Detra Note 2024-1 : Option pricing in the Heston model with Physics inspired neural networks

We are pleased to share with you our first Detra Note of the year on Option pricing in the Heston model with Physics inspired neural networks published by Donatien Hainaut (Scientific Advisor) and Alex Casas (Actuarial Consultant - TAP).

In absence of a closed form expression such as in the Heston model, the option pricing is computationally intensive when calibrating a model to market quotes. this article proposes an alternative to standard pricing methods based on physics-inspired neural networks (PINNs). A PINN integrates principles from physics into its learning process to enhance its effciency in solving complex problems. In this article, the driving principle is the Feynman-Kac (FK) equation, which is a partial differential equation (PDE) governing the derivative price in the Heston model. We focus on the valuation of European options and show that PINNs constitute an effcient alternative for pricing options with various specifications and parameters without the need for retraining.