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Market mill dependence pattern in the stock market: Multiscale conditional dynamics

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  • Zaitsev, Sergey
  • Zaitsev, Alexander
  • Leonidov, Andrei
  • Trainin, Vladimir

Abstract

Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a single time scale such as a characteristic shape of an asymmetry-generating component of the conditional probability distribution result in the “elementary” market mill pattern. This asymmetry-generating component matches the empirical distribution obtained from the market data. Multiple time scale considerations make the resulting “composite” mill similar to the empirical market mill patterns. Multiscale model also reflects a multi-agent nature of the market. Interpretation of variations of asymmetry patterns of individual stocks in terms of specific deformations of the fundamental market mill asymmetry patterns is described.

Suggested Citation

  • Zaitsev, Sergey & Zaitsev, Alexander & Leonidov, Andrei & Trainin, Vladimir, 2009. "Market mill dependence pattern in the stock market: Multiscale conditional dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4624-4634.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:21:p:4624-4634
    DOI: 10.1016/j.physa.2009.07.014
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    References listed on IDEAS

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    1. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
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    3. Leonidov, Andrei & Trainin, Vladimir & Zaitsev, Alexander & Zaitsev, Sergey, 2007. "Market mill dependence pattern in the stock market: Modeling of predictability and asymmetry via multi-component conditional distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 240-252.
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    6. Andrei Leonidov & Vladimir Trainin & Alexander Zatsev & Sergey Zaitsev, 2007. "Market Mill Dependence Pattern in the Stock Market: Modeling of Predictability and Asymmetry via Multi-Component Conditional Distribution," Papers physics/0701158, arXiv.org, revised Mar 2007.
    7. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 621-631.
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    Cited by:

    1. Vladimir Markov & Slava Mazur & David Saltz, 2014. "Design and Implementation of Schedule-Based Trading Strategies Based on Uncertainty Bands," Papers 1409.1441, arXiv.org.

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    Keywords

    Econophysics; Market mill;

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