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

Author

Listed:
  • Abi Jaber, Eduardo

    (Ecole Polytechnique)

  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Motte, Edouard

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

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.

Suggested Citation

  • Abi Jaber, Eduardo & Hainaut, Donatien & Motte, Edouard, 2025. "Signature approach for pricing and hedging path-dependent options with frictions," LIDAM Discussion Papers ISBA 2025023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2025023
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Bruno Bouchard & G. Loeper & Y. Zou, 2017. "Hedging of covered options with linear market impact and gamma constraint," Post-Print hal-01611790, HAL.
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    6. Bruno Bouchard & G Loeper & Y Zou, 2017. "Hedging of covered options with linear market impact and gamma constraint," Post-Print hal-01247523, HAL.
    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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