Option Pricing with Convolutional Kolmogorov-Arnold Networks
Zeyuan Li, Qingdao Huang
TL;DR
This work tackles option pricing accuracy by integrating the dividend-adjusted Black–Scholes–Merton framework with neural-network models. It introduces and evaluates Kolmogorov-Arnold Networks (KANs) and their convolutional variant (Conv-KANs), alongside Conv-LSTM/LSTM baselines, to capture nonlinear pricing dynamics; the dividend parameter $q$ is incorporated into the option pricing formulas via $c = S_{0}e^{-qT}N(d_{1})-K e^{-rT}N(d_{2})$ and $p = K e^{-rT}N(-d_{2})-S_{0}e^{-qT}N(-d_{1})$, where $d_{1}= rac{ \ln(S_{0}/K)+(r-q+ abla^{2}/2)T}{ abla ootoldsymbol{ abla} abla}$ and $d_{2}=d_{1}- abla ootoldsymbol{ abla} abla$. A novel data-selection strategy that injects white-noise-like perturbations is proposed to mimic real trading environments and improve generalization. Empirical results on CSI 300 option data show Conv-KANs achieving the lowest error metrics (MSE, RMSE, MAE) among models, with Conv-LSTM competitive on temporal structure, while the baseline B-S-M remains robust. Overall, the study demonstrates that convolutional nonlinear networks can provide meaningful gains for option pricing in realistic, noisy settings, though overfitting and architectural choices warrant careful attention.
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.