Singh, Renay2011-03-302011-03-302011-03-30http://hdl.handle.net/10539/9273This work aims to provide an introduction to the methodologies used for determining the loss distribution of a heterogeneous portfolio of credit default swaps. For all the methods considered, the theory and the algorithms are presented and their computational efficiency and accuracy investigated. The loss distribution is then used to value synthetic CDO tranches. The multi-step and the default-time approach are the primary methods considered. For the multi-step approach, three approaches in the literature to the computationally demanding task of obtaining the default thresholds are compared. A synthetic CDO tranche was then evaluated and it was found that the choice of method used to determine the default thresholds is significant. The default-time approach was found to be computationally more efficient than the multi-step approach though with significant differences in the tail region of the loss distribution. Both these approaches rely on Monte Carlo simulation, which is computationally inefficient. Semi-analytic approximations to the default-time approach are considered. These are the numerical inversion of the characteristic function, exact recursion and the compound Poisson approximation. A unique presentation that aids in the understanding and implementation of the numerical inversion of the characteristic function is given. The approximation techniques though computationally more efficient than Monte Carlo, are not as accurate.enThesis