Modeling correlation structure for collateralized debt obligations and determining the underlying credit default swap spread equations


Thesis Type: Doctorate

Institution Of The Thesis: Middle East Technical University, Turkey

Approval Date: 2015

Thesis Language: English

Student: Deniz İlalan

Consultant: AZİZE HAYFAVİ

Abstract:

Pricing complex financial derivatives such as collateralized debt obligations (CDOs) is considered as the main reason triggering the 2008 financial crisis. The correlation structure related to the credit risks involved in a portfolio for pricing issues have been tried to overcome via a Gaussian copula framework first introduced by David Li. This approach regards the correlation among the credit risks as normally distributed, enabling us to derive analytical solutions. However, despite its simplicity, this Gaussian copula approach is far from reality, which caused mispricing of the tranches of CDOs. This phenomenon is called the correlation smile. Firstly, this thesis approaches the correlation smile issue by considering a Lévy copula framework. When this is introduced to pricing equations we saw that the correlation smile is “corrected”. Thus we came up with a more accurate model of pricing the above mentioned tranches. The second part of the thesis aims to model the Itraxx 125 CDS spreads for different sectors which comprise the CDO. Here, we introduce an autocorrelation one process together with finite number of Fourier series terms. Introduction of Fourier series to estimate the dynamics of the process is not done in an ad-hoc manner or as done before in dealing with seasonality. Here the moving average is transformed to a “moving and fluctuating” average by the help of Fourier series. The rationale behind this “moving and fluctuating” averaging technique is due to its capability in removing high frequency structures like breaks, spikes and stochastic volatility. Instead of adding jump structures to the model which makes the parameter estimation quite cumbersome, our model in discrete time can easily be transformed to a well-known mean reverting continuous time process. Moreover, our alternative model