Extreme Value of Intraday Returns

Abstract

The aim of this research paper is to study the properties of intraday returns, in a time range from one to fifteen minutes. In order to perform this analysis, we consider four sets of historical intraday returns for FTSE-MIB index. The first series consist of intraday returns with one-minute frequency, represented in log scale, which includes the period from 01.04.2011 till 30.09.2011. The consideration period for the other series does not vary, but the frequencies which we calculate the returns with, do. In detail, we took in consideration returns generated in 1, 5, 10 and 15 minutes. First, the study analyses the distribution of intraday returns by employing both graphical methods and moments calculation on different time scales. Secondly, the study analyses the returns maximum distribution on different time scales, checking the type GEV (Generalized Extreme value) returns distribution goodness of fit. The GEV parameters estimation was made by maximum likelihood using EVIM toolbox in Matlab.