Spatio-temporal Evolution Of The Co-movement Of Asset Prices

Currently, the study on the behavior of Chinese stock market has become a hot topic. As we all known, Chinese stock market’s volatility is time-varying. Generally, stock market’s behavior always associated with the complicated relationships among stocks. However, multivariate statistical methods as traditional methods used to study the fluctuation correlation among the limited stock time series, which were hard to obtain effective empirical results. Recently, complex network theory is brought into revealing market’s behavior.From the view of complexity science by using the mature theory and methodology in complex network, I analyze the relationship between the co-movement of asset prices and the stock market stability. As a result, several productions of good theoretical values and contributions are given as follows:(1) Using a moving window to scan through every stock price time series over a period from2January2001to11March2011and mutual information to measure the statistical interdependence between stock prices, and construct a corresponding weighted and fully connected network of501Shanghai stocks for every given window. Then, I analyze the average path length, influence of the center node and the p-value for every maximal spanning tree which is extracted from every fully connected stock network. Then, a detailed analysis of the variation of maximal spanning trees at different periods of Shanghai stock market is given. The obtained results are as follows:the periods around8August2005,17October2007and25December2008are turning points; at turning points, the stability of Shanghai stock market gets weaker, the degree of separation between nodes increases, the structure becomes looser, the influence of the center node gets smaller, the maximal spanning tree’s topology structure is more chain-like and its degree distribution is no longer a power-law distribution. The variations of the single-step and multi-step survival ratios indicate that two stocks are closely bonded and hard to be broken in a short term, on the contrary, no pair of stocks remains closely bonded after a long time.(2) Two methods are employed to analyze topological characteristics of the fully connected stock-industry networks before and at turning point. On the one hand, we use the threshold method to simplify the networks, and find that the clustering coefficient of the network at turning point is much smaller than that of the network before the turning point, which indicates that the industry network at turning point is less cohesiveness and looser than that before. The center nodes of the network at turning point are ’Electronics’ and’ Textiles and Garments’, which are different from that of the network before. On the other hand, we extract the maximal spanning trees from the two fully connected networks, and find that at turning point, the degree of separation between nodes increases, the structure becomes looser, the influence of the center node gets smaller. Compared with the above two methods, although both of the them can reveal the characteristics well, the later one is more intuitive for observing the co-movement between stocks.All the above studies could help us learn more about the relationship between the co-movement of asset prices and the market stability, meanwhile can be a good guide to the risk management of stock investment.