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arXiv · 2511.23295

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

Eduardo Abi Jaber·Donatien Hainaut·Edouard Motte
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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.

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Eduardo Abi Jaber, Donatien Hainaut, Edouard Motte. 2025-11-28. Signature approach for pricing and hedging path-dependent options with frictions. https://arxiv.org/abs/2511.23295

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