Rough kernel hedging

TL;DR

This paper introduces a scalable, model-free signature-based algorithm for high-dimensional, path-dependent hedging that leverages operator-valued kernels and rough path theory, providing theoretical guarantees and practical flexibility.

Contribution

It develops a rigorous, signature-based hedging method using operator-valued kernels and rough paths, with proven convergence and the ability to incorporate diverse features.

Findings

Proposes a scalable, convergent signature-based hedging algorithm.

Provides theoretical guarantees on existence and uniqueness of solutions.

Allows integration of additional features like signals and news analytics.

Abstract

Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging problems. We make minimal assumptions about market dynamics by modelling them as general geometric rough paths, yielding a fully model-free approach. Furthermore, through a representer theorem, we provide theoretical guarantees on the existence and uniqueness of a global minimum for the resulting optimization problem and derive an analytic solution under highly general loss functions. Similar to the popular deep hedging approach, but in a more rigorous fashion, our method can also incorporate additional features via the underlying operator-valued kernel, such as trading signals, news analytics, and past hedging decisions, closely aligning with true machine-learning practice.