Before revision:  We establish a central limit theorem for the Hayashi-Yoshida  estimator under HBT in the case where prices process follows a continuous Ito process : we obtain an asymptotic bias.
After revision:  We establish a central limit theorem for the Hayashi-Yoshida (HY) estimator under HBT in the case where prices process follows a continuous Ito process : we obtain an asymptotic bias.