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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Path Shadowing Monte-Carlo

Résumé

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.
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Dates et versions

hal-04177835 , version 1 (06-08-2023)

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Rudy Morel, Stéphane Mallat, Jean-Philippe Bouchaud. Path Shadowing Monte-Carlo. 2023. ⟨hal-04177835⟩
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