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

ArXiv ID: 2511.23295 “View on arXiv”

Authors: 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.

Keywords: Path-Dependent Options, Market Impact, Signature Method, Stochastic Control, Derivatives

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs highly advanced mathematics including infinite-dimensional Riccati equations on the extended tensor algebra and non-standard stochastic control theory, warranting a near-maximum math score. The empirical rigor is strong due to explicit numerical experiments with signature approximations and backtesting in frictional markets, though the focus is more on theoretical proof and numerical implementation than on full-scale real-world backtesting datasets.

  flowchart TD
    A["Research Goal: Price & hedge path-dependent options with frictions"] --> B["Method: Signature Method & Stochastic Control"]
    B --> C["Data/Inputs: Price path + control variables"]
    C --> D["Process: Time-augmented signatures & Riccati equations"]
    D --> E["Process: Numerical simulation & hedging strategy"]
    E --> F["Outcome: Linear feedback strategies & smoothed trading"]
    F --> G["Outcome: Low-truncated signatures accurate in frictional markets"]