Real-time GARCH@CARR: A joint model of returns, realized measure of volatility and current intraday information

Recently, financial volatility models with Real-time information have attracted widespread attention. In this paper, we first consider the Real-time information in high-frequency data and then propose the Real-time GARCH@CARR model. Compared to previous Real-time volatility models, the new model regards current realized measure as Real-time information of high-frequency data and describes the volatility process as a mixture of past high-frequency information and current intraday random information. The model is further extended to two improved versions to contain leverage and volatility feedback effects. Under the framework of the proposed models, some important properties are discussed. The simulation results show that the estimators of our proposed models have good asymptotic performance over different sample sizes. And the empirical results and robustness analysis confirm that our proposed models outperform other benchmark models in terms of forecasting volatility, return density and risk.