Credit Derivatives
The Hidden Correlation of Collateralized Debt Obligations
Master Thesis in "Mathematical Finance", Oxford (2009)
We propose a model for the correlation structure of reference portfolios of collateralized debt obligations. The model is capable of exhibiting typical characteristics of the implied correlation smile (skew, respectively) observed in the market. Moreover, it features a simple economic interpretation and is computationally inexpensive as it naturally integrates into the factor model framework.
Assessment and Recognition of Counterparty Risk in Derivatives
Master Thesis in „Quantitative Finance“, Frankfurt School of Finance & Management (2009)
This document is presented as the Master Thesis in the framework of the program "Master
of Quantitative Finance" at the Frankfurt School of Finance and Management (FSFM). The
aim is to arrive at a well founded proposition of best practice in credit risk assessment and
recognition for derivatives portfolios. To this end an overview of the relevant regulatory requirements, available market information and mathematical tools is given. It is shown that the
most significant limitation of precision in the assessment of counterparty risk in derivatives
stems from the extraction of probabilities of default from market data. The main result of the
thesis is a quantitative estimate of the precision achieved in various valuation steps.
The findings of the thesis are comprised in three main chapters. A qualitative part summarizes
the regulatory and statutory specifications, gives an overview over the economic background
and outlines the market information available. Subsequently, the theoretical and methodological
background of the assessment of counter party risk related quantities is described. In a
quantitative part example applications are given and analyzed with respect to their mathematical
precision and applicability.
Approaches to Models of Default Dependence with a View on Basket Default Swaps and CDOs
Master Thesis in „Quantitative Finance“, Frankfurt School of Finance & Management (2008)
This work is devoted to various approaches to models of default dependence used in the treatment of products associated with portfolios of credit risk.
In a brief introduction to copula functions we cover dependence measures, the connection of extreme events and so-called tail dependence and a family of copula functions with radial asymmetry.
In the main part of this thesis we present the ingredients necessary to price basket CDS and CDO tranches in the context of factor models. We give a survey of different factor model specifications and show how these allow computing the individual probabilities of default. An overview of various useful techniques to compute the conditional loss distribution as well as an introduction to the computation of credit spread sensitivities in factor models is also provided.
The factor models discussed here are essentially static one-period models primarily useful to derive the loss distribution of a given portfolio for a single fixed maturity. While this is often sufficient for the valuation of plain vanilla contracts, it becomes a drawback when one would like to consider more sophisticated products. We therefore consider attempts to go beyond static factor models. Starting our discussion with full-fledged structural models, we conclude this survey with simplifying approaches trying to retain some dynamical properties while keeping the attractive features of static models.
Modelling Collateralized Debt Obligations using Variance Gamma Processes
Master Thesis in "Mathematical Finance", Oxford (2008)
This thesis deals with the valuation of synthetic Collateralized Debt Obligation tranches with
a Variance Gamma factor copula model. After a brief review of the valuation techniques for
synthetic CDO tranches, a two and a three parameter factor copula model are introduced.
Both model variants involve the combination of marginal Variance Gamma distributions via
a simple correlation structure. Calibrating these models to iTraxx tranche spreads shows
a convincing fit using one parameter set only. Consistent pricing of non-standard tranches
is thus possible. Furthermore, the behaviour of the tranche spreads as a function of the
model parameters is intuitive and the calibrated model parameters are stable through time.
Though, during the subprime crisis one observes fluctuating parameters reflecting strong
market dynamics. The usage of the Variance Gamma model for synthetic CDO valuation
finally allows for a powerful parameter-based risk management.
Valuation of nth to Default Swaps
Master Thesis in "Mathematical Finance", Oxford (2004)
This thesis deals with the valuation of the nth to default swap in the Gaussian copula model. After a brief description of the model and the numerical problems that arise in the naive Monte Carlo pricing algorithm, two more efficient valuation methods are presented.
Valuation of Multi-Name Credit DerivativesMaster Thesis in "Mathematical Finance", Oxford (2003)The subject of this thesis is modelling and valuation of multi-name credit derivatives such as basket default swaps and basket CDS tranches. After a description of the relevant products, models for valuation are presented. The key idea of modelling correlated default is the usage of copulae. In this thesis the valuation models are set up with Gaussian normal-, Student t- and Clayton copulae. Two different methods for valuation are described: The first is the standard Monte Carlo method for simulating the default times, with which multi-name credit derivatives can be priced. In the second approach the correlation structure is simplified by a factor copula model, in which semi-explicit fomulae for valuation of the multi-name credit products can be formulated. In this thesis the Monte Carlo valuation approach is implemented for the Gaussian normal-, the Student t- and the Clayton copula; the semi-explicit approach is implemented for the Gaussian normal copula. The implemented valuation methods are used to price a simple three credit basket and a real world basket CDS tranche. It is investigated what influence parameters like correlation and recovery rates have on the spread of credit products. For the Student t- and Clayton copula correlation structure the dependence of the spread on the copula parameters is examined.
