Efficient tree methods for option pricing

The aim of this dissertation is the study of efficient algorithms based on lattice procedures for dealing with two relevant issues arising in the recent literature on option pricing: the pricing of complex barrier-type options and the pricing of options when the equity model takes into account a stochastic interest rate. This research is developed with a twofold perspective: first, we propose a good solution from a numerical point of view through the introduction of efficient lattice procedures and secondly, we study the theoretical aspects related to the tackled problems (such as the convergence and the rate of convergence of the scheme proposed).