Observing stock market fluctuation in networks of stocks

In this paper we study the structural variation of the network formed by connecting Standard & Poor's 500 (S&P500) stocks whose closing prices (or price returns) are highly correlated. Specifically we consider S&P500 stocks that were traded from January 1, 2000 to December 31, 2004, and construct complex networks based on cross correlation between the time series of the closing prices (or price returns) over a fixed period of time. A simple threshold approach is used for establishing connections between stocks. The period over which the network is constructed is 20 trading days, which should be long enough to produce meaningful cross correlation values, but sufficiently short in order to avoid averaging effects that smooth off the salient fluctuations. A network is constructed for each 20-trading-day window in the entire trading period under study. The window moves at a 1-trading-day step. The power-law exponent is determined for each window, along with the corresponding mean error of the power law approximation which reflects how closely the degree distribution resembles a scalefree-like distribution. The key finding is that the scalefreeness of the degree distribution is disrupted when the market experiences fluctuation. Thus, the mean error of the power-law approximation becomes an effective indicative parameter of the volatility of the stock market.