We provide a set of probabilistic laws for range-based estimation of integrated variance of a continuous semi-martingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for non-parametric measurement of return variation. Assuming...

In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Itô semimartingale. We adapt the principle idea of regularization from linear regression to covariance estimation in a continuous-time high-frequency setting....

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be...