Volatility Analysis For CSI300Index: Based On A SWARCH-L Model

Volatility model is playing a key role in financial econometrics, the reason forwhich is that the conditional variance of asset price changes cannot be directly observed.Alternatively, a feasible method may be the parameterization way. Therefore areasonable model is very attractive to practitioners who are eager to get precise forecastsof future volatility. For instance, traders, portfolio managers and risk managers whoshould offer the equity options an appropriate price, hedge positions to decrease risk andcalculate the market risk respectively. On the other hand, volatility is of great importancefor governments so as to supervise and regulate the situation in financial markets.There have been many analysis papers for the volatility in stock markets. Engle(1982) initially suggested the ARCH model, and analyzed the phenomenon of volatilitycluster in detail, which got a great success and made the ARCH model one of the mostpopular tools in analyzing the financial time series. Bollerslev (1986) generalized theARCH model and got the GARCH model which is still widely used nowadays.Although there is a lot of improvement based on the ARCH model, the GARCH modelis lack of consideration of the structure changes in financial time series. Because thestructure changes in financial time series can divide the series into some state ofdifferent volatility levels. Nelson (1991) and Zakoian (1994) suggested the EGARCHmodel and TGARCH model respectively. After a lot of researches for the stock markets,the results show that there exists a high persistence of shock to volatility in ARCHmodel. However, the persistence character of volatility in stock markets can be depictedby ARCH model, Hamilton found that the performance of ARCH model in forecastingthe future volatility is weak. Hence, Hamilton (1994) suggested the MarkovRegime-switching ARCH model, called SWARCH model, which can resolve theconflict between the merit in describing the persistence of volatility and demerit inforecasting the future volatility of ARCH model.The purpose of this paper is to analyze the persistence of shock to volatility in theview of in-sample and out-of-sample respectively. We apply the SWARCH model withleverage effect which is estimated by Markov Chain Monte Carlo method to analyze the volatility of CSI300Index in China. We also use some diagnostic measures andposterior predictive analysis to assess the model-captured variance process.The results of this paper are as follows. First, during the whole observed period theSWARCH model divides the sample into two states of high volatility and low volatilityas well as four ARCH terms in the variance process, which can be represented asSWARCH-L (2,4)model. Second, after the estimation of SWARCH-L (2,4)modelunder the framework of Bayesian methodology, we estimate the GARCH (1,1) modelin the same way to compare the performance in fitting date between the two models.And we find that the persistence of shocks in volatility from the autoregressive part ofvariance process in SWARCH-L (2,4)model is lower than GARCH (1,1) model.According to the diagnostic measures, the two models can well capture the volatility inthe observed series, but the GARCH (1,1) model is a little better. Last, through theBayesian posterior predictive analysis, we compare the forecasting performancebetween SWARCH-L (2,4)model, GARCH (1,1) model and constant volatilitymodel out of sample. In terms of RMSE, RMSLE and MAPE, the forecastingperformance of GARCH (1,1) model is superior to SWARCH-L (2,4)model.However, with the increase of forecast level, the ability to explain the realized volatilityof SWARCH-L (2,4)model is increasingly raising.