Universal Fluctuations of AEX index

TL;DR

This paper analytically derives the probability distributions of positive and negative daily returns of the AEX index, demonstrating universality in stock market fluctuations through the application of the BHP distribution.

Contribution

It introduces a method to normalize and analyze AEX index returns using the BHP distribution, revealing universal fluctuation patterns in stock markets.

Findings

Optimal alpha values for positive and negative returns: 0.46 and 0.43.

Normalized fluctuations collapse onto the BHP distribution.

Evidence of universality in stock market fluctuations.

Abstract

We compute the analytic expression of the probability distributions F{AEX,+} and F{AEX,-} of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the \alpha re-scaled AEX daily index positive returns r(t)^\alpha and negative returns (-r(t))^\alpha that we call, after normalization, the \alpha positive fluctuations and \alpha negative fluctuations. We use the Kolmogorov-Smirnov statistical test, as a method, to find the values of \alpha that optimize the data collapse of the histogram of the \alpha fluctuations with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are \alpha+=0.46 and \alpha-=0.43. Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal universality in the stock exchange markets.