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arXiv · 2308.01486

Path Shadowing Monte-Carlo

Rudy Morel·Stéphane Mallat·Jean-Philippe Bouchaud
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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.

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Rudy Morel, Stéphane Mallat, Jean-Philippe Bouchaud. 2023-08-03. Path Shadowing Monte-Carlo. https://arxiv.org/abs/2308.01486

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