Universal fluctuations of the AEX index

We compute the analytic expression of the probability distributions FAEX,+FAEX,+ and FAEX,−FAEX,− of the normalized positive and negative AEX (Netherlands) index daily returns r(t)r(t). Furthermore, we define the αα re-scaled AEX daily index positive returns r(t)αr(t)α and negative returns (−r(t))α(−r(t))α, which we call, after normalization, the αα positive fluctuations and αα negative fluctuations. We use the Kolmogorov–Smirnov statistical test as a method to find the values of αα that optimize the data collapse of the histogram of the αα fluctuations with the Bramwell–Holdsworth–Pinton (BHP) probability density function. The optimal parameters that we found are α+=0.46α+=0.46 and α−=0.43α−=0.43. Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of stock exchange markets.