A Study On The Structure Of The Stock Market By Network Modelling

With the era of big data coming and the development of computer technology,some new progress has been made in the research and applications of complex network theory.In real life,many complex systems can be analyzed by using complex network model,such as social network,Internet and WWW networks.The complex network is not only a manifestation of data,but also a measure of scientific research.For example,the key character of complex networks should be discovered by summarizing ideas and methods of their common properties and be understood thoroughly.In complex network research,researchers can not only pay a close attention to the interaction between individuals in the system,but also focus on the overall interaction of the system from an ensemble perspective.During the development of the securities market,it has been accompanied by prosperity and crises,with the mix of ups and downs of security prices.The volatility of the stock price has become an important research object for investors and researchers.The change of the stock price is not only related to macroeconomic development and the fundamentals of listed companies,but also affected by some other listed companies in the market.How to understand the mutual interaction among stocks can help investors make a better portfolio and manage market risk as well.There are more than 2,000 stocks traded in Chinese stock market,and the relationship among them is complicated.It is important to find out the general characteristics from a large amount of traded data.According to financial statistic analysis,traditional theories about financial market,such as rational investors,random walk of stock price and efficient market hypothesis,are not suitable any more.However,the theories of complex network provides us with a new perspective and new method of complexity research.Application of complex network theory in the stock market helps us to recognize and understand the stock market.The development of stock market in China has gone through five stages,namely,the initial phase(1990-1991),the trial phase(1992-1997),the specification phase(1998-2001),the transition phase(2002-2004)and the remodeling phase(2005 to now).The non-tradable shares reform in 2005 was of great significance in the history of China's securities development.After non-tradable shares reform,the capital market has been provided with the function of financing and resource allocation.China's securities market has become one of the emerging markets,and trading is very active.The significant trading volume created the exceptional prosperity of the Chinese stock market.At the end of 2007,the Shanghai stock index rose from 998 points at the end of the shares reform to a maximum of 6124.Then the stock market went through a violent slump into a bear market.From 2007 to 2014,because of the influence of the global financial crisis and the European debt crisis caused by the sub-prime mortgage crisis,the stock market had been in the process of intense concussion.Since 2014,the rise of a new round of market market in China's securities market has caused the concern of investors and financial theory researchers.Based on the proximity between stocks,this work builds the stock network model with the stocks of Shanghai A share market and analyze the correlation between stocks as the basis for the construction of stock network model,analysis quantitative correlation degree of correlation,and as a basis for the construction of stock network model,the interaction mechanism between mining stock,structure characteristics and regularity of stock network from the angle of the system.In this paper,the data of daily closing price of 828 stocks in Shanghai A share market has been collected in recent three years(2014-2017).Based on different network generating mechanism,we analyzed the general characteristics of stock market in a long period and the structural variation of the stock market in different developmental stages.First,we have found that the most relationships between stock prices are nonlinear.In this paper,mutual information has been introduced as a measure of the correlation between variables and used to construct the stock networks.In the past three years,China's stock market has experienced a new round of sharp rise and fall,and the stock index has experienced abnormal fluctuations,showing a trend of nonlinear correlation.It is obvious that the traditional linear correlation can not explain the nonlinear relationship well.The measure of mutual information is introduced to describe the relationship between random variables,and the results are compared with the results of linear correlation coefficients.It is found that mutual information can reflect the changes exactly when the stock returns show abnormal fluctuations or the changes caused by dilution in stock value.Based on the correlation matrix generated between stock returns,we transform the correlation metric into the distance metric so as to build the minimum spanning tree of the stock network and analyze the topological structure.According to the characteristics of the sample data,prim algorithm has been used in construction of network,which does not constitute a loop.Based on the statistical index of node degree distribution,betweenness,average path and centrality,we analyze the topology of stock network,design a selection criteria of key nodes and identifies key nodes and tests their role in the network.And according to the trend of the development of the stock index,the stock network is constructed in stages and the characteristics of the network structure in different stages are compared.Clustering is an important feature of real networks.Because the Minimum Spanning Tree does not constitute a loop,it is impossible to analyze the clustering of the network.Threshold is a good measure for analyzing the clustering of network.The traditional threshold method,similar to the asset graph,only favors the strongest correlation,resulting in a large number of isolated nodes in the network.Here,we propose an optimization threshold method of setting a threshold for each stock's relationships.Strong correlations of each stock are connected to network.And we do analysis the clustering of the stock network and comparison of the clustering characteristics at different stages.In order to study the characteristics of clustering thoroughly,we consider the small clique in the network.Based on the clustering results above,we continue to filter information in the network through the Planar Maximum Filtered Graph,which can help us study the formation mechanism and diversity of cliques under the premise of ensuring the topological structure of the network.According to the research process mentioned above,we have obtained the relevant conclusions of the characteristics of the stock market.Firstly,the average correlation levels of sectors are similar,but the correlation levels between sectors are obvious.Particularly,the average correlation between financial sector and other sectors is the lowest level.Secondly,like the most real network,the stock network constructed from various algorithms have the characteristics of scale-free,small world and power law distributions.Only a small number of stock nodes directly connect the most of the stock nodes and most of the stocks are not directly connected,however,the average path of the network is relatively small.That is to say,there are only a few key nodes in the network.From the comparison study of the Minimum Spanning Tree in three different stages.In the bull market,the disparity among the degrees of the stock nodes decreases and the mutual influence between the stocks is more active.In the bear market,stocks are more likely to be connected to the key nodes directly,resulting in the intensified differences of degrees of nodes.And the delivery of bad news among stocks will be delayed on the grounds that average path of the network is a bit longer.The topological structure of network in the recovery stage is similar to both of that in the bull market and bear market,extreme unbalanced degree distribution and smaller average path.The importance of each sector in the market is different in three varied phases.Thirdly,the clustering of nodes in the network generated by the threshold method is significant.As the size of the network increases,the potential link is more likely to be connected to the key node.In the bull market,the clustering coefficient in the network rises obviously.In the bear market,the value of synchronization rises obviously as well as clustering coefficient.It shows that the prices of stocks are more likely to drop simultaneously than rise.After comparative analysis of three stages,the clustering degree and synchronization in the down stage network are the highest,and the clustering coefficient in the recovery stage varies apparently.It indicates that the stock market has characteristics of strong clustering and synchronization characteristics in the bear market.Thus the risk of bear market can be prevented in advance by these information.Finally,the information of the complex topology in the network is filtered out again on the basis of the Planar Maximum Filtered Graph,the 3-clique and 4-clique of small clusters are obtained.The number of 4-clique in the network is less than 3-clique,and the cliques in the bull market are obviously more than those in the bear market.Besides,even the 4-clique which is constituted by the same sector,the average level of relevance of the cliques are different,and cliques formed by different sectors are more than those in the bear market.Comparison of topological structure indicates that the stock market is asymmetric over the bull market and bear market.If the good news is delivered,the relevance of stocks are strengthened both inside sectors and cross sectors.However,the market panic will be seriously amplified virtually by the spread of bad news,resulting in the falling of most stock prices at the same time.