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Non-random topology of stock markets

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  • N. Vandewalle
  • F. Brisbois
  • X. Tordoir
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    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="$langle n rangleapprox 2$"] n2 [/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-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].

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 1 (2001)
    Issue (Month): 3 ()
    Pages: 372-374

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    Handle: RePEc:taf:quantf:v:1:y:2001:i:3:p:372-374

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    Cited by:
    1. Bolgorian, Meysam & Raei, Reza, 2010. "Convergence of fundamentalists and chartists’ expectations: An alarm for stock market crash," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3822-3827.
    2. Michael J. Naylor & Lawrence C. Rose & Brendan J. Moyle, 2006. "Topology of Foreign Exchange Markets using Hierarchical Structure Methods," Papers physics/0608084, arXiv.org, revised Nov 2006.
    3. A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach," Papers 1301.6506, arXiv.org.
    4. Lyócsa, Štefan & Výrost, Tomáš & Baumöhl, Eduard, 2012. "Stock market networks: The dynamic conditional correlation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4147-4158.
    5. Výrost, Tomáš, 2012. "Country effects in CEE3 stock market networks: a preliminary study," MPRA Paper 43481, University Library of Munich, Germany.
    6. Wiliński, M. & Sienkiewicz, A. & Gubiec, T. & Kutner, R. & Struzik, Z.R., 2013. "Structural and topological phase transitions on the German Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5963-5973.
    7. Bartolozzi, M. & Leinweber, D.B. & Thomas, A.W., 2006. "Symbiosis in the Bak–Sneppen model for biological evolution with economic applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 499-508.
    8. M. Wili\'nski & A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Structural and topological phase transitions on the German Stock Exchange," Papers 1301.2530, arXiv.org, revised Jul 2013.
    9. Nobi, Ashadun & Maeng, Seong Eun & Ha, Gyeong Gyun & Lee, Jae Woo, 2014. "Effects of global financial crisis on network structure in a local stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 135-143.

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