Path Shadowing Monte-Carlo

ArXiv ID: 2308.01486 “View on arXiv”

Authors: Unknown

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: Monte Carlo Simulation, Maximum Entropy, Path-Dependent Volatility, Option Pricing, Scattering Spectra, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail

  flowchart TD
    A["Research Goal:<br>Predict Future Paths & Prices"] --> B{"Key Methodology"}
    B --> C["Path Shadowing Monte-Carlo<br>Generate paths matching observed history"]
    B --> D["Maximum Entropy Model<br>Using Scattering Spectra"]
    C --> E["Computational Process:<br>Monte Carlo Simulation"]
    D --> E
    E --> F["Key Findings/Outcomes"]
    F --> G["State-of-the-art<br>Volatility Prediction"]
    F --> H["Superior Option Smiles<br>vs. PDV model & Market"]