Factor Overnight GARCH-It\^o Models

Abstract

This paper introduces a unified factor overnight GARCH-It\^o model for large volatility matrix estimation and prediction. To account for whole-day market dynamics, the proposed model has two different instantaneous factor volatility processes for the open-to-close and close-to-open periods, while each embeds the discrete-time multivariate GARCH model structure. To estimate latent factor volatility, we assume the low rank plus sparse structure and employ nonparametric estimation procedures. Then, based on the connection between the discrete-time model structure and the continuous-time diffusion process, we propose a weighted least squares estimation procedure with the non-parametric factor volatility estimator and establish its asymptotic theorems.