Nonlinearity of the volume-volatility correlation filtered through the pointwise Hurst-Hölder regularity

We identify market inefficiency as a pivotal explanatory variable of the puzzling volume– volatility relationship. The result, that can bring together into a coherent framework many apparently conflicting findings, follows from translating the realized volatility into the corresponding pointwise Hurst–Hölder exponent. This allows to measure, at any time t, markets’ departures from the martingale property, i.e. from efficiency as stated by the Efficient Market Hypothesis. We find that when efficiency is not accounted for, a positive contemporaneous relationship emerges; conversely, it disappears as soon as efficiency is taken into account.