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Several novel large volatility matrix estimation methods have been developed based on the high-frequency financial data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices. However, for predicting future volatility matrices, these nonparametric estimators do not have a dynamic structure to implement. In this paper, we introduce a novel It diffusion process based on the approximate factor models and call it a factor GARCH-It model. We then investigate its properties and propose a quasi-maximum likelihood estimation method for the parameter of the factor GARCH-It model. We also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties. Simulation studies are conducted to validate the finite sample performance of the proposed

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