The Analysis Of Volatility Of A-Stock Index In Shanghai Stock Exchange

Frequent volatility is one of the most important features of stock market. ARCH models are often used to simulate and forecast the volatility of thereturn of financial capitals. In this paper, the four primary models------ARCH,GARCH,EGARCH and GJR-GARCH were introduced and analyzed at first, then analyzed the volatility of the return series from Shanghai A-stock market based on these four models, using the Maximum Likelihood Estimation to estimate the variables in the models. After analyzing the results of the simulation of the four models, the paper compared the abilities of forecasting volatility of these four models. By introducing a new method which computes the real volatility of return series and comparing the three errors which measure the abilities of forecasting volatility and the histograms of these four models, this paper got the conclusion: it is the ARCH(4) model that would get more perfect results of simulation when supposed that the daily log return series used by this essay follow the normal distribution.This paper researched on multivariate time series then. It introduced the definitions of cross-correlation, cross-covariance matrix and vector autoregressive (VAR) models at first. Then the parameters of VAR(1) model were estimated by using the Composite Index of Shanghai stock market and the Ingredient Index of Shenzhen stock market. The conclusion is that there is a feedback relationship between Shanghai stock market and Shenzhen stock market, and Shenzhen stock market takes on more dependence on Shanghai stock market.Further more, this article studied multivariate volatility models especially on BEKK model. Also these two return series above were used for estimating the bivariate diagonal BEKK model and constructing the correlation graph of these two series. By comparing the volatilities and correlations of these two, it can get that there is almost the same trend in volatility of these two markets while the Shenzhen stock market appears to be more volatile than the Shanghai stock market. People who invest both these two markets also should pay more attention on the high correlation of these two markets to avoid risk.