Measurement Sensitivity of Apparent Volatility Roughness in Perpetual Futures

Abstract

Empirical associations involving estimated volatility roughness may depend on the construction of the measured path. This study compares an increment-variance slope on log realized variance, the same slope after pre-averaging, and a normalized p-variation diagnostic using Bitcoin and Ether perpetual-futures data from January 2020 through July 2026. The observation window and funding-rate variable are held fixed, while common-sample regressions separate changes in measurement from changes in sample composition. Paired coefficient tests preserve the six-hour calendar when the p-variation diagnostic is unavailable. After correcting spot-price alignment in the basis control, both slope estimators retain negative funding associations in levels and with month fixed effects. The p-variation association is negative for Bitcoin in the level regression but is not distinguishable from zero with month effects for either asset. Holm-adjusted comparisons resolve p-variation versus both slope estimators for Bitcoin and versus the pre-averaged slope for Ether. Other contrasts remain uncertain. The diagnostic is admissible in 83.7% and 81.1% of windows, respectively. Dynamic and non-overlapping-block results depend on the specification. These findings establish a conditional measurement comparison rather than a universal funding–roughness relation, an estimate of latent spot regularity, or evidence of trading profitability.

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