臺灣博碩士論文加值系統

八十年代儲蓄和貸款危機與九十年代亞洲金融危機，都是發生信用違約事件
所導致的金融市場危機，不僅造成一般公司發生倒閉事件，更使得金融機構因信
用違約發生而產生巨額的損失，因此如何處理信用風險成為市場上很重要的一環。
因此市場上陸續出現各類型的信用衍生性金融商品，以提供信用違約避險之用，
擔保債權憑證就是其中一種信用衍生性金融商品。
先前的研究中，Li(2000)利用 Gaussian copula 計算違約時間點，透過蒙地卡
羅模擬法來計算無風險套利價格。本研究將先研究各種 copula 模型的特色，和
以模擬分析對參數因子進行敏感度分析，再進行實證研究，探討該選擇何種
copula模型來評價CDO、避險和風險控管較為合適。
本文的模擬分析結果顯示：資產相關係數和回復率這兩個參數因子，對CDO
商品的不同分券會有不同的影響關係，要視分券所涵蓋資產比例而定，且這兩個
參數因子對分券的公平價差都有明顯的影響。
在實證研究方面結果顯示：同屬於 Elliptical copula 家族的 Gaussian copula
和 Student’s T copula模型和 Archimedean copula家族中的 Clayton copula模型，
這三種 copula模型在評價 CDO商品時，無論在分券的公平價差以及分券損失敘
述統計量的結果差異都不大。因此在選擇 copula 模型去評價、避險和風險管理
時，必須因資料所服從的分配來改變不同的copula模型。Student’s T copula較能
捕捉到連結資產的厚尾現象和連結資產間的尾部相關特性，且實際市場報酬資料
大多不服從常態分配，而是服從具有厚尾型態的 Student’s T 分配。而 Clayton
copula模型雖然具有尾部相關性但 Clayton copula模型不能捕捉到右尾的尾部相
關性(upper tail dependence)。Multivariate Gaussian Distribution 搭配邊際分配為
Student’s T Distribution 模型(MGmT)分配在尾部具有較小的機率，反之，
Multivariate Student’s T Distribution 搭配邊際分配為 Gaussian Distribution 模型
(MTmG)分配在尾部的機率比較大。

Due to its versatility, collateralized debt obligation (CDO) products have gained
its notorious popularity in the market. One important issue of CDO products is on the
effectiveness of its credit risk management. Due to its structural characteristic of the
assets in the asset pool upon which the CDO depends, we are mainly focus on the
discussion of robustness evaluation under variety of copulas and marginal distribution.
Through simulation and empirical studies, the main aim of this paper is to explore the
impact on fair spread calculation for the choices of two elliptical copulas, Gaussian
copula and t copula, treated with Gaussian and Student’s T marginal distribution.
Our simulation study shows that the pricing difference between the two copulas
is minor compare to the choice of marginal distribution. Finally, based on the daily
stock returns and market spreads on Dow Jones EuroStoxx 50 CDO, our empirical
results also support that the Student’s T copula together with Student’s T marginal
distribution is preferred due to its greater flexibility in capturing the wider distributed
spread and tail dependence. Multivariate Gaussian Distribution treated with Marginal
Student’s T has a small probability in the tail ; Multivariate Student’s T Distribution
treated with Marginal Gaussian has a big probability in the tail. This feature makes
these models have a better fit in extreme financial circumstances.

目錄
壹、緒論 ................................................................................................................................... 1
一、研究動機與目的 ........................................................................................................... 1
二、研究流程與架構 ........................................................................................................... 3
貳、文獻回顧 ........................................................................................................................... 4
一、文獻探討 ....................................................................................................................... 4
二、資產證券化 ................................................................................................................... 4
三、信用衍生性金融商品 ................................................................................................... 6
四、擔保債權憑證介紹 ....................................................................................................... 8
參、擔保債權憑證評價模型 ................................................................................................... 9
一、擔保債權憑證評價模型 ............................................................................................... 9
二、Copula 模型介紹 ........................................................................................................ 13
肆、模擬分析 ......................................................................................................................... 17
一、模擬結果 ..................................................................................................................... 18
二、參數敏感度分析 ......................................................................................................... 19
伍、實證研究 ......................................................................................................................... 22
一、資料描述 ..................................................................................................................... 22
二、實證結果 ..................................................................................................................... 23
陸、結論 ................................................................................................................................. 30
參考文獻 ................................................................................................................................. 31

Burtschell X., Grefory J., and Laurent J.P., “A Comparative Analysis of CDO Pricing
Models under the Factor Copula Framework”, 2009, Journal of
Derivatives,16,9-37.
Duffie D. and Garleanu N., “Risk and Valuation of Collateralized Debt Obligations”,
2001, Financial Analysts Journal, 57(1), 41-59.
Duffie D. J., and Singleton K. J., “Modeling Term Structures of Defaultable Bonds.”,
1998, Review of Financial Studies, 12, 687-720.
Duffie D. J., and Singleton K. J., “Simulation Correlated Defaults.”, 1999, Palo Alto,
CA : Stanford University.
Geske R., “The Valuation of Corporate Liabilities as Compound Options.”, 1977,
Journal of Financial and Quantitative Analysis, 541-552.
Gregory J., “Credit Dericatives: The Definitive Guide ”, 2003, London, Risk Books.
Leland H. E., “Corporate Debt Value, Bond Covenants and Optimal Capital
Structure.”, 1994, Journal of Finance, 1213-1252.
Li D.X., “On Default Correlation: A Copula Function Approach”, 2000, The Journal
of Fixed Income, 9(4), 43-54.
Longstaff F. A. and Schwartz E.S., “A Simple Approach to Valuing Risky Fixed and
Floating Rate Debt.”, 1995, Journal of Finance, 789-819.
Madan D. and Unal H., “Pricing the Risks of Default.”, 1999, Review of Derivatives
Research, 121-160.
Merton R., “On the Pricing of Corporate Debt : The Risk Structure of Interest Rate.”,
1974, Journal of Finance, 449-470.
Nelsen R. B., “An Introduction to Copulas.”, 1999, New York : Springer-Verlag.
Sklar A., “Fonctions de Repartition a n Dimensions et Leurs Marges”, 1959,
Publications de l’Institut de Statistique de L’Universite de Paris, 8, 229-231.
林意珊, “市場指數型擔保債權憑證之評價─Implied Copula 法之應用”,
2008。
陳文達, 李阿乙, 廖咸興, “資產證券化-理論與實務”, 2002, 初版, 台北, 智勝
文化。
廖四郎，擔保債權憑證(CDO)之評價與分析，演講投影片，2008。