Power-Law Return-Volatility Cross Correlations of Bitcoin

TL;DR

This study examines the return-volatility relationships in Bitcoin, revealing long-range power-law cross correlations at high frequency and dependence on the power of absolute returns, highlighting complex dynamics.

Contribution

It uncovers power-law long-range cross correlations between Bitcoin returns and volatility at high frequency, a novel insight into cryptocurrency market dynamics.

Findings

Insignificant daily return-volatility correlations.

Presence of power-law negative cross correlations at high frequency.

Correlation strength varies with the power of absolute returns.

Abstract

This paper investigates the return-volatility asymmetry of Bitcoin. We find that the cross correlations between return and volatility (squared return) are mostly insignificant on a daily level. In the high-frequency region, we find thata power-law appears in negative cross correlation between returns and future volatilities, which suggests that the cross correlation is \revision{long ranged}. We also calculate a cross correlation between returns and the power of absolute returns, and we find that the strength of \revision{the cross correlations} depends on the value of the power.