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

ArXiv ID: 2410.00419 “View on arXiv”

Authors: Unknown

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.

Keywords: Kolmogorov-Arnold Networks, American options, Least Square Monte Carlo, option pricing, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper introduces complex mathematical machinery by leveraging the Kolmogorov-Arnold representation theorem and adapting Kolmogorov-Arnold Networks (KANs) to the financial domain, indicating high math complexity. It provides a clear empirical evaluation with concrete comparisons against established baselines (standard LSMC with polynomial basis functions and deep MLPs) on specific American and Asian-American options, including metrics for pricing accuracy and delta hedging, demonstrating strong empirical rigor.

  flowchart TD
    A["Research Goal: <br>Improve American Option Pricing"] --> B["Methodology: <br>Kolmogorov-Arnold Networks KANs"]
    B --> C{"Data/Inputs: <br>American & Asian-American Options"}
    C --> D["Computational Process: <br>KANOP Model Integration with LSMC"]
    D --> E["Findings: <br>Higher Accuracy in Value & Delta Estimates"]