Learning standardized noise for risk-neutral option pricing via Generative Adversarial Networks

Abstract

This paper proposes a Generative Adversarial Network (GAN)–based framework for risk-neutral option pricing that learns the empirical distribution and temporal structure of log-return noise. By extracting and modeling stochastic noise from historical returns, the framework generates risk-neutral price paths for option valuation and delta prediction. We evaluate three state-of-the-art GAN architectures, including TimeGAN, QuantGAN, and SigCWGAN, against Monte Carlo simulation, the Black–Scholes–Merton, and Heston models across market regimes, maturities, moneyness levels, and option types. Empirical results show that QuantGAN and SigCWGAN accurately replicate key distributional and autocorrelation properties of return noise and consistently outperform benchmark models in option pricing, particularly in stable market environments and around at-the-money regions where pricing accuracy is most critical. Across a broad range of market conditions, these models deliver lower pricing errors and higher statistical confidence measures than traditional benchmarks. While pricing performance deteriorates during periods of abrupt volatility shifts, GAN-based models remain competitive overall. In contrast, improvements in delta prediction are limited, especially near mid-delta regions where payoff curvature is steepest. Overall, the findings demonstrate that learning stochastic noise offers an effective and flexible data-driven alternative for risk-neutral option pricing, while reliable sensitivity estimation requires models that jointly capture distributional features and local dynamic responses of the underlying asset.