| Volatility is one of the most important features in financial markets, and it is a core indicator of capital asset pricing, risk management and portfolio theory. There are two mainly widely used models to characterize the volatility of financial time series. One is the ARCH model, which assumes that the conditional variance is the linear combination of the past observations and the squared errors. The other is the SV model, which assumes that the conditional variance depends on a random unobservable process. The SV model is more flexible and suitable for actual research in finance. However, the standard SV model has its own shortage. In this paper, we propose a new SV model with leverage and jump to effectively characterize the asymmetric volatility and jumping feature of the return series on assets.Firstly, we build a generalized continuous time SV model and derive the discrete time form. Then, we analyze the parameters in the model, especially the leverage and jumping effects. Secondly, we exhaustively introduce the common estimation method for the SV model, MCMC estimation. Then we introduce the basic idea, sampling procedures, convergence criterion and model selection criteria. Lastly, we select the CSI 300 Index and Hang Seng Index to construct the standard SV model, the SV model with leverage, the SV model with jumping and the SV model with leverage and jumping. After that, we compare the performance between different models and compare the different characteristics in volatility between the CSI 300 Index and Hang Seng Index.Our research indicates that: there are obvious volatility persistence and leverage in both the CSI 300 Index and Hang Seng Index, but the leverage in the CSI 300 Index is stronger than the Hang Seng Index. In addition, there is no clear evidence about the jumping effects in the Hang Seng Index. However, the jumping effects in the CSI 300 Index are significant. On model fitting, the SV model with leverage and jumping surpasses other SV models for the CSI 300 Index and the SV model with leverage surpasses other SV models for the Hang Seng Index. |
