Apparent Volatility Roughness and Perpetual-Futures Funding: Persistent Association, Weak Transition Information

Abstract

A low Hurst estimate from realized volatility can describe latent variance, measurement error, or both. This paper asks a narrower empirical question: does the apparent roughness of realized volatility align with a directly observed leverage-related state in cryptocurrency perpetual futures? Using public Binance Vision data for BTCUSDT and ETHUSDT from January 2020 through July 2026, I estimate a rolling increment-variance exponent from hourly realized variance and match it to perpetual-futures funding and the perpetual-spot basis. In six-hour update samples, a one-standard-deviation increase in absolute funding is associated with a 0.010 decrease in apparent H for Bitcoin and a 0.006 decrease for Ether. The association survives month fixed effects and alternative 1-, 5-, and 15-minute realized-variance meshes. It does not survive the inclusion of lagged apparent H, and funding does not explain changes in apparent H. Non-overlapping 14-day blocks retain the relation for Bitcoin during extreme funding episodes but not for Ether. Recursive forecasts show no daily gain; an Ether one-hour gain is statistically detectable but economically small and does not generalize. The evidence therefore supports a persistent state association, not a transition signal, structural estimate of spot regularity, or trading rule. The distinction clarifies what a rolling roughness estimate can and cannot identify in noisy high-frequency markets.

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