Extend ELM-based PINNs to path-dependent derivatives with early exercise

Extend the Extreme Learning Machine-based Physics-Informed Neural Network framework to price path-dependent derivatives, specifically including American options and credit derivatives with early exercise features.

Background

The paper demonstrates that Extreme Learning Machines (ELMs) can efficiently solve supervised and unsupervised tasks in quantitative finance, including option pricing via Physics-Informed ELMs for Black–Scholes-type PDEs. The authors present empirical results for European options, two-asset rainbow options, and double-barrier options, highlighting fast training and competitive accuracy compared to deep neural networks.

While these results cover a range of PDE-based pricing problems, extending the ELM-based physics-informed approach to more complex path-dependent instruments with early exercise features remains unresolved. Such products, including American options and certain credit derivatives, introduce additional challenges beyond those addressed in the paper’s experiments.