Kolmogorov–Arnold Finance-Informed Neural Network in Option Pricing

Finance-Informed Neural Networks (FINNs), inspired by Physical Information Neural Networks (PINNs) and computational finance, aim to enhance risk assessment and support regulatory decision-making. Despite their promising potential, existing FINNs face significant challenges related to learning efficiency and overall performance. This paper examines the KAFIN framework, based on the Kolmogorov–Arnold representation, which aims to improve financial modeling and analytical calculations. To evaluate the performance of FINNs, this study uses generated data instead of real market data. This choice enables controlled simulations of various financial scenarios while avoiding the complexities and noise inherent in actual market data. By relying on generated data, we are able to isolate and assess the core capabilities of KAFIN under well-defined theoretical conditions, facilitating a clearer analysis of its performance. This study focuses on European option pricing as a case study, using generated input data that simulate a range of market scenarios, including typical regulatory conditions in financial markets. Testing KAFIN under these controlled conditions allows for a rigorous evaluation of its ability to handle the complexities of pricing options across different market assumptions and regulatory constraints. Empirical results demonstrate that KAFIN significantly outperforms the baseline method, improving pricing accuracy by minimizing residual errors and aligning closely with analytical solutions. The architecture of KAFIN effectively captures the inherent complexities of option pricing, integrating financial principles with advanced computational techniques. Performance indicators reveal that KAFIN achieves lower average total losses and reduces the variability in loss components, highlighting its advantage in modeling and analyzing complex financial dependencies while ensuring compliance with regulatory standards.