Universality in DAX index returns fluctuations

In terms of the stock exchange returns, we compute the analytic expression of the probability distributions FDAX,+ and FDAX,− of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the α re-scaled DAX daily index positive returns r(t) and negative returns (−r(t)) that we call, after normalization, the α positive fluctuations and α negative fluctuations. 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 BramwellHoldsworth-Pinton (BHP) probability density function. The optimal parameters that we found are α = 0.50 and α− = 0.48. Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal universality in the stock exchange markets.