Physics-Informed Neural Networks in Pricing Financial Options

Abstract

PINNs (Physics-Informed Neural Networks) are neural networks designed to solve Partial Differential Equations (PDEs) by integrating physical knowledge into the learning framework. Constructing a PINN involves defining a neural network to approximate the PDE solution, with the total loss calculated as a combination of the losses associated with the PDE, boundary conditions, initial conditions, and measured data. This concept is employed in practical applications to solve various PDEs, such as the Black-Scholes and Heston equations, which are fundamental in financial option pricing. This approach enables the modelling and pricing of financial options, with the added advantage of parallelising the training process across multiple economic scenarios.