Measurable inhomogeneities in stock trading volume flowA. A. G. Cortines, R. Riera and C. Anteneodo
Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro CP 38097, 22453-900, Rio de Janeiro, Brazil
received 23 May 2008; accepted in final form 16 June 2008; published August 2008
published online 1 July 2008
We investigate the statistics of volumes of shares traded in stock markets. We show that the stochastic process of trading volumes can be understood on the basis of a mixed Poisson process at the microscopic time level. The beta distribution of the second kind (also known as q-gamma distribution), that has been proposed to describe empirical volume histograms, naturally results from our analysis. In particular, the shape of the distribution at small volumes is governed by the degree of granularity in the trading process, while the exponent controlling the tail is a measure of the inhomogeneities in market activity. Furthermore, the present case furnishes empirical evidence of how power law probability distributions can arise as a consequence of a fluctuating intrinsic parameter.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
02.50.Ey - Stochastic processes.
89.65.Gh - Economics; econophysics, financial markets, business and management.
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