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Path Shadowing Monte-Carlo

Author

Listed:
  • Rudy Morel

    (LIENS - Laboratoire d'informatique de l'école normale supérieure - DI-ENS - Département d'informatique - ENS Paris - 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 - Capital Fund Management)

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.

Suggested Citation

  • Rudy Morel & Stéphane Mallat & Jean-Philippe Bouchaud, 2023. "Path Shadowing Monte-Carlo," Working Papers hal-04177835, HAL.
    • Handle: RePEc:hal:wpaper:hal-04177835
    Note: View the original document on HAL open archive server: https://hal.science/hal-04177835
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