KANHedge: Efficient Hedging of High-Dimensional Options Using Kolmogorov-Arnold Network-Based BSDE Solver

TL;DR

This paper introduces KANHedge, a novel BSDE-based hedging method using Kolmogorov-Arnold Networks with learnable B-spline activations, improving hedging performance in high-dimensional option markets.

Contribution

We propose KANHedge, a new BSDE-based hedging approach employing Kolmogorov-Arnold Networks with learnable B-spline activations, enhancing hedging accuracy and risk management.

Findings

KANHedge achieves comparable pricing accuracy to MLP-based methods.

KANHedge significantly reduces hedging costs across tested options.

Enhanced risk control demonstrated in high-dimensional market conditions.

Abstract

High-dimensional option pricing and hedging present significant challenges in quantitative finance, where traditional PDE-based methods struggle with the curse of dimensionality. The BSDE framework offers a computationally efficient alternative to PDE-based methods, and recently proposed deep BSDE solvers, generally utilizing conventional Multi-Layer Perceptrons (MLPs), build upon this framework to provide a scalable alternative to numerical BSDE solvers. In this research, we show that although such MLP-based deep BSDEs demonstrate promising results in option pricing, there remains room for improvement regarding hedging performance. To address this issue, we introduce KANHedge, a novel BSDE-based hedger that leverages Kolmogorov-Arnold Networks (KANs) within the BSDE framework. Unlike conventional MLP approaches that use fixed activation functions, KANs employ learnable B-spline activation functions that provide enhanced function approximation capabilities for continuous derivatives. We comprehensively evaluate KANHedge on both European and American basket options across multiple dimensions and market conditions. Our experimental results demonstrate that while KANHedge and MLP achieve comparable pricing accuracy, KANHedge provides improved hedging performance. Specifically, KANHedge achieves considerable reductions in hedging cost metrics, demonstrating enhanced risk control capabilities.