2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213032We 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 Itô 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.29 pages, including 4 picturesStatistics Theory62G05; 62F12text