Universal Fluctuations of the FTSE100

TL;DR

This paper derives the probability distributions of positive and negative FTSE100 index returns, introduces alpha rescaling to reveal universal fluctuations, and demonstrates the universality of stock market behavior through the BHP distribution.

Contribution

It provides an analytic expression for FTSE100 return distributions and identifies universal fluctuation patterns using alpha rescaling and the BHP distribution.

Findings

Optimal alpha values are 0.55 for positive and negative returns.

The rescaled fluctuations collapse onto the BHP distribution.

Evidence of universality in stock market fluctuations.

Abstract

We compute the analytic expression of the probability distributions F{FTSE100,+} and F{FTSE100,-} of the normalized positive and negative FTSE100 (UK) index daily returns r(t). Furthermore, we define the alpha re-scaled FTSE100 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+=0.55 and alpha-=0.55. Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal universality in the stock exchange markets.