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Statistical Signatures in Times of Panic: Markets as a Self-Organizing System

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  • Lisa Borland
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    Abstract

    We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in normal times. The co-movement of stock returns also increases in panic times. We define a simple statistic $s$, the normalized sum of signs of returns on a given day, to capture the degree of correlation in the system. $s$ can be seen as the order parameter of the system because if $s= 0$ there is no correlation (a disordered state), whereas for $s \ne 0$ there is correlation among stocks (an ordered state). We make an analogy to non-equilibrium phase transitions and hypothesize that financial markets undergo self-organization when the external volatility perception rises above some critical value. Indeed, the distribution of $s$ is unimodal in normal times, shifting to bimodal in times of panic. This is consistent with a second order phase transition. Simulations of a joint stochastic process for stocks use a multi timescale process in the temporal direction and an equation for the order parameter $s$ for the dynamics of the cross-sectional correlation. Numerical results show good qualitative agreement with the stylized facts of real data, in both normal and panic times.

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    File URL: http://arxiv.org/pdf/0908.0111
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    Paper provided by arXiv.org in its series Papers with number 0908.0111.

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    Date of creation: Aug 2009
    Date of revision: Aug 2009
    Handle: RePEc:arx:papers:0908.0111

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    Web page: http://arxiv.org/

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    Cited by:
    1. Frederic Abergel & Nicolas Huth & Ioane Muni Toke, 2009. "Financial bubbles analysis with a cross-sectional estimator," Papers 0909.2885, arXiv.org.

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