Market information of the fractional stochastic regularity model

ArXiv ID: 2409.07159 “View on arXiv”

Authors: Unknown

Abstract

The Fractional Stochastic Regularity Model (FSRM) is an extension of Black-Scholes model describing the multifractal nature of prices. It is based on a multifractional process with a random Hurst exponent $H_t$, driven by a fractional Ornstein-Uhlenbeck (fOU) process. When the regularity parameter $H_t$ is equal to $1/2$, the efficient market hypothesis holds, but when $H_t\neq 1/2$ past price returns contain some information on a future trend or mean-reversion of the log-price process. In this paper, we investigate some properties of the fOU process and, thanks to information theory and Shannon’s entropy, we determine theoretically the serial information of the regularity process $H_t$ of the FSRM, giving some insight into one’s ability to forecast future price increments and to build statistical arbitrages with this model.

Keywords: Fractional Stochastic Regularity Model (FSRM), Fractional Ornstein-Uhlenbeck (fOU), Hurst Exponent, Multifractality, Statistical Arbitrage, Equities

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with advanced stochastic calculus, fractional processes, and information theory, deriving serial information theoretically with heavy LaTeX, while the empirical component is limited to a conceptual forecasting procedure on three indices without detailed backtest implementation or performance metrics.

  flowchart TD
    A["Research Goal<br>Determine serial info of regularity process Ht<br>and its forecasting capability"] --> B
    subgraph B ["Key Methodology"]
        B1["Multifractional Process with<br>Random Hurst Exponent Ht"] --> B2["Fractional Ornstein-Uhlenbeck<br>fOU process as driver"]
        B2 --> B3["Information Theory<br>& Shannon's Entropy"]
    end
    B --> C{"Data Inputs"}
    C --> C1["Theoretical Properties of fOU"]
    C --> C2["Market Price Dynamics"]
    B3 --> D["Computational Processes"]
    D --> D1["Calculate Serial Information<br>of Regularity Process Ht"]
    D1 --> D2["Analyze Ht Deviation from 1/2"]
    D2 --> E["Key Findings & Outcomes"]
    E --> E1["Ht = 1/2 → Efficient Market Hypothesis"]
    E --> E2["Ht ≠ 1/2 → Predictable Trends<br>Mean-Reversion of Log-Price"]
    E --> E3["Statistical Arbitrage Opportunities<br>Identified via Entropy Analysis"]