Quasi-Monte Carlo Methods and Monte Carlo Methods

The first part gives a little insight into a special part of the number theory, namely, Quasi-Monte Carlo method and in the course of this introduces fundamental knowledge about discrepancy of point sequences. An illustrative proof of a famous result concerning the lower bound of the star discrepancy of sequences in [0,1) is presented. Furthermore an improvement of this bound is presented and analysed. In the second part focus on the valuation af an interest rate swap. The required theory and one special approach to carry out the valuation is presented. During this, the method of Monte Carlo simulation is used.