Scale-free Network in Financial Correlations

Details Scale-free Network in Financial Correlations Scale-free Network in Financial Correlations

2001-07-21

arxiv.org/abs/cond-mat/0107449v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1143/JPSJ.71.2133

We study the cross-correlations in stock price changes between the S&P 500 companies by introducing a weighted random graph, where all vertices (companies) are fully connected, and each edge is weighted. The weight assigned to each edge is given by the normalized covariance of the two modified returns connected, so that it is ranged from -1 to 1. Here the modified return means the deviation of a return from its average over all companies. We define influence-strength at each vertex as the sum of the weights on the edges incident upon that vertex. Then we found that the influence-strength distribution in its absolute magnitude $|s|$ follows a power-law, $P(|s|)\sim |s|^{-\delta}$, with exponent $\delta \approx 1.8(1)$.

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