Option Pricing with Convolutional Kolmogorov-Arnold Networks

TL;DR

This paper introduces Convolutional Kolmogorov-Arnold Networks (Conv-KANs) for option pricing, demonstrating improved accuracy and robustness over traditional models and other neural network architectures in a simulated trading environment.

Contribution

It presents Conv-KANs as a novel neural network architecture for option pricing, incorporating non-linear capabilities and a new data selection strategy for better real-world simulation.

Findings

Conv-KANs outperform traditional Black-Scholes models in prediction accuracy.

Enhanced non-linear networks show superior fitting performance.

The proposed data strategy improves model robustness in trading simulations.

Abstract

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.