The Complexity Of Financial Market And The Empirical Study Of Its Scaling Behavior

Complexity science is a new and developing interdisciplinary science nowadays. It has broken the linearity, equilibrium, determinate traditional style, devotes in the research of non-linearity, non-equilibrium and the many-body problems. Its appearance enormous develops non-linear science. But the economical system is one of most complex systems which the humanity creates, therefore the economical system is one of complexity science most important research directions. This article elaborates the basic concepts and the properties of complex system and the complex network, the appearance of econophyscis, the research contents, the main models, the trend of the development and the physical method and the models which be used frequently in the econophyscis. The main works of this article is the empirical research of the financial markets and can divide into two parts.The first part analyzes the change of price of 74 global currencies in the time interval from March 2002 to February 2006, defines the concept of relative return, and based on it, we research the distribution of relative return in which found the power law. Further, through the random matrix theory, we find that the distribution of eigenvalues of correlation matrix of relative return also follows a power law, at the same time, we observe that the distribution of correlation coefficients of relative return of currencies is time-dependent at some extent. So, by using the method of scaled factorial moment, we make detailed analysis and make a conclusion that the distribution of correlation coefficients has the dynamic fluctuation which shows the self- similarly property of the fractal.The second part introduces the long range correlation existed in the stock markets of Asia. We choose the N225 Index of Japan and SSEC Index of shanghai in China. We first define the generalized form of volatility, then use the detrended fluctuation analysis (DFA) on the generalized volatility, which find that there are the varying degree long range correlation existed in time series of two security index and discover the crossover phenomena obviously in the results. Regarding this we have done the detailed research, made the feasibility analysis on the probability of caused these phenomena, and obtained the significance conclusion.