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    Pricing Basket of Credit Default Swaps and Collateralised Debt Obligation by Lévy Linearly Correlated, Stochastically Correlated, and Randomly Loaded Factor Copula Models and Evaluated by the Fast and Very Fast Fourier Transform

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    S. M. Fadel.pdf (2.468Mb)
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    Publication date
    2011-06-16
    Author
    Fadel, Sayed M.
    Supervisor
    Shepherd, Simon J.
    Kenc, Turalay
    Keyword
    Lévy Factor Copula
    ; Stochastic Correlated Lévy Factor Copula
    ; Lévy Random Factor Loading Copula
    ; Lévy Skew Alpha-Stable
    ; Generalized Hyperbolic
    ; Credit Default Swaps; CDS
    ; Collateralised debt obligation; CDO
    ; Fast Fourier Transform; FFT
    ; Very Fast Fourier Transform; VFFT
    Rights
    Creative Commons License
    The University of Bradford theses are licenced under a Creative Commons Licence.
    Institution
    University of Bradford
    Department
    School of Engineering Design and Technology and School of Management
    Awarded
    2010
    
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    Abstract
    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 ).
    URI
    http://hdl.handle.net/10454/4902
    Type
    Thesis
    Qualification name
    PhD
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    Theses

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