Jump Diffusion-Informed Neural Networks with Transfer Learning for Accurate American Option Pricing under Data Scarcity

TL;DR

This paper introduces a novel neural network framework incorporating jump diffusion processes and transfer learning to improve American option pricing accuracy, especially under data scarcity, by combining multiple models and optimization techniques.

Contribution

It proposes a comprehensive, multi-module framework that integrates jump diffusion-informed neural networks with transfer learning and Bayesian optimization for enhanced American option pricing.

Findings

Accurate pricing of American options demonstrated across six case studies.

Framework outperforms existing models in pricing deep out-of-the-money options.

Shows strong convergence, physical consistency, and generalization capabilities.

Abstract

Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of determining optimal exercise times and modeling non-linear payoffs resulting from stochastic paths. Moreover, the prevalent use of the Black-Scholes formula in hybrid models fails to accurately capture the discontinuity in the price process, limiting model performance, especially under scarce data conditions. To address these issues, this study presents a comprehensive framework for American option pricing consisting of six interrelated modules, which combine nonlinear optimization algorithms, analytical and numerical models, and neural networks to improve pricing performance. Additionally, to handle the scarce data challenge, this framework integrates the transfer learning through numerical data augmentation and a physically constrained, jump diffusion process-informed neural network to capture the leptokurtosis of the log return distribution. To increase training efficiency, a warm-up period using Bayesian optimization is designed to provide optimal data loss and physical loss coefficients. Experimental results of six case studies demonstrate the accuracy, convergence, physical effectiveness, and generalization of the framework. Moreover, the proposed model shows superior performance in pricing deep out-of-the-money options.