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Über dieses Buch

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.



1. Introduction

The financial crisis which started in 2007 has shown a comprehensive undervaluation by the Financial Institutions, of the risk involved in credit derivatives, such as collateralized debt obligations (CDOs).
The complexity of CDOs, combined with inadequate tools for modeling the risk, solicited the formation of a more robust approach to measure and price them.
Enrico Marcantoni

2. CDO: general characteristics

Securitization has started to play a huge role in the market of the structured products since the beginning of the 1990s, reaching significant levels in the last decade. The terms "securitization" refers to the transfer of an asset pool into tradable securities.
Enrico Marcantoni

3. Credit Risk Modeling

This chapter will present an overview of the credit risk modeling literature. It will present the general setup which the most common models share and the derivation of the models themselves. This overview contains the models, which will be in the centre of the empirical part of the next chapters.
Enrico Marcantoni

4. Copula functions and dependency concepts

Modeling default of several obligors implies modeling the default probability of the single obligor as well as the dependence structure between obligors.
A general distribution function, in our example a distribution function of a portfolio of several obligors, contains information about both marginal obligor distribution and their correlation structure. However these two parts are implicit in it. A copula function is a tool, allowing a way of isolating the description of such dependence structure.
Enrico Marcantoni

5. Moment Matching Approximation

In this chapter will be presented the "Analytical Pricing of CDOs in a Multi-factor Setting by a Moment Matching Approach" by Castagna, Mercurio and Mosconi (2012).
The model will be extended and implemented in the next two chapters.
Enrico Marcantoni

6. Extensions to the Model

In this Chapter will be presented two extensions I bring to the original model of Castagna et al., representing the main research targets of the thesis.
In the first extension I have rewritten the original model in terms of Archimedean Copulas. The dependencies structure of the original loss distribution has been rewritten in terms of Clayton Copula. The proxy distribution used is the Large Portfolio loss distribution for Archimedean copulas, from which I derived the moments (Proposition 6.1 and 6.2). Finally I derived the ETL formula for this setup (Proposition 6.3).
Enrico Marcantoni

7. Implementation

In the following chapter a numerical implementation of the Moment Matching techniques will be proposed, aiming to price the tranches of a CDX.
In the first section the pricing of the CDX tranches will be obtained by implementing the original model of Castagna et al. reported in chapter 5. This is the first time that the method is numerically implemented with real data. The first implementation will be denoted in the following as Gaussian, referring to the dependence chosen.
Enrico Marcantoni


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