# Rough volatility of Bitcoin

## TL;DR

This paper investigates the roughness and multifractal nature of Bitcoin's log-volatility using multifractal analysis, revealing anti-persistence and distributional sources of multifractality.

## Contribution

It is the first to analyze Bitcoin volatility's roughness and multifractality, providing new insights into its complex stochastic behavior.

## Key findings

- Log-volatility increments are rough, with Hurst exponent less than 0.5.
- The Hurst exponent varies over time, indicating multifractality.
- Multifractality partly originates from the distributional properties of the data.

## Abstract

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.