Path shadowing Monte Carlo

Rudy Morel, Stéphane Mallat and Jean-Philippe Bouchaud
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Rudy Morel: DI-ENS - Département d'informatique - ENS-PSL - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique
Stéphane Mallat: DI-ENS - Département d'informatique - ENS-PSL - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique, Collège de France - Chaire Sciences des données - CdF (institution) - Collège de France
Jean-Philippe Bouchaud: CFM - Capital Fund Management

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Abstract: We introduce a Path Shadowing Monte Carlo method, which provides the prediction of future paths, given any generative model. At any given date, it averages future quantities over generated price paths whose past history matches, or ‘shadows', the actual (observed) history. We test our approach using paths generated from a maximum entropy model of financial prices, based on a recently proposed multi-scale analogue of the standard skewness and kurtosis called ‘Scattering Spectra'. This model promotes the diversity of generated paths while reproducing main statistical properties of financial prices, including stylized facts such as volatility roughness. Our method yields state-of-the-art predictions for future realized volatility and allows one to determine conditional option smiles for the S&P500 that outperform both the most recent low-parametric models and the option market itself. The code is available at https://github.com/RudyMorel/shadowing (This work is supported by the PRAIRIE 3IA Institute of the French ANR-19-P3IA-0001 program and the ENS-CFM models and data science chair.).

Keywords: Volatility prediction; Option pricing; Wavelets (search for similar items in EconPapers)
Date: 2024-10-25
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Published in Quantitative Finance, 2024, 24 (9), pp.1199-1225. ⟨10.1080/14697688.2024.2399285⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04993695

DOI: 10.1080/14697688.2024.2399285

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