Paper: arXiv 2601.11097

Authors: Rushikesh Handal, Masanori Hirano

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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel application of Kolmogorov-Arnold Networks (KANs) to solve BSDEs for high-dimensional European and American option pricing and hedging. It features a solid mathematical foundation linking PDEs to BSDEs and delivers strong empirical insights into hedging efficiency over standard MLPs.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve High-Dimensional Option Hedging via BSDEs] --> B[Input Data: European & American Basket Options across Multi-Dimensions]
    B --> C[Methodology: KANHedge Framework]
    C --> D[Computational Process: Replace MLPs with KANs using Learnable B-Spline Activations]
    D --> E[BSDE Solver Execution for Pricing & Delta Hedging]
    E --> F[Outcomes: Comparable Pricing Accuracy to MLPs]
    E --> G[Outcomes: Superior Hedging Performance & Reduced Cost Metrics]

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0 of 31 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.