Need for Speed: Fast and Accurate Pricing of American Options Using Parameterized Physics-Informed Neural Networks
- 1Department of Mathematics, Lahore University of Management Sciences (LUMS), Lahore 54792, Pakistan
Abstract
The 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 PINN inputs. The modified structure is called Parameterized-PINNs. It retains the physics-informed formulation of PINNs by incorporating the governing partial differential equation into the learning process while enabling a single trained network to generalize across a broad range of option configurations without requiring retraining. Numerical experiments demonstrate that the proposed model achieves high average pricing accuracy, with an L2 relative error of approximately 0.20% for call options and 0.09% for put options, over the full evaluation domain. However, 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 min for call options or 71 min for put options, PPINN inference takes almost 1.5 ms per option, approximately 1000 times faster than the Monte Carlo benchmark in the reported single-option evaluation, making it well suited to applications requiring repeated revaluation across a stable parameter regime. The framework is further evaluated using 1500 observed American option prices for two actively traded U.S. equities (Tesla and Amazon). The market-data experiment provides an additional empirical assessment of practical applicability. Overall, the numerical experiments demonstrate that PPINNs can provide accurate and low-latency approximations to the specified Black–Scholes American option pricing problem, with potential applicability to repeated valuation under stable model assumptions.
Related
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BibTeX
@article{ahmad2026need,
title = {{Need for Speed: Fast and Accurate Pricing of American Options Using Parameterized Physics-Informed Neural Networks}},
author = {Ayesha Ahmad and Adnan Khan},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203788},
url = {https://www.mdpi.com/2227-7390/14/20/3788},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Need for Speed: Fast and Accurate Pricing of American Options Using Parameterized Physics-Informed Neural Networks
AU - Ayesha Ahmad
AU - Adnan Khan
PY - 2026
DA - 2026/10/19
JO - Mathematics
DO - 10.3390/math14203788
UR - https://www.mdpi.com/2227-7390/14/20/3788
AB - The 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 PINN inputs. The modified structure is called Parameterized-PINNs. It retains the physics-informed formulation of PINNs by incorporating the governing partial differential equation into the learning process while enabling a single trained network to generalize across a broad range of option configurations without requiring retraining. Numerical experiments demonstrate that the proposed model achieves high average pricing accuracy, with an L2 relative error of approximately 0.20% for call options and 0.09% for put options, over the full evaluation domain. However, 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 min for call options or 71 min for put options, PPINN inference takes almost 1.5 ms per option, approximately 1000 times faster than the Monte Carlo benchmark in the reported single-option evaluation, making it well suited to applications requiring repeated revaluation across a stable parameter regime. The framework is further evaluated using 1500 observed American option prices for two actively traded U.S. equities (Tesla and Amazon). The market-data experiment provides an additional empirical assessment of practical applicability. Overall, the numerical experiments demonstrate that PPINNs can provide accurate and low-latency approximations to the specified Black–Scholes American option pricing problem, with potential applicability to repeated valuation under stable model assumptions.
SN - 2227-7390
ER -