On the emergence of a generalised Gamma distribution. Application to traded volume in financial markets

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Abstract
This letter reports on a stochastic dynamical scenario whose associated stationary probability density function is exactly a generalised form, with a power law instead of exponencial decay, of the ubiquitous Gamma distribution. This generalisation, also known as F-distribution, was empirically proposed for the first time to adjust for high-frequency stock traded volume distributions in financial markets and verified in experiments with granular material. The dynamical assumption presented herein is based on local temporal fluctuations of the average value of the observable under study. This proposal is related to superstatistics and thus to the current nonextensive statistical mechanics framework. For the specific case of stock traded volume, we connect the local fluctuations in the mean stock traded volume with the typical herding behaviour presented by financial traders. Last of all, NASDAQ 1 and 2 minute stock traded volume sequences and probability density functions are numerically reproduced.
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