This paper provides the first rigorous statistical analysis of estimating the Hurst parameter H in rough volatility models from discrete price observations. The authors establish minimax lower bounds and design optimal estimators based on adaptive wavelet methods. For a piecewise constant volatility model, they show the optimal rate is max(n^{-1/(4H+2)}, δ^{1/2}), where δ is the scale at which volatility is constant. In the general continuous model, the optimal rate becomes n^{-1/(4H+2)} for H in (0,3/4). The key innovation is the use of pre-averaging to mitigate the roughness of volatility paths and a bias correction procedure that iteratively improves the estimator. The results demonstrate that H can be estimated with accuracy approaching n^{-1/2} as H→0, comparable to regular parametric models. The paper also provides lower bounds for estimating the volatility-of-volatility parameter η, which includes an additional logarithmic factor.