Option pricing with Lévy processes: jump models for European-style options

Tese de mestrado em Matemática Financeira, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2013The goal of this dissertation is to explain how the pricing of European-style options under Lévy processes, namely jump and jump diffusion processes, can be performed and the mathematics associated with it. For this purpose, three models are exposed: Merton, Kou and Variance Gamma, each with different valuation approaches. A Monte Carlo path simulation is also explained. Finally, calibration of the models to real data takes place