Multifractality in Bitcoin Realised Volatility: Implications for Rough Volatility Modelling

ArXiv ID: 2507.00575 “View on arXiv”

Authors: Milan Pontiggia

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.

Keywords: rough volatility, Bitcoin, multifractal, realized volatility, wavelet leaders, cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 9.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical frameworks like the normalised p-variation estimator, multifractal analysis, and scaling laws, indicating high math complexity. It also demonstrates strong empirical rigor by using extensive high-frequency data (2017-2024), conducting robustness checks, multiple diagnostics (DFA, log-log scaling, wavelets), and addressing model assumptions and data limitations.

  flowchart TD
    A["Research Goal: Assess applicability of rough volatility models to Bitcoin using Cont and Das (2024) normalised p-variation estimator"] --> B["Data Input: High-frequency Bitcoin data 2017-2024"]
    B --> C["Core Methodology: Apply normalised p-variation across multiple sampling resolutions"]
    C --> D{"Is the normalised statistic positive?"}
    D -- No --> E["Estimation Failure: Statistic strictly negative precludes roughness index"]
    D -- Yes --> F["Roughness Index Estimated"]
    E --> G{"Check Explanatory Factors"}
    G -- Non-stationarity/Structural Breaks --> H["Disconfirmed: Stationarity tests show no significant evidence"]
    G -- Multifractal Structure --> I["Confirmed: Convergent evidence from MF-DFA, log-log moment scaling, and wavelet leaders"]
    H --> I
    I --> J["Key Finding: Bitcoin volatility exhibits multifractality, violating homogeneity assumptions required for rough volatility models"]
    J --> K["Implication: Rough volatility models are structurally misaligned with Bitcoin volatility features"]
    F --> K