Marcantoni Collateralized Debt Obligations

A Moment Matching Pricing Technique based on Copula Functions
2014
ISBN: 978-3-658-04846-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 102 Seiten

Reihe: BestMasters

The author focuses on a method to price Collateralized Debt Obligations (CDO) tranches. The original method is developed by Castagna, Mercurio and Mosconi in 2012. The Thesis provides an extension of the original work by generalizing the Gaussian dependence in terms of Copula functions. In particular the model is rewritten for the specific case of the Clayton copula. The method is applied to price the tranches of a CDX. By comparing the tranches prices, it is possible to notice that the Clayton approach leads to smaller equity and mezzanine tranches. The senior and super senior tranches levels are higher when the dependence is modeled by a Clayton copula.

Enrico Marcantoni obtained his Master Degree in Quantitative Finance at the University of Bologna (Italy) taking part in a Double Degree Program in collaboration with the Master in Quantitative Asset and Risk Management at the University of Applied Sciences (bfi) Vienna (Austria).

Autoren/Hrsg.

Marcantoni, Enrico

Inhaltsverzeichnis

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