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Option pricing in the Heston model with physics inspired neural networks

Author

Listed:
  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Casas, Alex

Abstract

In absence of a closed form expression such as in the Heston model, the option pricing is computationally intensive when calibrating a model to market quotes. this article proposes an alternative to standard pricing methods based on physics-inspired neural networks (PINNs). A PINN integrates principles from physics into its learning process to enhance its efficiency in solving complex problems. In this article, the driving principle is the Feynman-Kac (FK) equation, which is a partial differential equation (PDE) governing the derivative price in the Heston model. We focus on the valuation of European options and show that PINNs constitute an efficient alternative for pricing options with various specifications and parameters without the need for retraining.

Suggested Citation

  • Hainaut, Donatien & Casas, Alex, 2024. "Option pricing in the Heston model with physics inspired neural networks," LIDAM Reprints ISBA 2024043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2024043
    DOI: https://doi.org/10.1007/s10436-024-00452-7
    Note: In: Annals of Finance, 2024, vol. 20(3), p. 353-376
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    Cited by:

    1. Hainaut, Donatien & Dupret, Jean-Loup, 2025. "Optimal control by policy improvements and constrained Gaussian process regressions," LIDAM Discussion Papers ISBA 2025012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Tan, Jianguo & Zhang, Xingyu, 2026. "Improved constrained physics-informed neural networks (ICPINNs) to solve PDE and its application to option pricing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 908-924.
    3. Hainaut, Donatien, 2026. "American option pricing with model constrained Gaussian process regressions," Applied Mathematics and Computation, Elsevier, vol. 512(C).
    4. Hainaut, Donatien, 2024. "American option pricing with model constrained Gaussian process regressions," LIDAM Discussion Papers ISBA 2024023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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