Rough volatility: evidence from range volatility estimators

ArXiv ID: 2312.01426 “View on arXiv”

Authors: Unknown

Abstract

In Gatheral et al. 2018, first posted in 2014, volatility is characterized by fractional behavior with a Hurst exponent $H < 0.5$, challenging traditional views of volatility dynamics. Gatheral et al. demonstrated this using realized volatility measurements. Our study extends this analysis by employing range-based proxies to confirm their findings across a broader dataset and non-standard assets. Notably, we address the concern that rough volatility might be an artifact of microstructure noise in high-frequency return data. Our results reveal that log-volatility, estimated via range-based methods, behaves akin to fractional Brownian motion with an even lower $H$, below $0.1$. We also affirm the efficacy of the rough fractional stochastic volatility model (RFSV), finding that its predictive capability surpasses that of AR, HAR, and GARCH models in most scenarios. This work substantiates the intrinsic nature of rough volatility, independent of the microstructure noise often present in high-frequency financial data.

Keywords: Rough Volatility, Fractional Brownian Motion, Stochastic Volatility Models, Realized Volatility, Forecasting, Equities / Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts such as fractional Brownian motion and Hurst exponents, requiring sophisticated stochastic calculus and estimation theory. The empirical component is strong, involving extensive dataset analysis, comparison of multiple forecasting models (RFSV, AR, HAR, GARCH), and robustness checks against microstructure noise, making it highly backtest-ready.

  flowchart TD
    A["Research Goal<br>Confirm rough volatility with range estimators<br>addressing microstructure noise"] --> B["Data/Inputs<br>Diverse datasets: equities, derivatives,<br>high-frequency price data"]
    B --> C["Methodology<br>Compute log-volatility via range-based proxies<br>vs. realized volatility"]
    C --> D["Computational Process<br>1. Estimation of Hurst exponent H<br>2. RFSV model fitting<br>3. Comparative forecasting tests<br>(AR, HAR, GARCH)"]
    D --> E["Key Outcomes & Findings<br>• Confirmed fractional behavior H < 0.1<br>• Verified roughness is intrinsic<br>independent of microstructure noise<br>• RFSV outperforms standard models"]
    E --> F["Conclusion<br>Rough volatility is a fundamental,<br>robust property of financial markets"]