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

2025-11-28

AI Summary

This paper addresses the pricing and hedging of path-dependent options under both transient and permanent market frictions. To tackle the resulting nonlinearity and non-Markovian dynamics, we introduce the signature method—novel in this context—and construct a linear feedback hedging strategy on a time-augmented signature space. The strategy’s coefficients are characterized exactly via an infinite-dimensional Riccati equation. Theoretically, we show that market frictions induce smoother optimal trading trajectories, and that low-order signature truncations suffice to capture high-order path dependence efficiently. Numerical experiments demonstrate that the proposed approach achieves high accuracy, strong robustness, and computational tractability across diverse path-dependent options—including Asian and lookback options—significantly outperforming conventional local sensitivity–based or Monte Carlo hedging schemes.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Pricing path-dependent options with market frictions
• Hedging nonlinear non-Markovian control problems via signatures
• Solving infinite-dimensional Riccati equations for trading strategies

Innovation

• Signature approach transforms nonlinear control into tractable form
• Hedging strategies use linear feedback in time-augmented signature space
• Market impact enables accurate low-truncated signature approximations