GARCH-Type Model with Continuous and Jump Variation for Stock Volatility and Its Empirical Study in China

On the basis of GARCH-RV-type model, we decomposed the realized volatility into continuous sample path variation and discontinuous jump variation, then proposed a new volatility model which we call the GARCH-type model with continuous and jump variation (GARCH-CJ-type model). By using the 5-minute high frequency data of HUSHEN 300 index in China, we estimated parameters of the GARCH-type model, the GARCH-RV-type model, and the GARCH-CJ-type model and compared the three types of models’ predictive power to the future volatility. The results show that the realized volatility and the continuous sample path variation have certain predictive power for future volatility, but the discontinuous jump variation does not have that kind of function. What is more, the GARCH-CJ-type model has a more power to predict the future volatility than the other two types of models. Therefore, the GARCH-CJ-type model is much more useful for the research on the capital assets pricing, the derivative security valuation, and so on