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

Rushikesh Handal, Masanori Hirano

TL;DR

High-dimensional option valuation and hedging are hampered by computational complexity and unstable delta estimates in ML-based BSDE solvers. The authors introduce KANHedge, which embeds Kolmogorov-Arnold Networks with learnable B-spline activations into the BSDE hedging framework to model deltas at each time step. Empirical results show pricing accuracy on par with MLP-based solvers (errors below $1\%$) while achieving notable hedging improvements, with CVaR reductions up to $9\%$ for American baskets. This approach enhances delta smoothness and offers a scalable, robust hedging tool for high-dimensional derivatives.

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.

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

TL;DR

High-dimensional option valuation and hedging are hampered by computational complexity and unstable delta estimates in ML-based BSDE solvers. The authors introduce KANHedge, which embeds Kolmogorov-Arnold Networks with learnable B-spline activations into the BSDE hedging framework to model deltas at each time step. Empirical results show pricing accuracy on par with MLP-based solvers (errors below ) while achieving notable hedging improvements, with CVaR reductions up to for American baskets. This approach enhances delta smoothness and offers a scalable, robust hedging tool for high-dimensional derivatives.

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.
Paper Structure (15 sections, 25 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 15 sections, 25 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Foundational Mathematics
  4. Methodology
  5. Traditional MLP-Based Approach
  6. KANHedge
  7. Experimental Setup
  8. European Basket Options
  9. American Basket Options
  10. Evaluation criteria
  11. Results
  12. European Geometric Basket Options
  13. American Basket Options
  14. Discussion
  15. Conclusion

Figures (3)

  • Figure 1: Normalized Hedging Cost Distribution for European Geometric Basket Option: Baseline. KANHedge (red) shows slightly better hedging cost compared to MLP (green) when tail risk is used as hedging cost.
  • Figure 2: Normalized Hedging Cost Distribution for American Basket Option: $\sigma_1=0.3$, $\rho=0.3$, $K=35$. KANHedge (red) shows better hedging cost compared to MLP (green) when tail risk is used as hedging cost.
  • Figure 3: Delta estimation for single-dimensional European call option. KANHedge (red) shows superior approximation to the analytical Black-Scholes delta (blue) compared to MLP (green), particularly in out-of-the-money regions.