| Summary: | This 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.
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