在這篇論文中，我們將使用純統計的方法去分析在不同的相關係數(correlation)下，合成式債務抵押債券(synthetic CDOs)及一籃子違約交換(BDSs)的訂價。而之所以使用Copula function，因為它是目前所使用存活分析(survival analysis)方法中，可以將一個多維的分配，拆成單維的邊際函數及相關性的結構(dependent structure)兩個部分的一種方法，也是目前學術界非常熱門的一種統計方法。 使用常態Copula去找出標的債券的存活時間，利用它訂價synthetic CDOs及BDSs，可以發現不同的相關係數對於相關的信用衍生性金融商品如synthetic CDOs及BDSs影響很大，本篇最主要的目的就是討論相關係數對synthetic CDOs及BDSs的訂價影響程度。而不同的相關係數造成的風險，即所謂的相關係數風險，更是訂價信用衍生性金融商品所必須注意的。而本篇論文所推導求算出來的數據，更可以作為投資者或信用衍生性金融商品管理者一個參考的依據。 We analyzed the pricing of the Synthetic Collateralized Debt Obligations (synthetic CDOs) and Basket Default Swaps (BDSs) with different correction by using Statistical techniques in this paper. Copula function is a good way in present survival analysis method because it can divide multivariate distribution into two parts. One is marginal distribution, and the other is dependent structure. Therefore, copula is popularly used in many academic researches now. To specify the survival times of the underlying securities by using Normal Copula, and using the analyzing result to price the synthetic CDOs and BDSs. The credit derivatives products (such as synthetic CDOs and BDSs) with different correlation will affect pricing large. The correlation impact of underlying on prices of synthetic CDOs and BDSs is the purpose of this thesis. The risk caused by different correlation, that is correlation risk, we should pay more attention on it when we price the credit derivatives. Therefore, our results could be a reference for investors and manager of investing credit derivatives, no matter in pricing or risk management.
