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Path Shadowing Monte-Carlo

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  • Rudy Morel
  • St'ephane Mallat
  • Jean-Philippe Bouchaud

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 & St'ephane Mallat & Jean-Philippe Bouchaud, 2023. "Path Shadowing Monte-Carlo," Papers 2308.01486, arXiv.org.
    • Handle: RePEc:arx:papers:2308.01486
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    File URL: http://arxiv.org/pdf/2308.01486
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    References listed on IDEAS

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    1. Wu, Peng & Muzy, Jean-François & Bacry, Emmanuel, 2022. "From rough to multifractal volatility: The log S-fBM model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    2. Jean-François Muzy & Peng Wu & Emmanuel Bacry, 2022. "From Rough to Multifractal volatility: the log S-fBM model," Post-Print hal-03861566, HAL.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Vincent Vargas & Tung-Lam Dao & Jean-Philippe Bouchaud, 2015. "Skew And Implied Leverage Effect: Smile Dynamics Revisited," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-15.
    5. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    6. Peng Wu & Jean-Franc{c}ois Muzy & Emmanuel Bacry, 2022. "From Rough to Multifractal volatility: the log S-fBM model," Papers 2201.09516, arXiv.org, revised Jul 2022.
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    Cited by:

    1. Adil Rengim Cetingoz & Charles-Albert Lehalle, 2025. "Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance," Papers 2501.03993, arXiv.org, revised Apr 2025.

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