In the realm of option pricing, existing models are typically classified into principle-driven methods, such as solving partial differential equations (PDEs) that pricing function satisfies, and data-driven approaches, such as machine learning (ML) techniques that parameterize the pricing function directly. While principle-driven models offer a rigorous theoretical framework, they often rely on unrealistic assumptions, such as asset processes adhering to fixed stochastic differential equations (SDEs). Moreover, they can become computationally intensive, particularly in high-dimensional settings when analytical solutions are not available and thus numerical solutions are needed. In contrast, data-driven models excel in capturing market data trends, but they often lack alignment with core financial principles, raising concerns about interpretability and predictive accuracy, especially when dealing with limited or biased datasets. This work proposes a hybrid approach to address these limitations by integrating the strengths of both principled and data-driven methodologies. Our framework combines the theoretical rigor and interpretability of PDE-based models with the adaptability of machine learning techniques, yielding a more versatile methodology for pricing a broad spectrum of options. We validate our approach across different volatility modeling approaches-both with constant volatility (Black-Scholes) and stochastic volatility (Heston), demonstrating that our proposed framework, Finance-Informed Neural Network (FINN), not only enhances predictive accuracy but also maintains adherence to core financial principles. FINN presents a promising tool for practitioners, offering robust performance across a variety of market conditions.

翻译：在期权定价领域，现有模型通常分为两类：原理驱动方法（例如求解定价函数所满足的偏微分方程）与数据驱动方法（例如通过机器学习技术直接参数化定价函数）。原理驱动模型虽提供了严谨的理论框架，但常依赖不现实的假设（如资产过程遵循固定的随机微分方程），且在缺乏解析解需依赖数值解法时——特别是高维场景下——计算量显著增加。相比之下，数据驱动模型虽能有效捕捉市场数据趋势，却常偏离核心金融原理，导致可解释性与预测准确性受到质疑，尤其在处理有限或有偏数据集时更为突出。本研究提出一种混合方法，通过融合原理驱动与数据驱动方法的优势以应对上述局限。该框架结合了基于偏微分方程模型的理论严谨性、可解释性以及机器学习技术的适应性，形成了一种适用于广泛期权品种的通用定价方法。我们在不同波动率建模场景（常数波动率的Black-Scholes模型与随机波动率的Heston模型）中验证了该框架的有效性，结果表明所提出的金融信息神经网络（FINN）不仅提升了预测精度，同时保持了与核心金融原理的一致性。FINN为从业者提供了具有前景的工具，能够在多样化的市场条件下保持稳健性能。