Meshless methods for American option pricing through Physics-Informed Neural Networks

Nowadays, Deep Learning is drastically revolutionizing financial research as well as industry. Many methods have been discussed in the last few years, mainly related to option pricing. In fact, traditional approaches such as Monte Carlo simulation or finite difference methods are seriously harmed by multi-dimensional underlying and path dependency. Thus, dealing with particular contracts such as American multi-asset options is still rough. This paper addresses such a problem by pricing said put options with a novel meshless methodology, named Physics-Informed Neural Networks (PINNs), based on Artificial Intelligence. PINN paradigm has been recently introduced in Deep Learning literature. It exploits the theoretical background of the universal approximation theorem for neural networks to solve Partial Differential Equations numerically. This Deep Learning meshless method incorporates the equation and its initial and boundary conditions thanks to a specially designed loss function. We develop a suitable PINN for the proposed problem by introducing an algorithmic trick for improving the convergence of the free boundary problem. Furthermore, the worthiness of the proposal is assessed by several experiments concerned with single and multi-asset options. Finally, a parametric model is built to benefit further studies of option value behaviour related to particular market conditions.