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Statistical signatures in times of panic: markets as a self-organizing system

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  • Lisa Borland

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 ≠ 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.

Suggested Citation

  • Lisa Borland, 2012. "Statistical signatures in times of panic: markets as a self-organizing system," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1367-1379, October.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:9:p:1367-1379
    DOI: 10.1080/14697688.2011.653388
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    File URL: http://hdl.handle.net/10.1080/14697688.2011.653388
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    Cited by:

    1. Aleksejus Kononovicius & Julius Ruseckas, 2014. "Nonlinear GARCH model and 1/f noise," Papers 1412.6244, arXiv.org, revised Feb 2015.
    2. Kononovicius, A. & Ruseckas, J., 2015. "Nonlinear GARCH model and 1/f noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 74-81.
    3. Guevara Hidalgo, Esteban, 2017. "Bin size independence in intra-day seasonalities for relative prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 722-732.

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