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 Ph D 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 Goser for ongoing patience, en- couragement, and support, my family and especially my sister Wendy for being there at all times. Bemd Schmid 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 . . . . . .