Paper: arXiv 2507.00575

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 9.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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

Cited References (21)

  1. Volatility is Rough (2018) — link
  2. Consistent Estimation for Fractional Stochastic Volatility Model under High-Frequency Asymptotics (2022) — link
  3. Rough Volatility: Fact or Artefact? (2024) — link
  4. Trading and Arbitrage in Cryptocurrency Markets (2020) — link
  5. Volatility and Return Jumps in Bitcoin (2018) — link
  6. Modelling Volatility of Cryptocurrencies Using Markov-Switching GARCH Models (2019) — link
  7. Chaos, Randomness and Multi-Fractality in Bitcoin Market (2018) — link
  8. Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series (2002) — link
and 13 more
  1. Bootstrap for Empirical Multifractal Analysis (2007) — link
  2. Decoupling the Short- and Long-Term Behavior of Stochastic Volatility (2022) — link
  3. Power and Bipower Variation with Stochastic Volatility and Jumps (2004) — link
  4. Rough Volatility of Bitcoin (2020) — link
  5. Multifractality and Sample Size Influence on Bitcoin Volatility Patterns — → 2511.03314
  6. Surrogate Time Series (2000) — link
  7. Components of Multifractality in the Central England Temperature Anomaly Series (2013) — link
  8. Bitcoin Historical Data (2025) — link
  9. Tests for Hurst Effect (1987) — link
  10. Estimates of the Regression Coefficient Based on Kendall’s Tau (1968) — link
  11. Distribution of the Estimators for Autoregressive Time Series with a Unit Root (1979) — link
  12. Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root? (1992) — link
  13. Selective Review of Offline Change Point Detection Methods (2020) — link

1 of 21 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.