Research On Complex Characteristics Of Stock Networks Under Financial Crisis

At present, taking advantage of complex network theory to better understand and explain various phenomena in stock markets has roused great interest among scholars home and abroad. Lots of novel results have been reached on the basis of adopting data from mature markets during steady economic develop period. Research base on emerging markets such as Chinese stock market especially during financial crisis time is relatively deficient.Under the specific academic background combined with the financial crisis period, we empirically investigated the price fluctuations of S&P 500 stock market and CSI 300 stock market using daily close price under two different periods as corresponding to the time before the financial crisis and under the crisis. Two weighted networks are introduced according to price fluctuation correlation of S&P 500 stocks and CSI 300 stocks respectively. Furthermore, maximum spanning tree algorithm is used to establish undirected and unweighted networks to reveal the special market characteristics under financial crisis, which made us better understand the nature of the complex features in differential stock markets during financial crisis. The contribution of the paper is listed as follows:1. S&P 500 and CSI 300 all-connected stock networks showed a completely different phenomena under the financial crisis:the weight distribution of S&P 500 all-connected stock network is showing a special form as almost all stocks are positively correlated with majority of links imply strong positive correlation; IS values are significantly increased and node numbers with the IS value loses power-law distribution; in double logarithmic coordinates, front-end nodes present a linear increase and a small number of tail end nodes constitute a power-law curve with deviation. The weight distribution of CSI 300 all-connected stock network is relatively smooth under the influence of financial crisis, but the configuration did not change much; IS value appeared some extent of reduction and node numbers with the IS value turned into double 2. Under the influence of the financial crisis, the S&P 500 and CSI 300 undirected and unweighted networks both have emerged major changes in topology. As the two networks have became more compact, the distribution of intermediate nodes is more crowded; degree distribution has remained a power-law distribution, but the end of the deviation increased with larger power exponent. Few great Hub nodes with large degree value have been presented and majority of these nodes have small degree value before the financial crisis. The degree value of Hub nodes increased dramatically can be considered as foreshadow of financial crisis.3. By contrast the largest community network of S&P 500 and CSI 300 undirected and unweighted networks, we found that S&P 500 network has the characteristics of industry-clustering while CSI 300 network has broader coverage in the largest community. The post-crisis form of CSI 300's largest community is similar to the Pre-crisis form of S&P 500's largest community, which proves China's stock market is maturing gradually.4. We choose K-means algorithm to further analyze the community structure of S & P 500 and CSI 300 all-connected networks. Under the financial crisis, we found that in both networks the overlapping community area was expanding with accelerated overlap rate. We can infer that intensification of overlapping community could serve as the foreshadow of financial crisis.