本文以Hull and White(2004)與Anderson and Sidenius(2004)之理論模型為基礎，在單因子連繫結構模型(one-factor copula model)下，探討風險因子改變其分配之假設或考慮隨機風險因子承載係數(random factor loading)時，對擔保債權憑證之損失分配乃至於各分券信用價差所造成之影響。此外，文中亦將模型運用於實際市場資料上，對兩組Dow Jones iTraxx EUR 五年期之指數型擔保債權憑證(index tranches)與一組Dow Jones CDX NA IG指數型擔保債權憑證進行評價與分析。我們發現在三組資料下，使用double t-distribution 連繫結構模型(double t-distribution copula model)與隨機風險因子承載係數模型(random factor loading model)皆能比使用高斯連繫結構模型(Gaussian copula model)更接近市場上之報價。最後，在評價指數型擔保債權憑證外，本研究亦計算各分券之隱含違約相關係數(implied correlation)與基準違約相關係數(base correlation)。

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 ).

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 ).

本研究以Amraoui & Hitier (2008)隨機回復率模型(BNP model)以及Andersen and Sidenius(2004)隨機風險因子承載係數模型(RFL model)為基礎，進行對分劵信用價差、債劵群組累積損失機率分配，以及對基準違約相關係數的影響等分析。我們發現當回復率改成動態後可以反映更多系統風險，權益分劵信用價差絕大多數都會下降。在累積損失機率分配方面加入BNP後變為較平滑；改用RFL則會使機率分配在小額損失處又產生一次起伏；同時考量BNP與RFL會使小額損失發生機率減少、極端損失機率增加。實作三組市場資料時，發現不管市場違約機率高或低，共同考慮BNP與RFL的模型在四個模型中是最適合擬和市價的，顯示在市價的校準上有更多彈性，特別是在承擔名目本金60~100%先償分劵的校準上只有共同考慮BNP與RFL的模型能發揮功效。