Financial networks model based on random matrix

Abstract

Random matrix theory is applied to study the correlation between different financial correlation coefficient matrices in the financial field. Correlation coefficient matrix is a key factor for constructing a network. In this paper we relate the random matrix theory to the network construction to study the financial networks model in terms of the random matrix. We select the stock data of Shanghai stock market, and divide them into four stages. We discuss the statistical properties of eigenvalues in financial correlation coefficient matrix and random matrix based on the random matrix theory, and improve the existing denoising method to construct the correlation coefficient matrix and to make it more suitable for building financial networks. After that we can build the financial network model. Then we analyze and compare the original financial network, the denoising financial network and the noise financial network in terms of the random matrix theory and the key node of networks. It is found that the primary important information is still in the original network, and the noise information corresponds to the information which the nodes of small degree in the original network include. Finally we analyze the topological structure of the financial networks, such as the minimum spanning tree, the motif and community structure. We also find that the topological properties of the improved financial networks are more remarkable and the topological structure is more compact.