Multifractality in Bitcoin Realised Volatility: Implications for Rough Volatility Modelling

TL;DR

This paper investigates Bitcoin's realized volatility and finds it exhibits multifractal behavior, challenging the assumptions of rough volatility models and explaining their failure to accurately model Bitcoin volatility.

Contribution

It demonstrates that Bitcoin volatility is multifractal, which invalidates the homogeneity assumption of rough volatility models and explains their poor performance on Bitcoin data.

Findings

Bitcoin volatility shows multifractal structure.

Rough volatility estimators systematically fail on Bitcoin data.

Multifractal diagnostics outperform rough models in capturing Bitcoin volatility.

Abstract

We assess the applicability of rough volatility models to Bitcoin realized volatility using the normalised p-variation framework of Cont and Das (2024). Applying this model-free estimator to high-frequency Bitcoin data from 2017 to 2024 across multiple sampling resolutions, we find that the normalised statistic remains strictly negative, precluding the estimation of a valid roughness index. Stationarity tests and robustness checks reveal no significant evidence of non-stationarity or structural breaks as explanatory factors. Instead, convergent evidence from three complementary diagnostics, namely Multifractal Detrended Fluctuation Analysis, log-log moment scaling, and wavelet leaders, reveals a multifractal structure in Bitcoin volatility. This behaviour violates the homogeneity assumptions underlying rough volatility estimation and accounts for the estimator's systematic failure. These findings suggest that while rough volatility models perform well in traditional markets, they are structurally misaligned with the empirical features of Bitcoin volatility.