Dissertation Writing Help - Valuation of CDO sensitivities and the dynamics of the iTraxx index before and after the financial crisis

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In this thesis, sensitivities and dynamical properties of CDO tranches are assessed. First a general introduction is given, in which CDO contracts are characterized and a benchmark index, the iTraxx, is presented. In the following chapter, fundamental mathematical concepts are introduced which form the basis for the following discussion. Then, the theory of CDO pricing is first introduced in a general setting. In the limiting case of a large homogenous CDS portfolio, analytical formulae are derived for the expected loss and the CDO tranche spread. The validity of the approximation as well as limiting cases are discussed.

The first major result of this thesis are the derivation of analytical formulae for the sensitivity of the tranche spread to changes of the underlying default probability and correlation. These formulae have not been published before. They allow for a fast and accurate risk assessment of CDO tranches and can be readily implemented e.g. in risk or trading systems.
In the following chapter the concepts of tranche and base correlation are introduced and discussed. It is shown that the tranche correlation exhibits a non-monotic behaviour for mezzanine tranches, leading to the observation that different tranche correlations may result in the same tranche spread. This ambiguity is resolved by considering the base correlation instead, which exhibits a monotonic behaviour.

In the last chapter, the dynamics of the tranche spread and base correlation of the iTraxx Europe index before and after the financial crisis is characterized. This analysis compromises the second focus of this thesis.

By applying a principal component analysis, it is shown that both before and after the financial crisis, both the tranche spread and base correlation are characterized by a strong co-movement across tranches. In addition, it is shown that before and after the financial crisis, the tranche spread and base correlation as a function of the detachment point exhibit a universal shape which changed during the financial crisis. This type of analysis has not been presented so far in the literature.