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Natural Hedges With Immunization Strategies Of Mortality And Interest Rates

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  • Lin, Tzuling
  • Tsai, Cary Chi-liang

Abstract

In this paper, we first derive closed-form formulas for mortality-interest durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel movement, respectively, in μ* (the force of mortality-interest), the addition of μ (the force of mortality) and δ (the force of interest). We then build several mortality-interest duration and convexity matching strategies to determine the weights of whole life insurance and deferred whole life annuity products in a portfolio and evaluate the value at risk and the hedge effectiveness of the weighted portfolio surplus at time zero. Numerical illustrations show that using the mortality-interest duration and convexity matching strategies with respect to an instantaneously proportional change in μ* can more effectively hedge the longevity risk and interest rate risk embedded in the deferred whole life annuity products than using the mortality-only duration and convexity matching strategies with respect to an instantaneously proportional shift or an instantaneously constant movement in μ only.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:1:p:155-185_6
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    Cited by:

    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. 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.

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