Pricing European Derivatives via Constrained Gaussian Process Regression

Details

Supervisors

Hainaut, Donatien

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

enThis Master Thesis proposes a novel machine learning framework to price European derivatives, whose underlyings are driven by Jump-diffusion models, by formulating Gaussian process regression directly constrained by the Feynman-Kac partial integro-differential equation (PIDE). To overcome the potential intractability of the non-local jump operator, we formulate an operator-splitting scheme that decouples the pricing problem into a localized parabolic PDE governing the continuous diffusion dynamics and an integral jump term treated iteratively as a lagged source via a fixed-point method. By partitioning the state space into interior points and boundary points, the regression model simultaneously enforces the governing differential operator and the derivative's boundary conditions corresponding to the derivative payoff. A major analytical advantage of this Gaussian process framework is the derivation of closed-form expressions for both approximated option prices and their corresponding risk sensitivities (Greeks). To ensure practical viability, we implement dedicated numerical stabilization techniques to mitigate kernel ill-conditioning and introduce a novel hyperparameter estimation procedure.