Abstract
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.
Highlights
The research on asset volatility in financial market is the foundation of finance, such as capital assets pricing, financial derivatives pricing, and financial risk measurement
Comparing the AIC values for the generalized ARCH (GARCH)-realized volatility (RV)-type model and the GARCHtype model, we can see that the fitting for the GARCHRV model works better, which is consistent with Koopman et al [6]
In order to test the validity of the model, an empirical study is carried out using the 5-minute high frequency data of HUSHEN 300 index in China (April 20, 2007, to April 20, 2012), we estimate the parameters of the GARCH-type model, the GARCH-RVtype model, and the GARCH-CJ-type model and evaluate all models’ predictive power for future market volatility using a loss function (MAE, Heteroskedastic adjusted Mean Absolute Error (HMAE), Root Mean Squared Error (RMSE), and Heteroskedastic adjusted Root Mean Squared Error (HRMSE))
Summary
The research on asset volatility in financial market is the foundation of finance, such as capital assets pricing, financial derivatives pricing, and financial risk measurement. When Andersen et al and Huang et al [9, 10] studied the HAR-type RV model, they found that model built with continuous sample path variation and discontinuous jump variation that decomposed from RV has stronger power than the undecomposed HAR-RV model in measuring and predicting the asset volatility. For this reason, in studying the GARCH model with an introduction of an endogenous variable RV, it is more reasonable to decompose RV into C and J and introduce the two parts into the volatility equation of the GARCH model.
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