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The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours

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  • Anna Rita Bacinello
  • Pietro Millossovich
  • Alvaro Montealegre

Abstract

In this paper, we present a dynamic programming algorithm for pricing variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) under a general Lévy processes framework. The GMWB gives the policyholder the right to make periodical withdrawals from her policy account even when the value of this account is exhausted. Typically, the total amount guaranteed for withdrawals coincides with her initial investment, providing then a protection against downside market risk. At each withdrawal date, the policyholder has to decide whether, and how much, to withdraw, or to surrender the contract. We show how different policyholder’s withdrawal behaviours can be modelled. We perform a sensitivity analysis comparing the numerical results obtained for different contractual and market parameters, policyholder behaviours and different types of Lévy processes.

Suggested Citation

  • Anna Rita Bacinello & Pietro Millossovich & Alvaro Montealegre, 2016. "The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(5), pages 446-465, May.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:5:p:446-465
    DOI: 10.1080/03461238.2014.954608
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    Cited by:

    1. 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.
    2. Fontana, Claudio & Rotondi, Francesco, 2023. "Valuation of general GMWB annuities in a low interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 142-167.

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