Numerical analysis and stochastic modeling in mathematical finance

Abstract

The main goal of this thesis has been to study and develop faster and more accurate methods for pricing and hedging exotic options. This has involved work on models describing prices and hedges as well as the stochastics driving them. We have also put effort into algorithmic interpretation and implementation of the models to enable efficiency measurement with regards to computing time. In some of the articles we have aspired to find criteria to decide whether the pricing methods we have developed can be expected to perform well, enabling practicians to find a good numerical method for their given pricing/hedging problem easier. However, the most optimistic reader must be warned: We have not found one single method that works best for all types of option pricing problems, and we do not think that sucj a method exists. Pricing and hedging of exotic options involve thorough knowledge of the problem at hand, and the mastering of a tool box of numerical methods from which a suitible one can be picket. We beleive, however, that the thesis contributes som to the enlargement of the tool box.