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

TL;DR

This work introduces the KAN-based Option Pricing (KANOP) model, 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.

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.

Figures (2)

• Figure 1: $\hat{F}(\omega; \ t_k)$ values using the Weighted Laguerre model and Hermite model; indicating at $t_1$, Hermite model model provides a better approximation.
• Figure 2: $\hat{F}(\omega; \ t_k)$ values using the KANOP model and MLP model; indicating at $t_1$, KANOP model provides a better approximation.