Caroline Lundkvist presents her master's thesis


Probability distributions of maxima of Stochastic
Processes and Financial Indices

Abstract

The objective of this project is to investigate the activity on the
financial market during a trading day. We are mainly interested in
the probability distribution of times for intradaily minimum and maximum
of the stock value. The empirical part of the project is based on high
frequency data from the DAX index of the Frankfurt Stock Exchange.
Data is fitted to the beta distribution, with the parameters estimated
by maximum likelihood in MATLAB. Results show that the beta
distribution is a better fit of the location of maximum and minimum
than, for example, the arcsine distribution. The obtained beta density
is compared with a nonparametric estimation of the probability density
function. For this purpose the kernel estimation is used, with
Sheather-Jones plug-in method.