In the last decade, a considerable growth has been added to the volume of the credit risk
derivatives market. This growth has been followed by the current financial market
turbulence. These two periods have outlined how significant and important are the
credit derivatives market and its products. Modelling-wise, this growth has parallelised
by more complicated and assembled credit derivatives products such as mth to default
Credit Default Swaps (CDS), m out of n (CDS) and collateralised debt obligation
(CDO).
In this thesis, the Lévy process has been proposed to generalise and overcome the Credit
Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula
Model. One of the most important drawbacks is that it has a lack of tail dependence or,
in other words, it needs more skewed correlation. However, by the Lévy Factor Copula
Model, the microscopic approach of exploring this factor copula models has been
developed and standardised to incorporate an endless number of distribution alternatives
those admits the Lévy process. Since the Lévy process could include a variety of
processes structural assumptions from pure jumps to continuous stochastic, then those
distributions who admit this process could represent asymmetry and fat tails as they
could characterise symmetry and normal tails. As a consequence they could capture
both high and low events¿ probabilities.
Subsequently, other techniques those could enhance the skewness of its correlation and
be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the
'Stochastic Correlated Lévy Factor Copula Model' and 'Lévy Random Factor Loading
Copula Model'. Then the Lévy process has been applied through a number of proposed
Pricing Basket CDS&CDO by Lévy Factor Copula and its skewed versions and evaluated by V-FFT limiting and mixture cases of the Lévy Skew Alpha-Stable distribution and Generalized
Hyperbolic distribution.
Numerically, the characteristic functions of the mth to default CDS's and
(n/m) th to
default CDS's number of defaults, the CDO's cumulative loss, and loss given default
are evaluated by semi-explicit techniques, i.e. via the DFT's Fast form (FFT) and the
proposed Very Fast form (VFFT). This technique through its fast and very fast forms
reduce the computational complexity from O(N2) to, respectively, O(N log2 N ) and
O(N ).
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/4902 |
| Date | January 2010 |
| Creators | Fadel, Sayed M. |
| Contributors | Shepherd, Simon J., Kenc, Turalay |
| Publisher | University of Bradford, School of Engineering Design and Technology and School of Management |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Thesis, doctoral, PhD |
| Rights | <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>. |
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