Signature approach for pricing and hedging path-dependent options with frictions
(2025) , 34 pages
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- 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.
- Affiliations
Citations
Abi Jaber, E., Hainaut, D., & Motte, E. (2025). Signature approach for pricing and hedging path-dependent options with frictions (LIDAM Discussion Paper ISBA 2025/23).