Measuring Rough and Multifractal Volatility in Bitcoin

Summary

The study examines whether Bitcoin’s log volatility has rough, anti-persistent behavior. It applies multifractal detrended fluctuation analysis to increments in log volatility and estimates generalized Hurst exponents. Values below one half are reported, indicating roughness in those increments. The estimates also vary rather than remaining constant, which the authors interpret as evidence of multifractal behavior.

To investigate the source of that multifractality, the study compares the original increments with shuffled versions of the time series. The shuffled series suggest that distributional properties account for part of the multifractality. The abstract does not specify the data period, sampling frequency, detailed numerical estimates, or how much of the effect remains after shuffling. It presents statistical findings about Bitcoin volatility, not a trading rule or evidence that the measured properties can be exploited profitably.

Key ideas

• The study measures roughness in Bitcoin log-volatility increments using multifractal detrended fluctuation analysis.
• Generalized Hurst exponents below one half are reported as evidence of rough increments.
• Variation in the generalized Hurst exponent is interpreted as multifractal behavior.
• Shuffled-series analysis suggests that distributional properties contribute partly to the observed multifractality.
• The abstract reports volatility characteristics rather than a tested trading strategy.

Tags

# Rough volatility of Bitcoin


# Rough volatility of Bitcoin









Recent studies have found that the log-volatility of asset returns exhibit roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using the 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 log-volatility increments that are rough. Furthermore, we find that the generalized Hurst exponent is not constant. This observation indicates that the log-volatility has multifractal property. Using shuffled time series of the log-volatility increments, we infer that the source of multifractality partly comes from the distributional property.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.