Hybrid Neural Operator Framework for Stochastic Partial Differential Equation Based Option Pricing

Abstract

Classical models, such as the Black Scholes model, fail to account for non linear phenomena like stochastic volatility and jump dynamics, which are necessary for effective financial market option pricing. The Proposed SPDE Driven Financial Option Pricing Network (SPDE FinOpNet), a unique framework, combines the expressiveness of Stochastic Partial Differential Equations (SPDEs) with the rigor of Neural Operator Theory, including Fourier Neural Operators (FNOs) and Physics Informed Deep Operator Networks. The proposed SPDE FinOpNet reconsiders option pricing by utilizing stochastic models that include mean reverting volatility, Lévy driven jumps, and fractional Brownian motion memory effects. Standard solutions for these models are computationally expensive, particularly in large dimensions. The SPDE FinOpNet learns SPDE solution operators directly from data and physical principles, thereby generalizing function spaces independently of the mesh. The system captures long range associations via spectral convolution based FNOs. Variational energy based losses are employed to incorporate physical limitations in PI DeepONets, thereby ensuring the integrity of the governing dynamics. SPDE FinOpNet outperforms Monte Carlo, finite difference, and traditional physics free deep learning models in robust numerical testing on real world and simulated datasets. When market circumstances change, derivative portfolios are reevaluated quickly, and the approach is generalizable to previous volatility regimes. The scalable and physics consistent SPDE FinOpNet method for stochastic option pricing and risk assessment represents a significant advancement in data
driven quantitative finance. Experimental results show that SPDE FinOpNet is forty percent more accurate than baseline models such as DWMC and PINNs. On the other hand, the RMSE is 0.044 and the MAPE is 1.99%. It has a PSGS of 0.93 and a PIR loss of 0.011, which indicates that it is physically consistent. The model is accurate in a wide range of market situations.