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Diploma Thesis from the year 2003 in the subject Statistics, grade: 1,0, University of Cologne (Seminar für Wirtschafts- und Sozialstatistik), 86 entries in the bibliography, language: English, abstract: Finance experts and statisticians still have considerable difficulties to understand extremal movements in stock prices. Basically, there are two approaches to shed some light on this question: 1. Tail inference based on full parametric assumptions 2. "Letting the tails speak for themselves" This paper discusses both approaches, the stable Paretian distribution serving as a conceptual framework for the analysis.