With the rapid advancement of neural networks, methods for option pricing have evolved significantly. This study employs the Black-Scholes-Merton (B-S-M) model, incorporating an additional variable to improve the accuracy of predictions compared to the traditional Black-Scholes (B-S) model. Furthermore, Convolutional Kolmogorov-Arnold Networks (Conv-KANs) and Kolmogorov-Arnold Networks (KANs) are introduced to demonstrate that networks with enhanced non-linear capabilities yield superior fitting performance. For comparative analysis, Conv-LSTM and LSTM models, which are widely used in time series forecasting, are also applied. Additionally, a novel data selection strategy is proposed to simulate a real trading environment, thereby enhancing the robustness of the model.

翻译：随着神经网络的快速发展，期权定价方法已取得显著进展。本研究采用Black-Scholes-Merton（B-S-M）模型，通过引入额外变量以提升预测精度，相较于传统Black-Scholes（B-S）模型有所改进。此外，研究引入了卷积Kolmogorov-Arnold网络（Conv-KANs）与Kolmogorov-Arnold网络（KANs），证明具备增强非线性能力的网络能获得更优的拟合性能。为进行对比分析，同时应用了在时间序列预测中广泛使用的Conv-LSTM与LSTM模型。此外，本文提出一种创新的数据筛选策略以模拟真实交易环境，从而增强模型的鲁棒性。