The course summarises some leading models for the pricing of credit risk and the valuation of credit derivatives. The models are presented in a simplified fashion, with examples. The role of interest rate risk, default risk, and recovery risk are all given play in these models. We focus on three different pricing models: (a) Structural, (b) Reduced-form (Intensity), and (c) Rating-based transition matrix models. First, we take a look at the key credit derivative products, their structures and related markets issues. We will then examine the first of many models, restricting attention to modelling approaches which directly model the credit spread. We look at the components of the credit spread and the CDS basis in greater detail, and then move onto an explicit model. We examine in great details the Blackâ€“Scholes option-theoretic (Moodyâ€™sâ€“KMV) structural approach, which makes explicit assumptions about the dynamics of a firmâ€™s assets, its capital structure, its debt and shareholders. Default risk embedded in corporate securities priced into CDS are critically considered and analysed. In particular, the impact on default risk and CDS prices due to changes in dividend policy, debt- equity capital structure mix with varying seniority and refinancing schedules, investment policy, and convertible optionalities are examined. We then extend the methodology to include stochastic term structures with counterparty risk (reduced-form models) and credit rating transitions. In the last section we discuss, in brief, the application of the methods in this course to credit portfolios. A CDO is a financial claim to the cashflows generated by a portfolio of debt securities or, equivalently, a basket of CDS contracts. In this way, CDOs allow redistribution of credit risk in any given portfolio into new tranches with risk profiles that are different from the underlying assets. In this section, we clarify the basic concepts and methods for analysing structured credit transactions. We show how to determine the risk structure of CDOs both by simulation and analytically.