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Statistical pairwise interaction model of stock market

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  • Thomas Bury
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    Abstract

    Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or others are agent-based models with rules designed in order to recover some empirical behaviours. Here we show that the pairwise model is actually a statistically consistent model with observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach based only on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviours, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.

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    File URL: http://arxiv.org/pdf/1206.4420
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1206.4420.

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    Date of creation: Jun 2012
    Date of revision: Jan 2014
    Publication status: Published in Eur. Phys. J. B (2013) 86: 89
    Handle: RePEc:arx:papers:1206.4420

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    1. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1998. "Noise dressing of financial correlation matrices," Science & Finance (CFM) working paper archive 500051, Science & Finance, Capital Fund Management.
    2. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 235-60, April.
    3. Aoki,Masanao, 1998. "New Approaches to Macroeconomic Modeling," Cambridge Books, Cambridge University Press, number 9780521637695, November.
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    Cited by:
    1. Thomas Bury, 2013. "A statistical physics perspective on criticality in financial markets," Papers 1310.2446, arXiv.org, revised Jan 2014.
    2. Hongli Zeng & R\'emi Lemoy & Mikko Alava, 2013. "Financial interaction networks inferred from traded volumes," Papers 1311.3871, arXiv.org.

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