Ewald, Christian-Oliver & Zhang, Aihua, 2017. "On the effects of changing mortality patterns on investment, labour and consumption under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 105-115.

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