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The author gives a brief survey over capital markets, risk management, and the regulatory framework, which banks face today. Furthermore, the idea of stochastic processes and its applications is presented, partly in its historic context. Physics and stochastic processes have a close relationship (quantum mechanics, statistical mechanics as physics of large systems), this fact is recently utilized in finance, and a young branch of physics called econophysics is currently emerging. The second goal of the book is to develop some basic theory concerning stochastic processes and to apply the gained knowledge to do some model calculations, which are applied to stock and option price data of the Vienna Stock Exchange. The results of these model calculations confirm the expectations known from literature: The inadequacy of the Gaussian distribution and of the associated Black-Scholes analysis. The calculations show that the alternative Lévy models are better suited. Furthermore, the inclusion of stochastic volatilities is crucial to describe option prices sufficiently accurately.
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