Signature approach for pricing and hedging path-dependent options with frictions
Abstract
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an inherently nonlinear and non-Markovian stochastic control problem into a tractable form, yielding hedging strategies in (possibly infinite) linear feedback form in the time-augmented signature of the control variables, with coefficients characterized by non-standard infinite-dimensional Riccati equations on the extended tensor algebra. Numerical experiments demonstrate the effectiveness of these signature-based strategies for pricing and hedging general path-dependent payoffs in the presence of frictions. In particular, market impact naturally smooths optimal trading strategies, making low-truncated signature approximations highly accurate and robust in frictional markets, contrary to the frictionless case.
Keywords
Cite
@article{arxiv.2511.23295,
title = {Signature approach for pricing and hedging path-dependent options with frictions},
author = {Eduardo Abi Jaber and Donatien Hainaut and Edouard Motte},
journal= {arXiv preprint arXiv:2511.23295},
year = {2025}
}