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Applications of Mortality Durations and Convexities in Natural Hedges

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  • Tzuling Lin
  • Cary Chi-Liang Tsai

Abstract

Defining and deriving the mortality durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel shift, respectively, in μs (the forces of mortality), qs (the one-year death probabilities), ps (the one-year survival probabilities), ln (μ)s, (q/p)s, and ln (q/p)s, this article applies 24 proposed duration/convexity matching strategies classified into seven groups to determine the weights of two products in an insurance portfolio. The hedging performances of some qualified matching strategies selected as representatives are evaluated by comparing their Value at Risk (VaR) values and variance reduction ratios for a base scenario. We also test some specific scenarios for the population basis risk, model risk, volatility and jump risks, and interest rate risk to see the impacts on the matching strategies. Numerical examples show that some convexity matching strategies overall outperform the others in the VaR value and in the effectiveness of hedging both longevity and mortality risks for two kinds of insurance portfolios.

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  • 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.
    • Handle: RePEc:taf:uaajxx:v:18:y:2014:i:3:p:417-442
    DOI: 10.1080/10920277.2014.911108
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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. Lin, Tzuling & Wang, Chou-Wen & Tsai, Cary Chi-Liang, 2015. "Age-specific copula-AR-GARCH mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 110-124.
    3. Zhou, Kenneth Q. & Li, Johnny Siu-Hang, 2019. "Delta-hedging longevity risk under the M7–M5 model: The impact of cohort effect uncertainty and population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 1-21.
    4. 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.
    5. 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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