Realized Real-Time GARCH: A Joint Model for Returns, Realized Measures and Current Information

Existing high-frequency-based volatility models usually regard the volatility process of financial returns as a function of the past daily-frequency and high-frequency information, and cannot take full advantage of the current information. This paper incorporates the Real-time information into the Realized GARCH model and proposes the Realized Real-time GARCH model. The new model retains the basic structure of the Realized GARCH model and considers the volatility process as a mixed product of past information and current information. Then some significant properties of the proposed model are discussed. Also, the variation of this model, the Realized Real-time GARCH-L model, is proposed to describe the leverage effect of the Real-time information. Our empirical results show that considering Real-time information makes the model perform better in terms of dealing with sudden jumps of volatility, improves the in-sample empirical fitting, and contributes to the improvements in forecasting multi-step ahead volatility, conditional density of returns and value at risk (VaR). Besides, the leverage effect of Real-time information also provides substantial improvements over the Realized Real-time GARCH model.