Study On Nonlinear Behavior Of China Stock Markets

Nonlinear behavior of stock price is essential aspect in the frontier research of modern investment theory. In this study many modern mathematics and economics such as statistics, chaos theory, stochastic differential equations, wavelet analysis, change point, game theory and Econometrics etc., are used to analyze the nonlinear behavior of Chinese stock price and volatility. Then our focus is on looking for what causes nonlinear behavior of Chinese stock price. Besides that we analyze how to value stock and control investment risky. Some suggestions are given for the government and investors facing nonlinear behavior of stock price. With a careful study of previous researches, the nonlinear behavior of stock price will be analyzed in this dissertation from three facts.First, this study uses the chaos theory to analyze the nonlinear behavior of Chinese stock price. We use a applied statistics to examine the distribution of 5 days return series of composite stock index, then hurst exponent are derived from data of return series. Then we use fractional analysis to derive the fractional number of return series and analyze the complexity of Chinese stock markets. Based on previous researches, a series of new stock price model are derived with nonlinear mathematics. In this part, our findings are as follows: The empirical distribution of five days' return of SHCSPI (Shanghai composite stock price index) and SZCSPI (Shenzhen composite stock price index) has "fat tail" and no finite variance with sharp peak at mean, which cannot be normally distributed because the largest negative return possible. The hurst exponent of SHCSPI is 0.85, and it's non-period cycle is six months, but the hurst exponent of SZCSPI is 0.87 and his non-period cycle is four months. In addition, the return series belong to long-term memory fractal time series. As a matter of fact, the day's and week's return series show noisier than the monthly return series, but the months return series indicate strong fractal time series. The fractal number of SHCSPI is 3.24 and SZCSPI's is 4.6.Compared with world's developed stock market, such as New York stock exchange, the evidences of much complexity are found in China stock market. So China stock markets are not efficient markets because the chaos phenomena are strongly shown in the stock market.Second, our focus is on analyzing the volatility of China stock. The main contents are formed with the spillover effects and variance change points and the pricing model of volatility and forecasting for the stock price and volatility. Our findings are given by below three points. First, China stock markets appear to be much more volatile than American stock markets such as New York stock market. The variance change point of composite index can indicate the influence of international economic and national macroeconomic circumstances and especially policy on stock market. Second, the stock markets are interrelated to each other and there are apparent price and volatility spillover effects between the Shanghai and Shenzhen stock market. The change of on the previous trading day will lead to a negative 7.2 percent of , but the stock market in Shenzhen also, to some extent has negative spillover effects on that Shanghai, but not so great as Shanghai to Shenzhen. As for volatility spillover effect between the two market, one unit of the , so spillover effects of volatility are much greater than that of price. Third, the Grey system model GM(1,1) and GARCH model can respectively be used to predict for stock price and volatility. The study states the Grey system GM (1,1) can be used to the long term and mid-term prediction with prediction meeting the demands of precision. Besides that the leverage effect is found in Zhenzhen stock market. Moreover asymmetric volatility exists in the two stock markets.Finally, after introducing the theory of financial risks and further analyzing reasons that cause the nonlinear behavior and volatility and risk situation of China stock market, I give some suggestions in...