Deep kernel hedging

2026-09-28

AI Summary

This study addresses the lack of inductive bias in deep learning and the high computational cost of traditional kernel methods for financial derivative hedging by proposing a differentiable deep kernel architecture. The method embeds neural networks into reproducing kernel Hilbert spaces, leverages truncated time-augmented signature features to handle path dependence, and employs random Fourier approximations to significantly reduce the overhead of large-scale matrix operations. By optimizing risk based on the generalized representer theorem, this framework achieves robust hedging performance in small-sample scenarios, outperforming both standard kernel methods and classical deep hedging models.

Abstract

We introduce a deep kernel hedging framework that combines the flexibility of deep learning with the structural inductive bias of kernel methods. The hedging functional is restricted to a reproducing kernel Hilbert space whose kernel is parameterized through a neural network embedding of the input features. The framework minimizes a regularized empirical risk under convex loss functions and can accommodate path-dependent information through truncated time-augmented signature features. We derive a generalized representer theorem for the joint hedging problem, reducing the empirical optimization to a finite-dimensional problem. To further reduce the computational cost associated with large kernel matrices, we develop a scalable random Fourier feature approximation and establish convergence guarantees. The random Fourier parameters are sampled once and remain fixed throughout training, while the deep kernel adapts to market data through the learned neural representation. We evaluate the performance of the proposed deep kernel approach on both synthetic and real data and compare it with standard kernel methods and classical deep hedging architectures. Numerical results indicate competitive and robust hedging performance, particularly in low-data regimes, which highlights the benefits of combining expressive neural representations with the inductive bias of kernel methods.

Problem

• deep hedging
• kernel methods
• financial derivatives
• low-data regimes
• computational scalability

Innovation

• Deep kernel hedging
• Reproducing kernel Hilbert space
• Generalized representer theorem
• Random Fourier features
• Signature features