Abstract
We consider the α re-scaled Standard & Poor's 100 (SP100) daily index positive returns and negative returns ( that we call, after normalization, the α positive fluctuations and α 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) and the truncated generalized log-normal pdf f LN that best approximates the truncated BHP pdf. The optimal parameters we found are , , and . Using the optimal α′s, we compute analytical approximations of the probability distributions of the normalized positive and negative SP100 index daily returns r(t). Since the BHP pdf appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.
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