自從1997年東南亞金融風暴，許多跨國企業紛紛倒閉，造成一連串的金融危機連鎖效應，無論是金融機構或投資人皆蒙受巨大的損失，使得金融市場開始正視信用風險的問題，增加對風險管理的重視。除了信用風險的問題外，由於過去幾年利率是一路下滑，使反浮動利率的公司結構債廣受歡迎，如今利率反轉上升，結構債的價格就會下跌虧損，手上握有大筆結構債的基金或是投信公司便因此受到牽連，自2005年起開始發行的CBO，便是為了解決公司結構債的問題而發行。在此環境下，更加速了信用衍生性商品的發展。 資產證券化對金融機構來說，除了有可以將信用風險移轉給投資人的好處之外，也是減低籌資成本的一個管道。另外，還有能增加收入、克服資本限制以及流動性限制等優點。 但在CDO之債權群組中，當債務人間的違約情況具有相關性時，個別債務人發生違約將可能連帶使得整個CDO債務現金流量來源產生嚴重衝擊。因此，如何準確推估CDO與CDO-squared各個分券下合理之信用價差，乃本研究分析商品的重點。 本研究採用Gaussian Copula，並利用蒙地卡羅法以及Probability Bucketing Approach評價擔保債權憑證。雖然Probability Bucketing Approach與蒙地卡羅法所模擬出來的結果很接近，然而Probability Bucketing Approach卻是較有效率的評價方法。在Probability Bucketing Approach中，損失級距的切割將會影響到評價的準確性，切割地越細密，越能準確地計算出損失分配，進而得到精確的信用價差。本文亦發現違約回收率、相關係數、違約率以及債權重複性(Overlap)均會顯著影響分券信用價差的評價，顯示參數正確評估之重要性。

本文主要藉由逐次改變二次擔保債權憑證的內層分券金額佔資產池發行金額比例、內層分券下層信用保護金額佔資產池金額比例、資產池參考標的間違約相關性、到期期限、及違約回收率等五項影響二次擔保債權憑證損失發生機率的風險因子，結合蒙地卡羅模擬法及關聯結構法模擬交易架構中內層、外層分券不同損失率的發生機率，並利用彈性分析，衡量二次擔保債券憑證在每單位風險因子變動下，內層及外層分券的損失發生機率。 研究結果顯示，相同的風險因子對於內層與外層分券的損失發生機率的影響效果並不相同，此一現象有別於一般認為風險因子對內、外層分券損失發生機率影響效果相同的看法。此外，依據分券損失發生機率對每單位風險因子變化的彈性敏感性分析，分券損失發生機率受風險因子的影響可分為: 彈性為正且數值逐漸增加、彈性為正且逐漸下降、彈性為負且數值 (絕對值) 逐漸下降、及彈性為負且數值 (絕對值) 逐漸增加四類。外層夾層分券的損失發生機率對內層分券厚度占資產池金額比例的彈性為負，其數值 (絕對值) 隨著內層分券厚度占資產池金額比例的增加而下降。外層夾層分券的損失發生機率對內層分券下層信用保護金額佔資產池金額比例的彈性、及外層夾層分券的損失發生機率對參考標的違約回收率的彈性為負，且數值 (絕對值) 隨著下層信用保護比例及回收率的增加而上升。外層夾層分券的損失發生機率對參考標的違約相關係數的彈性為正，其數值隨著相關係數的增加而下降；外層夾層分券的損失發生機率對參考標的之到期期限的彈性為正，其數值隨著到期期限的增加而上升。 / The researchers of this study combined Monte Carlo simulation approach and copula method to change the following five risk factors: the thickness of inner CDOs tranche on CDO-squared, the subordination in master CDOs tranche, the correlation of reference entities, the maturity of reference entities, and the recovery rate of reference entities, with a purpose of simulating the loss possibility of CDOs-squared. Besides, by elasticity analysis, the researchers measured the change of loss rate according to the change of each risk factor per unit. The result of the study shows that the same risk factor has different influence on the loss rate of inner and master tranche of CDOs squared, which mismatches the general belief that the same risk factor has the same effect on the loss rate of inner and master CDOs tranche. In addition, according to the tranche loss possibility elasticity analysis to the risk factors, this research reveals that four categories can be made due to the effect which risk factors have on loss rate : positive and increasing elasticity, positive and decreasing elasticity, negative and increasing elasticity, and negative decreasing elasticity. We found that for the master mezzanine tranche: the elasticity of tranche loss possibility to the thickness of inner CDOs tranche of CDO-squared is negative and will decrease with the increasing thickness of inner CDOs tranche. The elasticity of tranche loss possibility to subordination in inner CDOs tranche and the elasticity of tranche loss possibility to the recovery rate of reference entities are both negative and will increase with the increasing subordination of inner CDOs tranche and the recovery rate of reference entities. The elasticity of the loss rate possibilities to the correlation of reference entities default is positive and will decrease with the increasing correlation of reference entities. The elasticity of loss possibilities to the maturity of reference entities is positive and will increase with the increasing maturity.

本文的主旨在評價二次擔保債權憑證。在條件獨立機率的假設下，我們使用factor copula的方法去刻劃違約事件間的相關係數，並提供了一個有效率的迴圈演算法去建構損失分配。本方法同時考慮違約數目及違約位置，同時亦可解決重疊性的問題。本文所建構的是Hull and White(2004)的延申模型。我們也對各參數作敏感度分析，以求得其對分券價差的影響。文中亦主張一些風險衝量指標，以量化重疊性的程度等風險議題。 / In this paper we address the pricing issues of CDO of CDOs. Underlying the conditional indepdence assumption we use the factor copula approach to characterize the correlation of defaults events. We provide an efficient recursive algorithm that constructs the loss distribution. Our algorithm accounts for the number of defaults, the location of defaults among inner CDOs, and in addition the degree of overlapping between inner CDOs. Our algorithm is a natural extension of the probability bucketing method of Hull and White (2004). We analyze the sensitivity of different parameters on the tranche spreads of a CDO-squared, and in order to characterize the risk-reward profiles of CDO-squared tranches, we introduces appropriate risk measures that quantify the degree of overlapping among the inner CDOs. Hull and White (2004) presents a recursive scheme known as probability bucketing approach to construct conditional loss distribution of CDO. However, this approach is insufficient to capture the complexities of CDO². In the case of the modeling of CDO, we are concerned for the probabilities of different number of defaults upon a time horizon t, e.g., the probabilities of 3 defaults happened within a year. With the mentioned probabilities, we can then calculate the expected loss within the time horizon, which enables us to figure out the spreads of CDO. However, in the modeling of CDO², an appropriate valuation should be able to overcome two more difficulties: (1) the overlapping structure of the underlying CDOs, and (2) the location where defaults happened, in order to get the fair spreads of CDO².