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Seminar paper from the year 2008 in the subject Economics - Finance, grade: 1,7, Christian-Albrechts-University of Kiel, language: English, abstract: There is a long tradition of scholars seeking to understand the distributionalregularities of financial returns. Research traces back to the turn of the 19thcentury. Since then, it underwent a lot of drastic changes, which are to be shownin this paper.The aim of this paper is to show theoretical models that account for the distributionalregularities in financial returns as well as to illustrate the empiricalanalysis. It is necessary to understand the evolution of research on this topicbecause it came about in a consecutive manner. Thus, this paper will documentover one hundred years of research on distributional properties of financial returns.The second chapter will start with the results of Louis Bachelier and his normaldistribution hypothesis. Then it will describe Benoît Mandelbrot's groundbreakingresults, which rejected Bachelier's normal hypothesis and introduced theLévy-stable distributions. Mandelbrot's work had such an impact that it will bedescribed in greater detail.The third chapter will present the results of research that followed after Mandelbrot'sfindings. It will also display and explain the results of recent research.