A Multifractal Model of Asset Returns

ArXiv ID: ssrn-78588 “View on arXiv”

Authors: Unknown

Abstract

This paper presents the “multifractal model of asset returns” (“MMAR”), based upon the pioneering research into multifractal measures by Man

Keywords: Multifractal Models, Asset Returns, Stochastic Processes, Time Series Analysis, Volatility Modeling, Equity

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like multifractal measures, long-dependence, and scaling laws, indicating high mathematical complexity. It also discusses empirical implications, comparisons with GARCH/FIGARCH, and references companion empirical work, showing substantial empirical rigor.

  flowchart TD
    Goal["Research Goal:<br>Create model for asset return volatility<br>(MMAR)"] --> Inputs["Data/Input:<br>Equity index returns<br>High-frequency time series"]
    Inputs --> Method["Key Method:<br>Multifractal measures &<br>stochastic cascade process"]
    Method --> Comp["Computational Process:<br>Model calibration &<br>time-scale analysis"]
    Comp --> Findings["Key Findings/Outcomes:<br>1. Captures heavy tails<br>2. Explains volatility clustering<br>3. Superior to GARCH models"]
    Findings --> Final["Conclusion:<br>MMAR accurately describes<br>multifractal nature of markets"]