Credit risk has become the central focus of risk management in the last decade for a number of reasons. First, for a typical continental bank, credit risk is still the predominant risk category. Second, the new Basel Capital Accord of June 2004 allows for more advanced methods to assess the risk related with a bank's credit portfolio. Third, the markets to reallocate credit risk between agents experience the highest growth rate of all derivative markets. Fourth, from a theoretical and an empirical point of view, the modelling and valuation of credit risk is a more demanding problem than the analysis of market risk. Especially, the appropriate modelling of correlation effects, e.g. the correlation between defaults of different creditors or between default probabilities and recovery rates, is'still not satisfactory resolved. Collateralised Debt Obligations (CDOs) represent important derivatives to synthesise and reallocate the risk of banks' credit portfolios. These instruments are of specific interest as they, first, call for a determination of the whole loss distribution of a credit portfolio and not only for a few moments. Second and even more interesting, this loss distribution is carved into senior, mezzanine and junior tranches according to the needs and risk attitudes of the bank and the market.