Rough volatility of Bitcoin

Recent studies have found that the log-volatility of asset returns exhibits roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using multifractal detrended fluctuation analysis, we obtain the generalized Hurst exponent of the log-volatility increments and find that the generalized Hurst exponent is less than 1/2, which indicates rough log-volatility increments. Furthermore, we find that the generalized Hurst exponent is not constant. This observation indicates that the log-volatility has a multifractal property. Using shuffled time series of the log-volatility increments, we infer that the source of multifractality partly derives from the distributional property.