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Application of Zhangs square root law and herding to financial markets

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  • Wagner, Friedrich

Abstract

We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is equivalent to the so called 32 model of stochastic volatility. The description of the unconditional distribution for the absolute returns is in good agreement with the DAX independent whether one uses the square root or a conventional linear relation. Only the statistic of extreme events prefers the former. The description of the autocorrelations are in much better agreement for the square root law. The volatility clusters are described by a scaling law for the distribution of returns conditional to the value at the previous day in good agreement with the data.

Suggested Citation

  • Wagner, Friedrich, 2006. "Application of Zhangs square root law and herding to financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 369-384.
    • Handle: RePEc:eee:phsmap:v:364:y:2006:i:c:p:369-384
    DOI: 10.1016/j.physa.2005.09.070
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    References listed on IDEAS

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    1. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
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    Cited by:

    1. Raddant, Matthias & Wagner, Friedrich, 2013. "Phase transition in the S&P stock market," Kiel Working Papers 1846, Kiel Institute for the World Economy (IfW Kiel).
    2. Friedrich Wagner, 2011. "Market clearing by maximum entropy in agent models of stock markets," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 6(2), pages 121-138, November.

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