This thesis describes a new approach for the valuation of credit derivatives. The interest rate and the default intensity are modelled by a CIR++ model (possibly extended by exponential jumps). The analytical price of CDS options (Brigo and Alfonsi (2005)) is used for calibration. Based thereon an analytical price for contingent credit lines is derived as the sum over single period options.A motivating statistical analysis of historical time series by an EM algorithm indicates that the distribution of default intensity depends on the regime. This results in a RS CIR++ model in which the CIR parameters can be different in each regime.Tree models are used for numerical valuation. Two different models, the model of Brigo and Mercurio (2006) and the model of Nawalkha and Beliaeva (2007), are presented and compared. Based thereon a tree is used for the inclusion of the extensions which combines the best properties of both models. Besides the tree extensions, the shift parameter, the jump component and the default, a new procedure is shown to enclose the regime switching component into a CIR tree.Schönbucher´s (2000) idea of modelling interest rate and default intensity in one single tree is captured resulting in a two-dimensional CIR tree. The correlation between interest rate and default intensity is incorporated by a new copula model, and it is shown that this model provides results superior to those of the existing procedure by Hull and White (1994).The results show a very good approximation of the tree prices to the analytical ones for CDS options, the advantage of the copula model for correlations and the impact of the regime switching on the price. Furthermore different credits are priced including different options, the draw down and the prepayment option as well as contingent credit lines as sum of options.
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