Signature approach for pricing and hedging path-dependent options with frictions

Eduardo Abi Jaber (), Donatien Hainaut () and Edouard Motte ()
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Eduardo Abi Jaber: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Donatien Hainaut: UCL - Université Catholique de Louvain = Catholic University of Louvain
Edouard Motte: UCL - Université Catholique de Louvain = Catholic University of Louvain

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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: path-signatures; path-dependent options; market frictions; non-Markovian stochastic control; infinite-dimensional Riccati equations (search for similar items in EconPapers)
Date: 2025-11-28
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