Universal fluctuations of the AEX index

Abstract

We compute the analytic expression of the probability distributions F A E X , + and F A E X , − 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.