Rough kernel hedging
File(s)
Preprint version
OA Location
Author(s)
Muca Cirone, Nicola
Salvi, Cristopher
Type
preprint
Abstract
Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels [38], we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging problems. We make minimal assumptions on market dynamics by modelling them as general geometric rough paths, yielding a fully model-free approach. Moreover, by means of a representer theorem, we provide theoretical guarantees on the existence and uniqueness of a global minimum of the resulting optimization problem, and derive an analytic solution under highly general loss functions. Similar to the popular deep hedging [5]-but in a more rigorous fashion-our method can also incorporate additional features by means of the underlying operator-valued kernel, such as trading signals, news analytics, and past hedging decisions, aligning closely with true machinelearning practice. Keywords Rough paths • Signature kernels • Hedging Mathematics Subject Classification (2020) 46C07 • 60L10 • 60L20 1 Introduction In idealized, complete, and frictionless markets, it is theoretically possible to perfectly hedge financial derivatives, thereby eliminating risk through appropriate hedging strategies. However, real markets are incomplete due to transaction costs, market impact, liquidity constraints, and other frictions, making
Date Issued
2025-02-05
Citation
arXiv, 2025
Journal / Book Title
arXiv
Copyright Statement
Copyright © 2025 The Authors. This work is licensed under a Creative Commons Attribution 4.0 International License.
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Description
Preprint version