Efficient covariance estimation for asynchronous noisy high-frequency data

We focus on estimating the integrated covariance of log-price processes in the presence of market microstructure noise. We construct an efficient unbiased estimator for the quadratic covariation of two It^{o} processes in the case where high-frequency asynchronous discrete returns under market microstructure noise are observed. This estimator is based on synchronization and multi-scale methods and attains the optimal rate of convergence. A Monte Carlo study analyzes the finite sample size characteristics of our estimator.