  We consider the problem of estimating the roughness of the volatility in a
stochastic volatility model that arises as a nonlinear function of fractional
Brownian motion with drift. To this end, we introduce a new estimator that
measures the so-called roughness exponent of a continuous trajectory, based on
discrete observations of its antiderivative. We provide conditions on the
underlying trajectory under which our estimator converges in a strictly
pathwise sense. Then we verify that these conditions are satisfied by almost
every sample path of fractional Brownian motion (with drift). As a consequence,
we obtain strong consistency theorems in the context of a large class of rough
volatility models. Numerical simulations show that our estimation procedure
performs well after passing to a scale-invariant modification of our estimator.
