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: Ecole Polytechnique
Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium
Edouard Motte: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2025023, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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 inthe 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)
Pages: 34
Date: 2025-11-28
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