Efficient estimation of drift parameters in stochastic volatility models

We study the parametric problem of estimating the drift coefficient in a stochastic volatility model Yt = ∫ t 0 √ Vs dWs , where Y is a log price process and V the volatility process. Assuming that one can recover the volatility, precisely enough, from the observation of the price process, we construct an efficient estimator for the drift parameter of the diffusion V . As an application we present the efficient estimation based on the discrete sampling (Yiδn)i=0,...,n with δn → 0 and nδn →∞. We show that our setup is general enough to cover the case of ‘microstructure noise’ for the price process as well.