This new edition is a greatly extended and updated version of my earlier monograph "Pricing Credit Linked Financial Instruments" (Schmid 2002). Whereas the first edition concentrated on the re search which I had done in the context of my PhD thesis, this second edition covers all important credit risk models and gives a general overview of the subject. I put a lot of effort in explaining credit risk factors and show the latest results in default probability and recovery rate modeling. There is a special emphasis on correlation issues as well. The broad range of financial instruments I consider covers not only defaultable bonds, defaultable swaps and single counterparty credit derivatives but is further extended by multi counterparty in struments like index swaps, basket default swaps and collateralized debt obligations. I am grateful to Springer-Verlag for the great support in the realiza tion of this project and want to thank the readers of the first edition for their overwhelming feedback. Last but not least I want to thank Uli Gser for ongoing patience, en couragement, and support, my family and especially my sister Wendy for being there at all times. BemdSchmid Stuttgart, November 2003 Cpntents 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Objectives, Structure, and S:ummary . . . . . . . . . . . . . . . . . . . . . . 5 2. Modeling Credit Risk Factors. . . . . . . . . . . . . . . . . . . . . . . 13 . . . . . . 2. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2. 2 Definition and Elements of Credit Risk . . . . . . . . . . . . . . .. 13 . . . . 2. 3 Modeling Transition and Default Probabilities. . . . . . . . . . . . . 14 . 2. 3. 1 The Historical Method . . . . . . . . . . . . . . . . . . . . . . 15 . . . . .