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Pricing and hedging GLWB in the Heston and in the Black–Scholes with stochastic interest rate models

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  • Goudenège, Ludovic
  • Molent, Andrea
  • Zanette, Antonino

Abstract

Valuing Guaranteed Lifelong Withdrawal Benefit (GLWB) has attracted significant attention from both the academic field and real world financial markets. As remarked by Forsyth and Vetzal (2014) the Black and Scholes framework seems to be inappropriate for such a long maturity products. They propose to use a regime switching model. Alternatively, we propose here to use a stochastic volatility model (Heston model) and a Black–Scholes model with stochastic interest rate (Hull–White model). For this purpose we present four numerical methods for pricing GLWB variables annuities: a hybrid tree-finite difference method and a Hybrid Monte Carlo method, an ADI finite difference scheme, and a Standard Monte Carlo method. These methods are used to determine the no-arbitrage fee for the most popular versions of the GLWB contract, and to calculate the Greeks used in hedging. Both constant withdrawal and optimal withdrawal (including lapsation) strategies are considered. Numerical results are presented which demonstrate the sensitivity of the no-arbitrage fee to economic, contractual and longevity assumptions.

Suggested Citation

  • Goudenège, Ludovic & Molent, Andrea & Zanette, Antonino, 2016. "Pricing and hedging GLWB in the Heston and in the Black–Scholes with stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 38-57.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:38-57
    DOI: 10.1016/j.insmatheco.2016.05.018
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    References listed on IDEAS

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    Cited by:

    1. Maya Briani & Lucia Caramellino & Giulia Terenzi & Antonino Zanette, 2019. "Numerical Stability Of A Hybrid Method For Pricing Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-46, November.
    2. Andrea Molent, 2019. "Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model," Papers 1901.11296, arXiv.org, revised May 2020.
    3. Kirkby, J. Lars, 2023. "Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(2), pages 961-978.
    4. Mrad, Fatma & Hamdi, Haykel & Naoui, Kamel & Abid, Ilyes, 2023. "The GMWB guarantee embedded in Life Insurance Contracts: Fair Value Pricing Problem," Finance Research Letters, Elsevier, vol. 51(C).
    5. Ludovic Goudenège & Andrea Molent & Antonino Zanette, 2021. "Gaussian process regression for pricing variable annuities with stochastic volatility and interest rate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 57-72, June.

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