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研究生： 邱嬿燁
Chiou, Yan ya
論文名稱： 探討單因子複合分配關聯結構模型之擔保債權憑證之評價
Pricing CDOs with One Factor Double Mixture Distribution Copula Model
指導教授： 劉惠美
Liu, Hui mei
學位類別： 碩士
Master
系所名稱： 商學院 - 統計學系
Department of Statistics
論文出版年： 2008
畢業學年度： 96
語文別： 英文
論文頁數： 50
中文關鍵詞： 擔保債權憑證 、單因子關聯結構模式 、多變量封閉常態分配 、複合分配
外文關鍵詞： collateralized debt obligation, one factor copula model, closed skew normal distribution, mixture distribution
相關次數： 點閱：212  下載：229 
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    • 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.

    Chapter 1 Introductions 1
    1.1. What Does Asset Securitization Means? 2
    1.2. Collateralized Debt Obligations 3
    1.2.1. Synthetic CDOs 4
    1.3. Credit Default Swaps 5
    1.3.1. Credit Default Swaps Index 5
    Chapter 2 Literature Review 8
    2.1. Binomial Expansion Technique (BET) 8
    2.2. Copula Model 9
    2.3. One Factor Copula Model 9
    2.4. Normal Inverse Gaussian Distribution 11
    2.5. Closed Skew Normal Distribution 11
    Chapter 3 One Factor Double NIG Copula Model for Pricing CDOs 13
    3.1. The Loss Distribution and Fair CDO Premium 13
    3.2. Copula Method 15
    3.3. One Factor Copula Model 17
    3.4. Main Properties of the NIG Distribution 18
    3.5. LHP Approximation in the One Factor Double NIG Copula Method 21
    Chapter 4 One Factor Double Mixture Distribution Copula Models for Pricing CDOs 24
    4.1. The Introduction of Closed Skew Normal Distribution 24
    4.2. One Factor Double CSN Copula Model 29
    4.3. One Factor Double Mixture Distribution of NIG and CSN Distribution Copula Model 34
    Chapter 5 Numerical Results: Pricing the DJ iTraxx 36
    5.1. Price iTraxx Tranches with the Four Models 36
    5.2. The Loss Distributions for Four Models 38
    5.3. Comparison of the Compound and Base Correlation 41
    5.4. Conclusion 43
    References 45
    Appendix 48

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