Before revision:  In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices follow pure-diffusion processes .
After revision:  In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices process follows a continuous Ito process: we obtain an asymptotic bias. We provide an estimator of the latter as well as a bias-corrected estimator of the high-frequency covariance. In addition, we give a consistent estimator of the associated standard error .