信用連結債券的價值主要取決於所連結資產池內的資產違約情況，因此過去有許多文獻在評價時會利用Copula模擬各資產的違約時點，或是用Factor Copula估算他們在各時點下的違約機率。而本研究以Gaussian Factor Copula模型為主軸，對資產池違約機率做估計，以得到連結該資產池的信用連結債券價值。但過去文獻較常以給定參數的方式進行評價，本研究進一步利用市場實際資料估出模型參數並加入產業因子，以期達到符合市場的效果。 本研究利用已知的違約資訊對照模型結果，發現在給定原油價格成長率、產業GDP成長率及CAPM殘差之後，使用Factor Copula模型在資產池小且違約比例過高時容易低估損失，主要原因在於各資產的違約機率並非逼近1。且模型算出的預期損失會隨著距今時間變長而增加，但若資產池實際上沒有更多違約公司，模型的結果就可能會高估損失。而所有的變數又以參考價差對該商品價值的影響最大，因參考價差的數值取決於該公司的信用評等，因此可知信用連結債券價值主要還是與各公司信評有最大相關。 / The value of credit linked notes depends on whether the reference entities in the linked asset pool default or not, so some previous studies used Copula model to simulate the times to default or Factor Copula model to get the default probability. In this paper, with the Gaussian Factor Copula model adopted and industry factors taken into account, the default probability is estimated in order to obtain the value of the credit linked notes. Then, unlike other previous studies using the given parameters, this paper evaluated the parameters by using the model as well as market data, hoping to achieve the goal that results can reflect the real market situation. With real default information compared with the modeling results, three findings can be drawn given the growth rate of oil price, the growth rate of industrial GDP and the residuals of CAPM. First, the loss will be underestimated if the asset pool is small and the default proportion is too high mainly because not all the default probability approximates one. Second, expected default probability will be directly proportional to the time period between the present and the expected moment. So if there are not so many defaulting companies, then the loss might be overestimated. Last, the reference spread has the most impact on the product value among all the variables, and as we know, the reference spread of a company depends on its credit rating. Therefore, compared with other factors, credit rating remains the most essential to credit linked notes.

本論文在Li(2000)的Gaussian Copula的背景之下，將資產價值服從常態分配的假設改為服從Variance Gamma分配，利用Copula模型模擬債權群組內各個標的資產的違約時點，並利用蒙地卡羅抽取亂數的方法，取平均之後求得信用連結債券所連結的資產債權組合價值。除此之外，本論文比較假設資產價值服從常態分配、Student t分配和Variance Gamma分配下，計算求得的資產池價值。實證結果顯示，假設服從Variance Gamma分配最接近市場的真實違約資料。這是由於Variance Gamma分配具備Student t分配的厚尾性質，能有效捕捉常態分配缺少的尾端損失機率，並可調整偏態係數和峰態係數，可以求出更接近市場價值的評價結果。最後，在敏感度分析方面，改變影響資產池價值的兩大因子：平均違約回收率和資產間相關係數。結果顯示，當平均違約回收率高於0.7時，相關係數越高的債權群組，其資產池價值亦越高。若平均違約回收率越低且資產間相關係數越高的話，越容易出現一起違約的現象，因此資產池價值會下降。因此投資人在挑選信用連結債券時，應注意所連結的標的資產群組內資產報酬的相關性，最好避免相關性高的資產群組，以免金融海嘯來臨的時候，多個資產同時違約的情形發生。

The main goal of this thesis is to develop Bayesian model for studying the influence of covariate on dependence between random variables. Conditional copula models are flexible tools for modelling complex dependence structures. We construct Bayesian inference for the conditional copula model adapted to regression settings in which the bivariate outcome is continuous or mixed (binary and continuous) and the copula parameter varies with covariate values. The functional relationship between the copula parameter and the covariate is modelled using cubic splines. We also extend our work to additive models which would allow us to handle more than one covariate while keeping the computational burden within reasonable limits. We perform the proposed joint Bayesian inference via adaptive Markov chain Monte Carlo sampling. The deviance information criterion and cross-validated marginal log-likelihood criterion are employed for three model selection problems: 1) choosing the copula family that best fits the data, 2) selecting the calibration function, i.e., checking if parametric form for copula parameter is suitable and 3) determining the number of independent variables in the additive model. The performance of the estimation and model selection techniques are investigated via simulations and demonstrated on two data sets: 1) Matched Multiple Birth and 2) Burn Injury. In which of interest is the influence of gestational age and maternal age on twin birth weights in the former data, whereas in the later data we are interested in investigating how patient’s age affects the severity of burn injury and the probability of death.

The main goal of this thesis is to develop Bayesian model for studying the influence of covariate on dependence between random variables. Conditional copula models are flexible tools for modelling complex dependence structures. We construct Bayesian inference for the conditional copula model adapted to regression settings in which the bivariate outcome is continuous or mixed (binary and continuous) and the copula parameter varies with covariate values. The functional relationship between the copula parameter and the covariate is modelled using cubic splines. We also extend our work to additive models which would allow us to handle more than one covariate while keeping the computational burden within reasonable limits. We perform the proposed joint Bayesian inference via adaptive Markov chain Monte Carlo sampling. The deviance information criterion and cross-validated marginal log-likelihood criterion are employed for three model selection problems: 1) choosing the copula family that best fits the data, 2) selecting the calibration function, i.e., checking if parametric form for copula parameter is suitable and 3) determining the number of independent variables in the additive model. The performance of the estimation and model selection techniques are investigated via simulations and demonstrated on two data sets: 1) Matched Multiple Birth and 2) Burn Injury. In which of interest is the influence of gestational age and maternal age on twin birth weights in the former data, whereas in the later data we are interested in investigating how patient’s age affects the severity of burn injury and the probability of death.

在市場上最常被用來評價抵押債務債券(Collateralized Debt Obligation, CDO)的分析方法即為應用大樣本同質性資產組合(Large Homogeneous Portfolio, LHP)假設之單因子關聯結構模型(One Factor Copula Model)。由過去文獻指出，自2008年起，抵押債務債券的商品結構已漸漸出現改變，而目前所延伸之各種單因子關聯結構模型在新型商品的評價結果中皆仍有改善空間。 在本文中使用標準化偏斜Student-t分配(Standardized Skew Student-t distribution, SSTD)取代傳統的高斯分配進行抵押債務債券之分券的評價，此分配擁有控制分配偏態與峰態的參數。但是與Student-t分配相同，SSTD同樣不具備穩定的摺積(convolution)性質，因此在評價過程中會額外消耗部分時間。而在實證分析中，以單因子SSTD關聯結構模型評價擔保債務債券新型商品之分券時得到了較佳的結果，並且比單因子高斯關聯結構模型擁有更多參數以符合實際需求。 / The most widely used method for pricing collateralized debt obligation(CDO) is the one factor copula model with Large Homogeneous Portfolio assumption. Based on the literature of discussing, the structure of CDO had been changed gradually since 2008. The effects for pricing new type CDO tranches in the current extended one factor copula models are still improvable. In this article, we substitute the Gaussian distribution with the Standardized Skew Student-t distribution(SSTD) for pricing CDO tranches, and it has the features of heavy-tail and skewness. However, similar to the Student-t distribution, the SSTD is not stable under convolution as well. For this reason, it takes extra time in the pricing process. The empirical analysis shows that the one factor SSTD copula model has a good effect for pricing new type CDO tranches, and furthermore it brings more flexibility to the one factor Gaussian copula model.

根據以往探討評價合成型抵押擔保債務憑證之文獻研究，最廣泛使用的方法應為大樣本一致性資產組合(large homogeneous portfolio portfolio；LHP)假設之單因子常態關聯結構模型來評價，但會因為常態分配的厚尾度及偏斜性造成與市場報價間的差異過大，且會造成相關性微笑曲線現象。故像是Kalemanova et al.在2007年提出之應用LHP假設的單因子Normal Inverse Gaussian(NIG)關聯結構模型以及邱嬿燁(2007)提出NIG及Closed Skew Normal(CSN)複合分配之單因子關聯結構模型(MIX模型)皆是為了改善其在各分劵評價時能達到更佳的評價結果 ，然而過去的文獻在評價合成型抵押擔保債務憑證時，需要將CDS價差、各分劵真實報價之資訊導入模型，並藉由此兩種資訊進而得到相關係數及報價，故靜態模型大多為事後之驗證，在靜態模型方面，我們嘗試使用不同概念之CDS取法以及相對到期日期數遞減之概念來比較此兩種不同方法與原始的關聯結構模型進行比較分析，在動態模型方面，我們應用與時間序列相關之方法套入以往的評價模型，針對不同商品結構的合成型抵押擔保債券評價，並由實證分析來比較此兩種模型，而在最後，我們利用時間序列模型來對各分劵進行預測。

根據以往探討評價合成型抵押擔保債券之文獻研究，最廣為使用的方法應用大樣本一致性資產組合(large homogeneous portfolio portfolio ; LHP)假設之單因子常態關聯結構模型來評價，但會造成合成型抵押擔保債券憑證與市場報價間的差異過大，且會造成相關性微笑曲線現象。由文獻顯示，單因子關聯結構模型若能加入厚尾度或偏斜性能夠改善以上問題，且對於分券評價時也會有較好的效果，像是Kalemanova et al. (2007) 提出應用LHP假設之單因子Normal Inverse Gaussian(NIG)關聯結構模型以及邱嬿燁(2007)提出NIG及Closed Skew Normal(CSN)複合分配之單因子關聯結構模型(MIX模型)在實證分析中得到極佳的評價結果。自2008年起，合成型抵押擔保債券商品結構開始出現變化，而以往評價合成型抵押擔保債券價格時，商品結構皆為同一種型式。本文將利用常態分配、NIG分配、CSN分配以及NIG與CSN複合分配作為不同的單因子關聯結構模型，藉由絕對誤差極小化方法，針對不同商品結構的合成型抵押擔保債券評價，並進行模型比較分析。由最後實證分析結果顯示，單因子NIG(2)關聯結構模型優於其他模型，也證明NIG分配的第二個參數 β 能夠帶來改善的評價效果，此項證明與過去文獻結論有所不同，但 MIX模型則為唯一一個符合LHP假設的模型。 / Based on the literature of discussing the approach for pricing synthetic CDOs, the most widely used methods used application of Large Homogeneous Portfolio (LHP) assumption of the one factor Gaussian copula model, however , it fails to fit the prices of synthetic CDOs tranches and leads to the implied correlation smile. The literature shows that one factor copula model adding the heavy-tail or skew can improve the above problem, and also has a good effect for pricing tranches such as Kalemanova et al (2007) proposed the application of LHP assumption of one factor NIG copula model and Qiu Yan Ye (2007) proposed the application of LHP assumption of one factor NIG and CSN copula model. This article found that the structure of synthetic CDOs began to change since 2008. The past of pricing synthetic CDOs, the structure of synthetic CDOs are the same type, so this article will use different one factor copula model for pricing different structure of synthetic CDOs by using the absolute error minimization. This article will observe whether the above model can be applied in the new synthetic CDOs and implement of different type model for comparative analysis. The last empirical analysis shows that one factor NIG (2) copula model is superior to other models, more meeting the actual market demand, also proving the second parameter β of the NIG distribution able to bring about improvements in pricing results. This proving is different for the past literature conclusions. However, the MIX model is the only one in line with the LHP assumptions.

依據之前的文獻研究，市場上主要是在LHP (Large Homogeneous Portfolio) 假設下利用單因子常態關聯結構模式(One factor double Gaussian copula model) 評價擔保債權憑證 (Collateralized debt obligation, CDO)。但這會造成擔保債權憑證的評價與市場報價的差距過大，且會造成base correlation偏斜的情況。Kalemanova et al. (2007) 提出用Normal inverse Gaussian (NIG) 取代常態分配評價擔保債權憑證，此模型不但計算快速而且可以準確估計權益分券 (equity tranche) 的價格，但是它也過於高估了其它的分券的價格。 在本文中使用多變量封閉常態分配(Closed skew normal, 簡稱CSN) 分配取代NIG分配作擔保債權憑證分券的評價，CSN分配具有常態分配的性質，其線性組合仍具有封閉性的特質，且具有較多的參數以控制分配的偏態與峰態。但是與單因子常態關聯結構模式相同，多變量封閉常態分配的單因子關聯結構模式仍然無法估計的很準確，僅有在最高等級分券(senior tranche)的評價上有明顯的改進。 因此在本文中我們使用NIG與CSN複合分配之單因子關聯結構模式評價擔保債權憑證分券，在實例分析時得到極佳的評價結果，並且比單因子常態關聯結構模型具有更多的的參數以使模型更符合實際的需求。 / This article extends the Large Homogeneous Portfolio (LHP) and one factor double Gaussian copula approach for pricing CDOs. In the literature, the one factor double Gaussian copula model under LHP assumption fails to fit the prices of CDO tranches, moreover, it leads to the implied base correlation skew. Some researchers proposed using one factor double NIG copula model to price CDO tranches. It not only economizes on time but also fits the equity tranches exactly, but NIG models do not price other tranches well simultaneously. On the other hand, we substitute the NIG distribution with the Closed Skew normal (CSN) distribution. This family also has properties similar to the normal distribution, which is closure under convolution, and has extra parameters to control the shape. By using this model we get a better fit in the senior tranches, but it seriously overprices subordinate tranches. Thus we consider a mixture distribution of NIG and CSN distributions. The employments of this mixture distribution are comparatively well, and furthermore it brings more flexibility to the dependence structure.

The dissertation is composed of three empirical research papers analyzing the development on credit derivatives markets in recent years characterized by the global financial crisis in 2007- 2009 and subsequent European sovereign debt crisis. The basic motivation of the thesis is to contribute to the clarification of the turbulent development on credit derivatives markets. The first paper addresses main flaws of a collateralized debt obligation (CDO) market during the global financial crisis. The second paper examines the impact of the Greek debt crisis on sovereign credit default swap (CDS) reliability. The third paper analyzes whether a resulting change in CDS terms restored confidence in CDS contracts. An introductory chapter presents a common framework for the three papers. In the first paper, we examine valuation of a Collateralized Debt Obligation (CDO) in 2007- 2009. One Factor Gaussian Copula Model is presented and five hypotheses regarding CDO sensitivity to entry parameters are analyzed. Four main deficiencies of the CDO market are then articulated: i) an insufficient analysis of underlying assets by both investors and rating agencies; ii) investment decisions arising from the valuation model based on expected cash-flows and neglecting other factors such as mark-to-market losses; iii)...