Signature approach for pricing and hedging path-dependent options with frictions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917112229920768 |
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| author | Jaber, Eduardo Abi Hainaut, Donatien Motte, Edouard |
| author_facet | Jaber, Eduardo Abi Hainaut, Donatien Motte, Edouard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signature approach for pricing and hedging path-dependent options with frictions Jaber, Eduardo Abi Hainaut, Donatien Motte, Edouard Portfolio Management Optimization and Control Mathematical Finance Pricing of Securities 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. |
| title | Signature approach for pricing and hedging path-dependent options with frictions |
| topic | Portfolio Management Optimization and Control Mathematical Finance Pricing of Securities |
| url | https://arxiv.org/abs/2511.23295 |