Several Researches In Complex Financial Network

Financial market is a complex system. It receives interaction of a large number of different object, thus showing a variety of complex phenomena. With the advent of econophysics and others emerging interdisciplinary, the methods and ideas of mathematics, statistics physics, geometry are used to the financial market. The dissertation start from two types of complex network, and shift the focus to the correlation coefficient of time series. Analyze and discuss the financial market of different sizes and different object.First of all, we study mutual investment behavior of hundreds of economy of the world from2001to2006and construct30complex network. By analyzing the statistical properties of the world investment networks, we find that the investment behavior of the world is an increas-ing globalization. In addition, we also find that the world investment networks are scale-free, and have the characteristics of small world. Distribution of weight obey Weibull distribution and distribution of node strength obey power-law distribution. World investment networks have the rich-club and disassortative property. The topological scaling exponent is1.17±0.02and the flow scaling exponent is1.03±0.01.Secondly, we study daily return of stock indices of57countries and regions of the world. We use the correlation coefficient of time series of daily return to construct complex network. By calculating the planar maximally filtered graph (PMFG) of complex network and the com-munity structure of PMFG, we find the indices can be divided by geographic region. Fast dynamics of the average weight of complex network is well associated with the financial crisis event in history. We provide evidence that the time window of3trading months can be better used for study. The mutual information of PMFG, the degree of PMFG and the first and second eigenvalues and eigenvectors are carrying information. We change the correlation coefficient to the distance between the corresponding node, and construct minimum spanning tree (MST) with distance. When we analyze the normalized tree length, single-step survival ratio and allo-metric scaling, we find that large changes of the normalized tree length of MST, a lot of edge replacement and high-efficient transmission of construction is happened at the financial crisis event.Thirdly, we analyze and compare the correlation coefficient and partial correlation coef-ficient of255stock on the Shanghai Stock Exchange. The projection of return on the first eigenvector has a linear relationship with return of the Shanghai Composite Index. We separate the correlation coefficient matrix and partial correlation coefficient matrix, and calculate the Block of separated matrix. We find that partial correlation coefficient is better than correlation coefficient at categorization.Then, we introduce the nonsynchronous correlation coefficient algorithm proposed by Hayashi and Yoshida. We calculate Pearson correlation coefficient and nonsynchronous corre- lation coefficient for active stocks of six stock exchanges in Europe. Synchronous correlation coefficient of1minute for nonsynchronous correlation coefficient has a "downward" bias. By comparing MST based on the Pearson correlation coefficient to MST correction with nonsyn-chronous correlation coefficient, we find more structural changes for Pearson correlation co-efficient "downward" bias in Amsterdam, London, Brussels and Madrid stock exchange. And the average time between successive transactions of these four stock exchanges is similar or larger than1minute. MST based on Pearson correlation coefficient or nonsynchronous corre-lation coefficients are clustered into one class with each stock exchange. And different stock exchanges is connected to the same economic sector.Finally, we use nonsynchronous correlation coefficient to analyze on the inventory varia-tions on the600019(Baoshan Iron And Steel Co., Ltd.) and580000(Baoshan Iron And Steel JTB1). Distribution of the correlation coefficients in a certain range obey exponential distribu-tion, and they near0obey power-law distribution. Analyzing eigenvalue and eigenvector of the nonsynchronous correlation coefficient matrix of580000, we find the projection of inventory variations on the first eigenvector has different linear relationship with return of580000as the time divided into two. The difference of slope is nearly three times. We defined ultimate return is positive when the components of the second eigenvector is negative, otherwise the opposite. When the components of the second eigenvector is near0, the positive or negative of ultimate return is not clear. With the components of the second eigenvector from small to large, profits after one minute of investors into an upward trend. In addition, short-term investment is main profit means of investors. In these short-term investment behavior, active turnover have more profit than passive turnover.