标题： 比特币实现波动率中的尺度依赖性多分形：对粗糙波动率建模的影响 显示英文标题

标题： Scale-Dependent Multifractality in Bitcoin Realised Volatility: Implications for Rough Volatility Modelling

摘要： 我们使用Cont和Das（2024）的归一化p-变分框架，评估粗糙波动率模型在比特币实现波动率中的适用性。 将这种无模型估计量应用于2017年至2024年多个采样分辨率的高频比特币数据，我们发现归一化统计量始终保持严格负值，排除了有效粗糙度指数的估计。 平稳性检验和稳健性检查未发现非平稳性或结构突变作为解释因素的显著证据。 相反，三种互补诊断方法——多分形去趋势波动分析、对数-对数矩标度和小波领导者——提供了汇聚的证据，揭示了比特币波动率的多分形结构。 这种尺度依赖的行为违反了粗糙波动率估计的基础同质性假设，并解释了估计量系统性失败的原因。 这些发现表明，尽管粗糙波动率模型在传统市场中表现良好，但它们在结构上与比特币波动率的经验特征不匹配。 显示英文摘要

摘要： We assess the applicability of rough volatility models to Bitcoin realised 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 throughout, 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 scale-dependent 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.