Non-random topology of stock markets

N. Vandewalle, F. Brisbois and X. Tordoir

Quantitative Finance, 2001, vol. 1, issue 3, 372-374

Abstract: We have analysed the cross correlations of daily fluctuations for [iopmath latex="$N=6358$"] N = 6358 [/iopmath] US stock prices during the year 1999. From those [iopmath latex="$N(N-1)/2$"] N ( N -1)/2 [/iopmath] correlation coefficients, the minimum spanning tree (MST) has been built. We have investigated the topology exhibited by the MST. Even though the average coordination number of stocks is [iopmath latex="$langle n rangleapprox 2$"] n 2 [/iopmath], the variance [iopmath latex="$sigma$"] [/iopmath] of the topological distribution [iopmath latex="$f(n)$"] f ( n ) [/iopmath] diverges! More precisely, we have found that [iopmath latex="$f(n) sim n^{-2.2}$"] f ( n )~ n -super--2.2 [/iopmath] holds over two decades. We have studied the topological correlations for neighbouring nodes: an extremely broad set of local configurations exists, confirming the divergence of [iopmath latex="$sigma$"] [/iopmath].

Date: 2001
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DOI: 10.1088/1469-7688/1/3/308

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