Universality in PSI20 fluctuations

Abstract

We consider the α re-scaled PSI20 daily index positive returns r(t)α and negative returns ( − r(t))α called, after normalization, the α positive and negative fluctuations, respectively. We use the Kolmogorov-Smirnov statistical test as a method to find the values of α that optimize the data collapse of the histogram of the α fluctuations with the truncated Bramwell-Holdsworth-Pinton (BHP) probability density function (pdf) f { BHP} and the truncated generalized log-normal pdf f LN that best approximates the truncated BHP pdf. The optimal parameters we found are α { BHP}_+ = 0. 48, α { BHP}_− = 0. 46, α LN + = 0. 50 and α LN − = 0. 49. Using the optimal α′s we compute analytic approximations of the probability distributions of the normalized positive and negative PSI20 index daily returns r(t). Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.