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Characteristics of distributions for the stock returns and trading volumes |
| Rafał Rak 1, Stanisław Drożdż 2, Jarosław Kwapień 2, Paweł Oświęcimka 2 |
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1. Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów 35-959, Poland |
| Abstract |
| The statistics of the returns and the trading volumes distributions is one of the most characteristics for financial dynamical system. Moreover, one of the fundamental question is the relationship between the power law fat-tailed distribution of trading volumes and returns. We present a systematic study of the Polish stock market return distributions and identify consistency of those distributions with the inverse cubic power law for the shortest time scales available. In order to verify the degree of convergence towards a Gaussian distribution [1] we extend this study to the time lags of increasing length and, as a result, we report a fast departure from the inverse cubic power-law. For several stocks we in parallel study the distribution of fluctuations of the volume traded and find that it also develops the power-law tails whose scaling indices are consistently about a factor of 2 smaller (tails thicker) than the ones describing the corresponding distributions of returns. Such a correspondence was originally postulated in the context of the inverse cubic power-law [2]. A particularly vital result of the present contribution is that this relation remains preserved even for the larger time lags when the departure from the inverse cubic power-law in the direction of thinner tails is sizeable. This observation opens room for giving a firmer ground to the model introduced in [2] and for extending its range of significance. The above analysis has been systematically performed using the formalism of the q-Gaussians as it follows from the concept of the nonextensive entropy [3]. This functional form allows to consistently describe the whole range of fluctuations, its asymptotics is power-law type and the corresponding scaling index is uniquely determined by the nonextensivity parameter q. [1] S.Drożdż, M.Forczek, J.Kwapień, P.Oświęciimka, R.Rak, Stock market return distributions: from past to present, Physica A, 383, 2007, 59. |
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Presentation: Oral at 5 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Rafał RakSee On-line Journal of 5 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych" Submitted: 2010-10-08 15:41 Revised: 2010-10-09 13:27 |