Self-organized critical topology of stock markets

Abstract

We have analyzed the cross-correlations of daily fluctuations for N=6 358 US stock prices during the year 1999. From those $N(N-1)/2$ correlations coefficients, the Minimum Spanning Tree (MST) has been built. We have investigated the topology exhibited by the MST. Eventhough the average topological number is $<n>\approx 2$, the variance $\sigma$ of the topological distribution f(n) diverges. More precisely, we have found that $f(n)\sim n^{-2.2}$ holding over two decades. We have studied the topological correlations for neighbouring nodes: an extremely broad set of local configurations exists, confirming the divergence of $\sigma$.

7pages, 3 figures, see also an interactive presentation of this paper on www.market-topology.com. Quantitative Finance, in press