KANOP: A Data-Efficient Option Pricing Model using Kolmogorov-Arnold Networks

TL;DR

KANOP introduces a data-efficient, adaptable option pricing model based on Kolmogorov-Arnold Networks, outperforming traditional methods in accuracy and reliability for American-style options.

Contribution

The paper presents KANOP, a novel option pricing approach utilizing KANs that require fewer layers and adapt basis functions, improving estimation accuracy over conventional methods.

Findings

KANOP yields more reliable option value estimates.

KANOP provides more accurate delta estimates for hedging.

The model performs well in both single and multi-variable scenarios.

Abstract

Inspired by the recently proposed Kolmogorov-Arnold Networks (KANs), we introduce the KAN-based Option Pricing (KANOP) model to value American-style options, building on the conventional Least Square Monte Carlo (LSMC) algorithm. KANs, which are based on Kolmogorov-Arnold representation theorem, offer a data-efficient alternative to traditional Multi-Layer Perceptrons, requiring fewer hidden layers to achieve a higher level of performance. By leveraging the flexibility of KANs, KANOP provides a learnable alternative to the conventional set of basis functions used in the LSMC model, allowing the model to adapt to the pricing task and effectively estimate the expected continuation value. Using examples of standard American and Asian-American options, we demonstrate that KANOP produces more reliable option value estimates, both for single-dimensional cases and in more complex scenarios involving multiple input variables. The delta estimated by the KANOP model is also more accurate than that obtained using conventional basis functions, which is crucial for effective option hedging. Graphical illustrations further validate KANOP's ability to accurately model the expected continuation value for American-style options.