Factor Overnight GARCH-It\^o Models

TL;DR

This paper develops a comprehensive factor GARCH-Itô model for large-scale volatility matrix estimation, capturing intra-day market dynamics with a novel low-rank plus sparse structure and nonparametric estimation techniques.

Contribution

It introduces a unified model combining discrete-time GARCH and continuous-time diffusion processes, with new estimation procedures and asymptotic analysis for large volatility matrices.

Findings

Effective estimation of latent factor volatility using low-rank plus sparse structure.

Asymptotic properties established for the proposed weighted least squares estimator.

Model captures intra-day market dynamics through separate open-close and close-open processes.

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.