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VIX-linked fees for GMWBs via Explicit Solution Simulation Methods

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  • Michael A. Kouritzin
  • Anne MacKay

Abstract

In a market with stochastic volatility and jumps, we consider a VIX-linked fee structure for variable annuity contracts with guaranteed minimum withdrawal benefits (GMWB). Our goal is to assess the effectiveness of the VIX-linked fee structure in decreasing the sensitivity of the insurer's liability to volatility risk. Since the GMWB payoff is highly path-dependent, it is particularly sensitive to volatility risk, and can also be challenging to price, especially in the presence of the VIX-linked fee. In this paper, we present an explicit weak solution for the value of the VA account and use it in Monte Carlo simulations to value the GMWB guarantee. Numerical examples are provided to analyze the impact of the VIX-linked fee on the sensitivity of the liability to changes in market volatility.

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  • Michael A. Kouritzin & Anne MacKay, 2017. "VIX-linked fees for GMWBs via Explicit Solution Simulation Methods," Papers 1708.06886, arXiv.org, revised Apr 2018.
    • Handle: RePEc:arx:papers:1708.06886
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Anne Mackay & Marie-Claude Vachon, 2023. "On an Optimal Stopping Problem with a Discontinuous Reward," Papers 2311.03538, arXiv.org, revised Nov 2023.
    4. Yaowen Lu & Duy-Minh Dang, 2023. "A semi-Lagrangian $\epsilon$-monotone Fourier method for continuous withdrawal GMWBs under jump-diffusion with stochastic interest rate," Papers 2310.00606, arXiv.org.

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