Donatien Hainaut

Université Catholique de Louvain (UCLouvain)

Title

Option pricing with model constrained Gaussian process regressions

Authors

Donatien Hainaut

Abstract

In this talk, 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. Next, we discuss the extension of this method to American options. The variational equation driving theses options is converted into a penalized FK PDE that is solved by iterations to manage the non-linearity of the differential operator. The method is illustrated in the Heston model.