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A new option for mortality–interest rates

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  • Tzuling Lin
  • Cary Chi‐Liang Tsai

Abstract

We propose a new type of mortality–interest option related to a new random variable, the force of mortality–interest denoted as μ * ${\mu }^{* }$, the addition of the force of mortality and the force of interest. We assume μ* ${\mu }^{* }$ moves approximately linearly, design the new mortality–interest option, and then derive closed‐form formulas for its expected values. We show that using the new mortality–interest options, an annuity provider and a life insurer can, respectively, hedge the longevity and mortality risks with interest rate risk; a financial intermediary selling the new options can benefit from natural hedges resulted from two‐side businesses with the annuity provider and life insurer.

Suggested Citation

  • Tzuling Lin & Cary Chi‐Liang Tsai, 2023. "A new option for mortality–interest rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 273-293, February.
    • Handle: RePEc:wly:jfutmk:v:43:y:2023:i:2:p:273-293
    DOI: 10.1002/fut.22390
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    References listed on IDEAS

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    1. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    2. 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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Lin, Tzuling & Tsai, Cary Chi-Liang, 2016. "Hedging mortality/longevity risks of insurance portfolios for life insurer/annuity provider and financial intermediary," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 44-58.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    5. Schmeck, Maren Diane & Schmidli, Hanspeter, 2021. "Mortality options: The point of view of an insurer," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 98-115.
    6. Tzuling Lin & Cary Chi‐liang Tsai, 2015. "A Simple Linear Regression Approach to Modeling and Forecasting Mortality Rates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(7), pages 543-559, November.
    7. Tsai, Cary Chi-Liang & Chung, San-Lin, 2013. "Actuarial applications of the linear hazard transform in mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 48-63.
    8. Tzuling Lin & Cary Chi-Liang Tsai, 2014. "Applications of Mortality Durations and Convexities in Natural Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(3), pages 417-442, July.
    9. Johnny Siu‐Hang Li & Andrew Cheuk‐Yin Ng & Wai‐Sum Chan, 2011. "On the calibration of mortality forward curves," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(10), pages 947-970, October.
    10. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    11. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    12. Cary Chi-Liang Tsai & Shuai Yang, 2015. "A Linear Regression Approach to Modeling Mortality Rates of Different Forms," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(1), pages 1-23, January.
    13. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    14. Lin, Tzuling & Tzeng, Larry Y., 2010. "An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 423-435, April.
    15. Paul Dawson & Kevin Dowd & Andrew J. G. Cairns & David Blake, 2009. "Options on normal underlyings with an application to the pricing of survivor swaptions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(8), pages 757-774, August.
    16. Jeffrey, Andrew, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(4), pages 619-642, December.
    17. Lin, Tzuling & Tsai, Cary Chi-liang, 2020. "Natural Hedges With Immunization Strategies Of Mortality And Interest Rates," ASTIN Bulletin, Cambridge University Press, vol. 50(1), pages 155-185, January.
    18. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    19. Amy Finkelstein & James Poterba, 2002. "Selection Effects in the United Kingdom Individual Annuities Market," Economic Journal, Royal Economic Society, vol. 112(476), pages 28-50, January.
    20. Andrew Mark Jeffrey, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Yale School of Management Working Papers ysm46, Yale School of Management.
    21. Lin, Tzuling & Tsai, Cary Chi-Liang, 2013. "On the mortality/longevity risk hedging with mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 580-596.
    22. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
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