  We provide a simple explicit estimator for discretely observed
Barndorff-Nielsen and Shephard models, prove rigorously consistency and
asymptotic normality based on the single assumption that all moments of the
stationary distribution of the variance process are finite, and give explicit
expressions for the asymptotic covariance matrix.
  We develop in detail the martingale estimating function approach for a
bivariate model, that is not a diffusion, but admits jumps. We do not use
ergodicity arguments.
  We assume that both, logarithmic returns and instantaneous variance are
observed on a discrete grid of fixed width, and the observation horizon tends
to infinity. As the instantaneous variance is not observable in practice, our
results cannot be applied immediately. Our purpose is to provide a theoretical
analysis as a starting point and benchmark for further developments concerning
optimal martingale estimating functions, and for theoretical and empirical
investigations, that replace the variance process with a substitute, such as
number or volume of trades or implied variance from option data.
