The σ-Entropy Curve And The Application In The Financial Market

In order to depict the heterogeneity of the weighted networks, and investigate theheterogeneity in stock networks and the source of heterogeneity, Construct the stocknetworks based on the distance of stocks, give the new concept of σ-entropy curveand τ-value based the network structure entropy, Proof a basic properties of τ-value,explain the rationality of the definition and different networks’ heterogeneity couldbeen compared by τ-value. The τ-value more of less than1corresponding theheterogeneity network bigger, and more close to1corresponding the heterogeneity ofnetwork smaller. Calculated the τ-value of stock set corresponding CSI300index andthe S&P500index which representative with the market in different years. and tocompare the differences between industry and The whole market, calculate the τ-valueof stock network corresponding a few industries which have more listed companies,compare the τ-value of corresponding different industries and index in different period.On the other hand, calculate the largest eigenvalues and the corresponding firstprincipal components based on the correlation coefficient matrix of stock set, Verifythere are a few economic factors existing in the market. Use the geometric Brownianmotion constructs the stock networks model, calculate the τ-value of correspondingnetworks, Finally according to the σ-entropy curve and τ-value concept of the value ofthe property and some numerical calculation inspection.The calculation results show that in this paper, the τ-value of networks whichbased on the Stock closing price are less than1, show the heterogeneity ofnetworks, and the τ-value of simulation network based on geometric Brownianmotion is equal to1, no present the heterogeneity. Based on the results of the analysisof τ-value and the First principal component and Random matrix theory, analysis thesource of the heterogeneity of the networks, The source of stock Networksheterogeneity is the elements in the reaction of information have heterogeneity, thestock networks heterogeneity embodies the complexity of the financial market.