1;Foreword;6 2;Contents;8 3;List of Figures;10 4;List of Tables;11 5;List of Abbreviations;12 6;Abstract;13 7;1 Introduction;14 7.1;1.1 Selection and relevance topics;14 7.2;1.2 Formulating the research questions;15 7.3;1.3 State of the literature;16 7.4;1.4 Methodology;17 7.5;1.5 The structure of the thesis;17 8;2 CDO: general characteristics;19 8.1;2.1 Introduction and definition;19 8.2;2.2 The tranches role;19 8.3;2.3 Classification of CDOs;20 8.4;2.4 Reasons for the utilization of CDOs;21 8.5;2.5 Typical cash flow CDO structure;22 8.6;2.6 Synthetic CDO;24 8.7;2.7 Credit default swap index;26 8.7.1;2.7.1 Definition;26 8.7.2;2.7.2 Synthetic CDS index tranches;27 8.7.3;2.7.3 Synthetic tranches target;28 8.8;2.8 CDO Pricing: a general approach;29 8.8.1;2.8.1 Loss Distribution;29 8.8.2;2.8.2 Spread;32 9;3 Credit Risk Modeling;33 9.1;3.1 The Bernoulli Model;33 9.2;3.2 A Bernoulli mixture Model;34 9.2.1;3.2.1 The general case;34 9.2.2;3.2.2 Uniform default probability and uniform correlation case;35 9.3;3.3 Moody's KMV's and RiskMetrics' Model Approach;36 9.4;3.4 One-Factor Model;39 9.5;3.5 The large portfolio approximation;42 9.6;3.6 Multifactor models;45 10;4 Copula functions and dependency concepts;47 10.1;4.1 Copulas Basics;47 10.2;4.2 Examples of copulas;49 10.2.1;4.2.1 Product copula;49 10.2.2;4.2.2 Gaussian Copula;49 10.2.3;4.2.3 t-Copula;51 10.2.4;4.2.4 Archimedean Copulas;51 10.3;4.3 Tail dependence;54 10.4;4.4 Loss Dependence by Means of Copula;57 11;5 Moment Matching Approximation;59 11.1;5.1 Introduction;59 11.2;5.2 The Model;59 11.3;5.3 The Moment Matching;61 11.4;5.4 Approximating distributions;64 12;6 Extensions to the Model;67 12.1;6.1 Archimedean Copulas;67 12.1.1;6.1.1 Moments of the original distribution;67 12.1.2;6.1.2 Approximating distribution;68 12.2;6.2 Risk Management;71 12.2.1;6.2.1 Risk Measures;71 12.2.2;6.2.2 The method;72 13;7 Implementation;75 13.1;7.1 Gaussian implementation;75 13.1.1;7.1.1 Data;75 13.1.2;7.1.2 Bootstrapping the default term structure;75 13.1.3;7.1.3 Regressions;77 13.1.4;7.1.4 Clustering;79 13.1.5;7.1.5 Original Moments;83 13.1.6;7.1.6 Moment Matching;84 13.1.7;7.1.7 Pricing CDX Tranches;85 13.2;7.2 Clayton Approach;87 13.2.1;7.2.1 Construction of the Data;88 13.2.2;7.2.2 Original Moments;89 13.2.3;7.2.3 Moment Matching;89 13.2.4;7.2.4 Pricing CDX Tranches;90 13.3;7.3 Results comments;91 14;8 Conclusion;93 15;9 Bibliography;94 16;10 Appendix A;96 17;11 Appendix B;99 18;12 Appendix C;102