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

TL;DR

This paper introduces a signature-based method for pricing and hedging complex path-dependent options considering market frictions, transforming a nonlinear control problem into a linear feedback form using signatures.

Contribution

It develops a novel signature approach that recasts nonlinear stochastic control problems into a linear form, enabling effective hedging strategies under market impact.

Findings

Signature methods effectively handle path-dependence in options.

Market impact smooths trading strategies, improving robustness.

Low-truncated signatures provide accurate approximations in frictional markets.

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.