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Determining rational prices of financial derivatives is of a key importancein Financial Mathematics. Currently, the demand from financial institutionsfor qualified mathematicians is substantial and also there is an increasingneed for professional training of existing staff. This book presents studentand practitioners orientated introduction into this rapidly growing area.Our objective is to introduce the key principles of Financial Mathematics ina clear way. We explain everything that is not contained in the earlyCalculus and Probability courses. Building on this background, theBlack-Scholes pricing formula and more advanced Levy driven models aredeveloped in details. This leads to practical formulas to determineno-arbitrage option prices.