Need for Speed: Fast and Accurate Pricing of American Options Using Parameterized Physics-Informed Neural Networks

Source abstract

Financial world and the field of quantitative finance face the challenge of accurate and rapid valuation of American-style options, particularly in high-frequency trading and market-making environments. In this study, we propose a deep learning-based framework for pricing American options using parameterized physics-informed neural networks (PPINNs). The proposed approach extends standard PINNs by incorporating key model parameters (strike price, volatility, and interest rate) as network inputs along with the standard practice of using stock price and time to maturity as PINNs inputs. The modified structure is called Parameterized-PINNs, it preserves the advantages of PINNs, including its grid-free and unsupervised nature, while ensuring consistency with the governing partial differential equation. Additionally, the parameterized structure allows the trained network to generalize across a wide range of option configurations without requiring retraining. Numerical experiments demonstrate that the proposed model achieves high average pricing accuracy, with a global L2 relative error below 0.20% for call options and below 0.10% for put options across the training domain, though local relative errors in deep out-of-the-money regions under extreme parameter combinations can be substantially higher, primarily due to near-zero option values rather than large absolute mispricings. Once trained with a one-time offline cost of approximately 65 minutes, the model prices individual options in under 1.5 milliseconds, roughly 1,000 times faster per evaluation than Monte Carlo simulation, making it well-suited to applications requiring repeated revaluation across a stable parameter regime. The results are further validated against finite difference schemes and real market data across multiple actively traded U.S. equities. These findings highlight the effectiveness of PPINNs as a fast and reliable alternative for American option pricing in time-sensitive real world situations.