The Measuring Of Volatility Of CSI 300 Returns

Volatility is a key indicator in the research field of finance, which not only reflects the variance of financial assets or financial indexes directly, but also measures the risk or uncertainty of future returns. Hence studies on the volatility not only contribute to deepening the researchers’ comprehension on it, but also help investors take proper control of the risk of financial assets.The researches on the volatility of China stock market generally use each stock index in Shanghai Stock Exchange and Shenzhen Stock Exchange. However, there does not exist a stock index connecting the two exchanges. China Security Index 300(CSI 300, for short), is the first representative stock index, reflecting the overall market trend and meeting the need of Chinese stock markets. The launch of CSI 300 stock index futures also indirectly confirms the vital position of CSI 300. Hence this paper studies the volatility via employing CSI 300.Earlier studies have suggested that the volatility of returns is constant. This moment, the main method is Exponential Weighted Average Model and so on. However, with the development of the financial market, enormous researches have found that time series of returns have the leptokurtic distribution, and volatility clustering, violating Efficient Market Hypothesis. To capture these features, Engel creatively puts forward Autoregressive Conditional Heteroskedasticity Model(ARCH, for short). The class of ARCH model has been the mainstream in the measurement of volatility, which well reflects the property of short-term autocorrelation.However, Fractal Market Hypothesis(FMH, for short) suggests that most financial time series have the feature of the fractal dimension which reflects the long-term memory. And the long-term memory means that history information has consistent influence on future series, unlike short-term autocorrelation which deceases rapidly. If we still use the integral dimension, we will lose some important information. Hence we should consider the fractal dimension and long-term memory on the studies about the volatility.The method in this paper is that based on Fractal Market Hypothesis, we capture the fluctuation of CSI 300 returns via combining the fractal dimension and long-term memory with different distributions and different volatility features. And this paper makes the following researches:Choose all the data of CSI 300, including 2419 samples. The first 2401 samples are used to estimate parameters and the last 18 samples to test the ability of forecasting. Firstly, make the logarithmic difference treatment to obtain the series of returns. Secondly, make normal distribution tests. Present related statistics, graphs and tests, including the mean, variance, skewness, kurtosis, QQ graph, JB test, and so on, which find that the distribution of returns does not obey the normal distribution but approximately obeys the t distribution. Thirdly, using ADF and correlation tests, we suggest that the series of returns is stationary and has higher order autocorrelation obviously. Fourthly, make BDS test and the result shows that the series of returns has nonlinear correlation obviously. To test whether the nonlinear correlation have relation with the long-term memory, we employ the R/S analysis, seeing that the Hurst Exponent of the series of returns is 0.6342 which suggests the existence of the long-term memory. To make significant comparisons, we make twelve models such as ARMA-GARCH and ARFIMA-GARCH models. Concerning forecasting, we employ the error component analysis to make evaluations.The advantages are the following: firstly, many studies on the volatility of CSI 300 emphasize the measuring techniques, lack of theoretical basis. So, my thesis is established in FMH. Secondly, a lot of literatures regard the distribution of returns as the normal distribution, not reflecting the real distribution. On the basis of the features of the distribution of CSI 300 returns, we find that t distribution is appropriate. Lastly, a great many of researches concern the measuring of short-term fluctuation, well reflecting heteroskedasticity. However, there is short of the measuring of the long-term memory. We employ ordinary GARCH models and fractal GARCH models in the empirical analysis, finding that ARFIMA(1,0.1342,1)-EGARCH(1,1) model in the t distribution is more efficient.