American Options Pricing under Heston Model via Curriculum Learning in Coupled PINNs

TL;DR

This paper introduces a novel deep learning framework using coupled PINNs with curriculum learning to accurately price American options under the Heston model, capturing the free boundary and stochastic volatility.

Contribution

It presents a new training strategy combining coupled PINNs and curriculum learning to efficiently solve American option pricing under the Heston model, including free boundary estimation.

Findings

Demonstrates accurate American option pricing under stochastic volatility.

Provides a robust and efficient alternative to traditional numerical methods.

Enables rapid inference and precise free boundary estimation.

Abstract

In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an unknown, time-varying exercise boundary. The Heston model is one of the most popular ways to model real market behavior because it allows volatility to change over time. However, unlike European options, there is no closed-form solution for American options under the Heston model, so we have to use numerical methods. In this paper, we propose a novel approach to solving the stochastic Heston partial differential equation for American options, using coupled physics-informed neural networks (PINNs) to predict both the option price and the free boundary, while employing curriculum learning and adaptive resampling to stabilize model training. Our work builds on recent deep learning methods but introduces a more effective training strategy to address the limitations of these approaches. The numerical results demonstrate the effectiveness of the proposed learning framework, providing a robust and efficient alternative to pricing American options, enabling rapid inference and accurate estimation under stochastic volatility.