European option pricing with model constrained Gaussian process regressions

27 Pages Posted: 25 Nov 2024

See all articles by Donatien Hainaut

Donatien Hainaut

Catholic University of Louvain (UCL)

Frédéric D. Vrins

LFIN/LIDAM, UCLouvain

Date Written: October 08, 2024

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 closedform 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.

Keywords: Gaussian process regression, Option pricing, Feynman-Kac equation, partial differential equation, Heston model, machine learning

Suggested Citation

Hainaut, Donatien and Vrins, Frederic Daniel, European option pricing with model constrained Gaussian process regressions (October 08, 2024). Available at SSRN: https://ssrn.com/abstract=4982344 or http://dx.doi.org/10.2139/ssrn.4982344

Donatien Hainaut (Contact Author)

Catholic University of Louvain (UCL)

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