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Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model

Author

Listed:
  • Zhenyu Cui
  • Runhuan Feng
  • Anne MacKay

Abstract

The Chicago Board of Options Exchange (CBOE) advocates linking variable annuity (VA) fees to its trademark VIX index in a recent white paper. It claims that the VIX-linked fee structure has several advantages over the traditional fixed percentage fee structure. However, the evidence presented is largely based on nonparametric extrapolation of historical data on market prices. Our work lays out a theoretical basis with a parametric model to analyze the impact of the VIX-linked fee structure and to verify some claims from the CBOE. In a Heston-type stochastic volatility setting, we jointly model the dynamics of an equity index (underlying the value of VA policyholders’ accounts) and the VIX index. In this framework, we price a guaranteed minimum maturity benefit with VIX-linked fees. Through numerical examples, we show that the VIX-linked fee reduces the sensitivity of the insurer's liability to market volatility when compared to a VA with the traditional fixed fee rate.

Suggested Citation

  • Zhenyu Cui & Runhuan Feng & Anne MacKay, 2017. "Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 458-483, July.
    • Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:458-483
    DOI: 10.1080/10920277.2017.1307765
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    Citations

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    Cited by:

    1. David Landriault & Bin Li & Dongchen Li & Yumin Wang, 2021. "High‐water mark fee structure in variable annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1057-1094, December.
    2. Jennifer Alonso-Garcia & Len Patrick Dominic M. Garces & Jonathan Ziveyi, 2025. "Variable annuities: A closer look at ratchet guarantees, hybrid contract designs, and taxation," Papers 2507.07358, arXiv.org.
    3. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    4. Yang, Yang & Chen, Shaoying & Cui, Zhenyu & Zhang, Zhimin, 2024. "Valuation of guaranteed lifelong withdrawal benefit with the long-term care option," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 179-193.
    5. Jin Sun & Pavel V. Shevchenko & Man Chung Fung, 2018. "The Impact of Management Fees on the Pricing of Variable Annuity Guarantees," Risks, MDPI, vol. 6(3), pages 1-20, September.
    6. Michael A. Kouritzin & Anne MacKay, 2017. "VIX-linked fees for GMWBs via Explicit Solution Simulation Methods," Papers 1708.06886, arXiv.org, revised Apr 2018.
    7. Philippe Artzner & Karl‐Theodor Eisele & Thorsten Schmidt, 2024. "Insurance–finance arbitrage," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 739-773, July.
    8. Anne Mackay & Marie-Claude Vachon, 2023. "On an Optimal Stopping Problem with a Discontinuous Reward," Papers 2311.03538, arXiv.org, revised Mar 2026.
    9. Kouritzin, Michael A. & MacKay, Anne, 2018. "VIX-linked fees for GMWBs via explicit solution simulation methods," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 1-17.
    10. Feng, Runhuan & Jing, Xiaochen & Ng, Kenneth Tsz Hin, 2025. "Optimal investment-withdrawal strategy for variable annuities under a performance fee structure," Journal of Economic Dynamics and Control, Elsevier, vol. 170(C).
    11. Wing Fung Chong & Haoen Cui & Yuxuan Li, 2021. "Pseudo-Model-Free Hedging for Variable Annuities via Deep Reinforcement Learning," Papers 2107.03340, arXiv.org, revised Oct 2022.
    12. Wenyuan Li & Haoqi Lyu, 2026. "Valuation of variable annuities under the Volterra mortality and rough Heston models," Papers 2604.00472, arXiv.org, revised Apr 2026.
    13. Charles Guy Njike Leunga & Donatien Hainaut, 2022. "Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 963-990, June.
    14. Feng, Runhuan & Yi, Bingji, 2019. "Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 60-73.
    15. Zhenyu Cui & Anne MacKay & Marie-Claude Vachon, 2022. "Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation," Papers 2207.14793, arXiv.org.
    16. Bégin, Jean-François, 2020. "Levelling the playing field: A VIX-linked structure for funded pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 58-78.
    17. Yichen Han & Lianxia Wu & Dongchen Li & Jiaqi Han, 2024. "Guaranteed minimum withdrawal benefits with high-water mark fee structure," PLOS ONE, Public Library of Science, vol. 19(5), pages 1-17, May.
    18. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    19. Chen, An & Guillen, Montserrat & Rach, Manuel, 2021. "Fees in tontines," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 89-106.
    20. Rupak Chatterjee & Zhenyu Cui & Jiacheng Fan & Mingzhe Liu, 2018. "An efficient and stable method for short maturity Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1470-1486, December.
    21. Daniel Bauer & Thorsten Moenig, 2023. "Cheaper by the bundle: The interaction of frictions and option exercise in variable annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 459-486, June.
    22. Anne MacKay & Adriana Ocejo, 2022. "Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1021-1049, June.

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