Beyond Black-Scholes and Heston: A Unified Deep Learning Architecture for Rough-Jump Option Pricing

The landscape of financial derivatives pricing has long been dominated by foundational models such as Black-Scholes and Heston, which provide elegant analytical or semi-analytical solutions under specific assumptions. However, these models often struggle to capture empirical market phenomena like volatility smile, skew, and sudden price discontinuities, leading to systematic mispricing. This paper introduces a novel, unified deep learning architecture designed for option pricing under complex market dynamics characterized by both rough volatility and abrupt jumps. Moving beyond the restrictive assumptions of classical models, our approach leverages the representational power of neural networks to implicitly learn intricate relationships within high-dimensional input spaces, integrating fractional Brownian motion characteristics for roughness and Poisson processes for jumps. The proposed architecture combines elements capable of processing time-series data for volatility estimation and feature extraction for jump detection, providing a robust framework for pricing European and American-style options. We demonstrate that this deep learning framework can effectively capture the complexities arising from coexisting rough and jump components, offering superior accuracy and adaptability compared to traditional and hybrid models. The abstract discusses the challenges of reconciling model tractability with market realism and posits deep learning as a promising avenue for developing more comprehensive and robust pricing tools.