Overnight GARCH-Itô Volatility Models

Abstract

Various parametric volatility models for financial data have been developed to incorporate high-frequency realized volatilities and better capture market dynamics. However, because high-frequency trading data are not available during the close-to-open period, the volatility models often ignore volatility information over the close-to-open period and thus may suffer from loss of important information relevant to market dynamics. In this article, to account for whole-day market dynamics, we propose an overnight volatility model based on Itô diffusions to accommodate two different instantaneous volatility processes for the open-to-close and close-to-open periods. We develop a weighted least squares method to estimate model parameters for two different periods and investigate its asymptotic properties.

Keywords:

• High-frequency financial data
• Low-frequency financial data
• Quasi-maximum likelihood estimation
• Stochastic differential equation
• Volatility estimation and prediction

Supplementary Materials

Supplementary materials include detailed simulation setup, additional empirical results, proofs of Theorems 1–2, and R codes for the simulation and empirical studies.

Additional information

Funding

The research of Donggyu Kim was supported in part by National Research Foundation of Korea (2021R1C1C1003216). The research of Yazhen Wang was supported in part by NSF grants DMS-1707605 and DMS-1913149.