Rough volatility: evidence from range volatility estimators
Rough volatility: evidence from range volatility estimators
This paper extends the rough volatility hypothesis, originally demonstrated using realized volatility, to range-based volatility estimators such as Garman-Klass and Parkinson. By analyzing a diverse dataset including non-standard assets (e.g., S&P 400, IBEX 35, individual stocks), the author confirms that log-volatility exhibits scaling properties consistent with fractional Brownian motion with a Hurst exponent significantly below 0.5, often below 0.1. This finding addresses concerns that rough volatility might be an artifact of microstructure noise in high-frequency data, as range-based estimators are robust to such noise. The study validates the rough fractional stochastic volatility (RFSV) model and demonstrates its superior forecasting performance compared to traditional models like AR, HAR, and GARCH. The results provide strong evidence against the fractional stochastic volatility (FSV) model, which assumes long memory with Hurst exponent > 0.5, and support the intrinsic rough nature of volatility across various asset classes.
Highlights
- 1Extends rough volatility analysis to range-based volatility estimators, confirming fractional behavior with Hurst exponent below 0.1 across a broad dataset including non-standard assets.
- 2Addresses concerns that rough volatility may be an artifact of microstructure noise by using range-based proxies that are robust to such noise.
- 3Validates the rough fractional stochastic volatility (RFSV) model, showing its predictive power surpasses AR, HAR, and GARCH models in most scenarios.
- 4Provides evidence against the fractional stochastic volatility (FSV) model, which assumes Hurst exponent > 0.5.
Methods
- MRange-based volatility estimation using Garman-Klass and Parkinson estimators.
- MScaling analysis of log-volatility increments to estimate Hurst exponent via absolute moment scaling.
- MComparison of RFSV model forecasting performance against AR, HAR, and GARCH models.
Results
- RLog-volatility from range-based proxies behaves like fractional Brownian motion with Hurst exponent below 0.1, often approaching 0.
- RRange-based estimators, particularly Garman-Klass, exhibit similar regularity to realized volatility and are robust to microstructure noise.
- RRFSV model outperforms AR, HAR, and GARCH models in volatility forecasting for most assets tested.
- RFindings support the intrinsic rough nature of volatility, independent of high-frequency data noise.
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