Universal fluctuations of the AEX index

We compute the analytic expression of the probability distributions FAEX,+ and FAEX,− of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the α re-scaled AEX daily index positive returns r(t)α and negative returns (−r(t))α, which 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 Bramwell–Holdsworth–Pinton (BHP) probability density function. The optimal parameters that we found are α+=0.46 and α−=0.43. Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of stock exchange markets.