European option pricing with model constrained Gaussian process regressions

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 boundary. The regression function is then estimated to fit the option values 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 closed-form expressions of approximated option prices and their Greeks. We demonstrate the performance of the procedure on call options in the Black-Scholes and Heston models.

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Hainaut, D., & Vrins, F. (2024). European option pricing with model constrained Gaussian process regressions (LIDAM Discussion Paper ISBA 2024/21). https://hdl.handle.net/2078.5/248229