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Optimal Static Hedging of Variable Annuities with Volatility-Dependent Fees

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  • Junsen Tang

    (Department of Mathematics, University of St. Thomas, 2115 Summit Avenue, Saint Paul, MN 55105, USA)

Abstract

Variable annuities (VAs) and other long-term equity-linked insurance products are typically difficult to hedge in the incomplete markets. A state-dependent fee tied with market volatility for VAs is designed to contribute the risk-sharing mechanism between policyholders and insurers. Different from prior research, we discuss several aspects on a fair valuation, fee-rate determination and hedging with volatility-dependent fees from the perspective of a VA hedger. A method of efficient hedging strategy as a benchmark compared to other strategies is developed in the stochastic volatility setting. We illustrate this method in guaranteed minimum maturity benefits (GMMBs), but it is also applicable to other equity-linked insurance contracts.

Suggested Citation

  • Junsen Tang, 2023. "Optimal Static Hedging of Variable Annuities with Volatility-Dependent Fees," Risks, MDPI, vol. 12(1), pages 1-20, December.
    • Handle: RePEc:gam:jrisks:v:12:y:2023:i:1:p:7-:d:1310602
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    References listed on IDEAS

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    1. Daniel Bauer & Jin Gao & Thorsten Moenig & Eric R. Ulm & Nan Zhu, 2017. "Policyholder Exercise Behavior in Life Insurance: The State of Affairs," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 485-501, October.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    4. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
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