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Stochastic Evolution of Stock Market Volume-Price Distributions

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  • Paulo Rocha
  • Frank Raischel
  • Jo\~ao P. da Cruz
  • Pedro G. Lind
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    Abstract

    Using available data from the New York stock market (NYSM) we test four different bi-parametric models to fit the correspondent volume-price distributions at each $10$-minute lag: the Gamma distribution, the inverse Gamma distribution, the Weibull distribution and the log-normal distribution. The volume-price data, which measures market capitalization, appears to follow a specific statistical pattern, other than the evolution of prices measured in similar studies. We find that the inverse Gamma model gives a superior fit to the volume-price evolution than the other models. We then focus on the inverse Gamma distribution as a model for the NYSM data and analyze the evolution of the pair of distribution parameters as a stochastic process. Assuming that the evolution of these parameters is governed by coupled Langevin equations, we derive the corresponding drift and diffusion coefficients, which then provide insight for understanding the mechanisms underlying the evolution of the stock market.

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    File URL: http://arxiv.org/pdf/1404.1730
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1404.1730.

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    Date of creation: Apr 2014
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    Handle: RePEc:arx:papers:1404.1730

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    Web page: http://arxiv.org/

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