Stock Market Volatility Networks And Applications

The volatility of the stock market has been the focus of research, fluctuations intheoretical studies is quite mature. In recent years the complex network theory used morewidely, theory and empirical research is rich, developing rapidly. In the securities market hasbeen proved to be a complex system,complex network in the application of financial marketresearch also developed, the paper discusses the overall stock market characteristics andproperties start in the micro level.We began with the consideration in the important role of similarity and similarity theoryin many subjects firstly. Then we deeply probing and analyzing, studied similar questionsconcerning different subjects, and generalized the basic similar characteristics of two differentobjects. In connection with the characteristics of complex network, we give the definition ofthe similar elements in complex network. We displayed the similarity degree of similarelements, making use of the linear dependence of vectors and correlative random variable. Onthe basis of it, given the similar definition c of complex network.Comparison the similarityand self-similarity between several stocks and index stocks and analysis the similarity andself-similarity of the individual stock volatility network. This paper is divided into three parts,as follows:The first part introduces the background of the stock market volatility in the network andtheoretical knowledge, including the stock market volatility in the network situation, the basictheory of complex networks, the stock market and the related knowledge of stock market andsimilarity of complex network.The second part focuses on the description of self-similarity in various disciplines atpresent. Summarized the common characteristics of self-similarity, then give definition ofsimilar elements similarity and self-similarity and also the method of calculation, theoreticallygave a solution to the complicated calculation problem.The third part established complex network model with methods of coarse-grained. Thenwe compared the self-similarity of the networks in different time and the similarity betweenindividual stocks and indexes in same time period, taking the advantage of the similarity ofindices between its concept and measurement network, so as to illustrate some commonfeatures of fluctuating networks in various regions...