Modelització de bons i tipus d’interès a temps discret

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Josep Vives i Santa Eulàlia[en] The aim of this work is to model the bond prices. In order to achieve this goal, we start presenting the fixed income securities in discrete time, in particular the zero-coupon bonds. We will also analyze how to deal with these types of bonds in the case of coupon emission, in a forward contract and in the case of interest rate swaps. We will define models in order to find bond prices in a future. The tool used are binomial trees and we are going to apply a light tracking of the Cox-Ross-Rubinstein model but of course adjusting it to the market bonds. Then, we introduce the short rates and we will notice that they will also allow us to determine the bond prices with certain extra conditions. Furthermore, we will present adaptations in discrete time of the Merton, the Vasicek and the Ho-Lee models, as models that determine the short rate