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European option pricing with model constrained Gaussian process regressions

Author

Listed:
  • Hainaut, Donatien

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

  • Vrins, Frédéric

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

Abstract

We propose a method for pricing European options based on Gaussian processes. We convert the problem of solving the Feynman-Kac (FK) partial differential equation (PDE) into a model-constrained regression. We form two training sets by sampling state variables from the PDEs inner domain and terminal boundary. The regression function is then estimated to fit the option payoffs on the boundary sample while satisfying the FK PDE on the inner sample. We adopt a Bayesian framework in which payoffs and the value of the FK PDE in the boundary and inner samples are noised. Assuming the regression function is a Gaussian process, we find a closed- form approximation for the option prices. We demonstrate the performance of the procedure on call options in the Heston model and basket call options in a Black- Scholes market.

Suggested Citation

  • Hainaut, Donatien & Vrins, Frédéric, 2024. "European option pricing with model constrained Gaussian process regressions," LIDAM Discussion Papers ISBA 2024021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2024021
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    References listed on IDEAS

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    1. St'ephane Cr'epey & Matthew Dixon, 2019. "Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations," Papers 1901.11081, arXiv.org, revised Oct 2019.
    2. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    3. Joan Gonzalvez & Edmond Lezmi & Thierry Roncalli & Jiali Xu, 2019. "Financial Applications of Gaussian Processes and Bayesian Optimization," Papers 1903.04841, arXiv.org.
    4. Hainaut, Donatien, 2024. "Valuation of guaranteed minimum accumulation benefits (GMABs) with physics-inspired neural networks," Annals of Actuarial Science, Cambridge University Press, vol. 18(2), pages 442-473, July.
    5. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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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. Hainaut, Donatien, 2026. "American option pricing with model constrained Gaussian process regressions," Applied Mathematics and Computation, Elsevier, vol. 512(C).
    3. 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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