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Variable annuities in a Lévy-based hybrid model with surrender risk

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  • Laura Ballotta
  • Ernst Eberlein
  • Thorsten Schmidt
  • Raghid Zeineddine

Abstract

This paper proposes a market consistent valuation framework for variable annuities (VAs) with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and uses time-inhomogeneous Lévy processes as risk drivers. Further, we allow for dependence between financial and surrender risks. Our model leads to explicit analytical formulas for the quantities of interest, and practical and efficient numerical procedures for the evaluation of these formulas. We illustrate the tractability of this approach by means of a detailed sensitivity analysis of the fair value of the VA and its components with respect to the model parameters. The results highlight the role played by the surrender behaviour and the importance of its appropriate modelling.

Suggested Citation

  • Laura Ballotta & Ernst Eberlein & Thorsten Schmidt & Raghid Zeineddine, 2020. "Variable annuities in a Lévy-based hybrid model with surrender risk," Quantitative Finance, Taylor & Francis Journals, vol. 20(5), pages 867-886, May.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:5:p:867-886
    DOI: 10.1080/14697688.2019.1687929
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    Cited by:

    1. Jir^o Akahori & Yuuki Ida & Maho Nishida & Shuji Tamada, 2020. "The Thermodynamic Approach to Whole-Life Insurance: A Method for Evaluation of Surrender Risk," Papers 2012.09606, arXiv.org.
    2. Tiziano De Angelis & Alessandro Milazzo & Gabriele Stabile, 2024. "On variable annuities with surrender charges," Papers 2405.02115, arXiv.org.
    3. Ballotta, Laura & Eberlein, Ernst & Schmidt, Thorsten & Zeineddine, Raghid, 2021. "Fourier based methods for the management of complex life insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 320-341.
    4. Zhang, Zhimin & Zhong, Wei, 2024. "Efficient valuation of guaranteed minimum accumulation benefits in regime switching jump diffusion models with lapse risk," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    5. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    6. Kira Henshaw & Cedric H. A. Koffi & Olivier Menoukeu Pamen & Raghid Zeineddine, 2024. "On the valuation of life insurance policies for dependent coupled lives," Papers 2410.11849, arXiv.org.
    7. Philippe Artzner & Karl-Theodor Eisele & Thorsten Schmidt, 2020. "Insurance-Finance Arbitrage," Papers 2005.11022, arXiv.org, revised Nov 2022.

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