In this dissertation we study models for the valuation of portfolios of credit risky securities and collateralised debt obligations. We start with models for single security of the reduced form type and investigate means of extending these to the portfolio level concentrating on default dependence between obligors. The Gaussian copula model has become a market standard and we study how the model deals with dependence between portfolio constituents. We implement the model and confirm analytical formulae for certain risk measures. Simplifying assumptions made eases implementation of this model but causes inconsistencies with observed market prices. Evidence of this is the observed correlation smile, highlighted by the recent global credit crises. This has caused researchers to look to extensions of the model to better fit current market pricing. We study a number of these extensions and compare the credit losses for various tranches to those under the standard model. A number of these extensions are able to replicate observed prices by accounting for some observed feature overlooked by the standard model. Of these the most promising appear to be those having default and recovery rates negatively correlated. Various empirical studies have found this to hold true. Another promising advancement is in the area of stochastic correlation. The main problems with such extensions is that no single one has been adopted as standard while all require more sophisticated numerical implementation than the convenient recursive algorithm available for the standard model. Even if such problems are overcome questions still remain. No current usable model is able to provide simultaneously both a term structure of credit spreads for the portfolio and individual constituents. This prevents the valuation of the next generation of credit products. An answer may well be beyond capabilities of the now familiar copula framework which has served the market for the last decade. / Dissertation (MSc)--University of Pretoria, 2010. / Mathematics and Applied Mathematics / unrestricted