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

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Listed:
  • Eduardo Abi Jaber
  • Donatien Hainaut
  • Edouard Motte

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.

Suggested Citation

  • Eduardo Abi Jaber & Donatien Hainaut & Edouard Motte, 2025. "Signature approach for pricing and hedging path-dependent options with frictions," Papers 2511.23295, arXiv.org.
    • Handle: RePEc:arx:papers:2511.23295
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    References listed on IDEAS

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    1. Umut Çetin & H. Soner & Nizar Touzi, 2010. "Option hedging for small investors under liquidity costs," Finance and Stochastics, Springer, vol. 14(3), pages 317-341, September.
    2. repec:hal:journl:hal-01611790 is not listed on IDEAS
    3. Soner, H. Mete & Cetin, Umut & Touzi, Nizar, 2010. "Option hedging for small investors under liquidity costs," LSE Research Online Documents on Economics 28992, London School of Economics and Political Science, LSE Library.
    4. Ibrahim Ekren & Sergey Nadtochiy, 2022. "Utility‐based pricing and hedging of contingent claims in Almgren‐Chriss model with temporary price impact," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 172-225, January.
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    7. Owen Futter & Blanka Horvath & Magnus Wiese, 2023. "Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals," Papers 2308.15135, arXiv.org, revised Aug 2023.
    8. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2020. "Non-parametric Pricing and Hedging of Exotic Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(6), pages 457-494, November.
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