Research On Herd Behavior Of Stock Market Based On Cellular Automata

Recently, many physicists have a significant interest in application of physical methods in economical sciences, financial sciences especially. As a complex system which possesses numerous mutual reaction units, there may be some general acts and rules in financial market, just as the generality observed in statistical physics. According to traditional financial theory based on the efficient market hypothesis, investors are completely rational. The fluctuation of stock follows random-walking process, and the distribution of returns presents normal distribution. However, a number of empirical researches show that the distribution of asset returns present sharp peak fat-tail that deviates from the Gaussian distribution, and the volatility clustering emerges in the time series of returns. These characteristics in stock market relate to the herd behavior of investors. With uncertain information, the behavior of investors is affected by other investors, inducing imitation of each others. This leads to herd behaviors. In this thesis, behaviors of investors with limited rational are investigated. Since more income is the initial impulse of investors to buy shares, investors will consider the income before take action, instead of desperately following others. By using cellular automata with simple rules which reflects the essential features of the system, we study the complex system of stock market based on the cellular automata method. Based on previous researches, we modify the herd rule of investors with the cellular automata method. Finally, we study the herd behavior of investors in the small world network. Through improving the rules of herd, "one-side" phenomenon does not appear in the stock market, the fluctuation of volume is not obvious. The simulation results show some typical characteristics of stock market, such as peak fat tail, volatility clustering, and so on.In this thesis, herd behaviors of stock markets are investigated in following three aspects:First of all, we analyze the statistical properties of financial market and the cause of herd behavior from the perspective of behavioral finance. The statistical properties of financial market include the peak fat tail, the relevance of price fluctuation, volatility clustering, and so on. From the perspective of behavioral finance, the factors leading to herd behavior of investors include incomplete information, influence of group members, compensation, reputation.Secondly, we discuss when the investors will herd. A model of herd behavior of investors will be established based on the cellular automata. Considering the psychology of investors, we believe that investors will calculate the factor of income to determine whether herd or not. The simulation shows, the time series of returns present volatility clustering, the distribution of returns present sharp peak fat-tail that deviate from the Gaussian distribution. The simulation is compared to the distribution of returns of Shanghai and Shenzhen 300 index. The result shows that simulating the stock market based on cellular automata is feasible.Finally, we change the form of neighbors of investors and establish a model of herd behavior in the small world networks. By setting different rewiring probability, it produces different results. We compare the distribution of returns when rewiring probability p=0.0,0.1,1.0. It is found that when p=0.1, it fits better. We also discuss the autocorrelation of returns and the autocorrelation of volatility. It is found that the autocorrelation coefficient of returns rapidly decayed to 0 with time, but the autocorrelation coefficient of volatility decayed slowly. After a long time step, the autocorrelation coefficient of volatility is still not equal to 0. This shows that volatility associated with long-range.