This study enhances option pricing by presenting unique pricing model fractional order Black-Scholes-Merton (FOBSM) which is based on the Black-Scholes-Merton (BSM) model. The main goal is to improve the precision and authenticity of option pricing, matching them more closely with the financial landscape. The approach integrates the strengths of both the BSM and neural network (NN) with complex diffusion dynamics. This study emphasizes the need to take fractional derivatives into account when analyzing financial market dynamics. Since FOBSM captures memory characteristics in sequential data, it is better at simulating real-world systems than integer-order models. Findings reveals that in complex diffusion dynamics, this hybridization approach in option pricing improves the accuracy of price predictions. the key contribution of this work lies in the development of a novel option pricing model (FOBSM) that leverages fractional calculus and neural networks to enhance accuracy in capturing complex diffusion dynamics and memory effects in financial data.

翻译：本研究通过提出基于Black-Scholes-Merton（BSM）模型的独特分数阶Black-Scholes-Merton（FOBSM）定价模型，增强了期权定价能力。主要目标是提升期权定价的精确性与真实性，使其更贴合金融市场的实际环境。该方法整合了BSM模型与神经网络（NN）在处理复杂扩散动力学方面的优势。本研究强调了在分析金融市场动态时考虑分数阶导数的必要性。由于FOBSM能够捕捉序列数据中的记忆特性，因此在模拟现实系统方面优于整数阶模型。研究结果表明，在复杂扩散动力学条件下，这种混合方法在期权定价中提高了价格预测的准确性。本工作的关键贡献在于开发了一种新颖的期权定价模型（FOBSM），该模型利用分数阶微积分与神经网络，以增强对金融数据中复杂扩散动力学和记忆效应的捕捉能力。