Options pricing with Physics-Informed Neural Networks

Details

Supervisors

Hainaut, Donatien

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

This thesis explores the use of Physics-Informed Neural Networks (PINNs) for option pricing in complex financial contexts. We developed models to evaluate European call and Bermudian put options, incorporating stochastic interest rates modelled by Hull & White. For European options, the results were validated with a closed-form solution, while validation for Bermudian puts has been more challenging. Numerical analyses demonstrate that PINNs offer a robust parametric tool that can be able of well capturing the price dynamics, outperforming traditional methods in scenarios with multiple risk factors and requiring minimal recalibration across different market conditions. However, challenges remain in optimizing network architecture selection and calibration procedure, which currently rely on trial and error. Future work could enhance these models by exploring alternative neural network architectures, expanding to more complex frameworks like Svensson or Heston models, and applying these methods to life insurance. This research contributes to advancing PINNs as a versatile tool in financial modelling.