Stochastic calculus i a semi-Markov environment and financial applications

(eng) This thesis is concerned with the study of semi-Markov switching models as applied to financial derivatives. The idea is to model the underlying of the derivatives with a model whose parameters switch between different values according to some hidden semi-Markov process. The first part of the thesis studies the necessary mathematical aspects and tools. We then turn to studying discrete time switching models of both interest rates and equities. We move on to study continuous time models of equities and interest rates and provide a detailed study of the switching Black-Scholes model. The last part is concerned with the estimation and calibration of a semi-Markov switching diffusion.