Path Shadowing Monte-Carlo

Rudy Morel (), Stéphane Mallat and Jean-Philippe Bouchaud
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Rudy Morel: LIENS - Laboratoire d'informatique de l'école normale supérieure - 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 - CNRS - Centre National de la Recherche Scientifique
Stéphane Mallat: 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 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 diversity of generated paths while reproducing the main statistical properties of financial prices, including stylized facts on 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 current version of the Path-Dependent Volatility model and the option market itself.

Keywords: Volatility prediction; Option pricing; Wavelets (search for similar items in EconPapers)
Date: 2023-08-06
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