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博碩士論文 etd-0601107-040500 詳細資訊
Title page for etd-0601107-040500
論文名稱
Title
以光譜分解進行一籃子違約交換之評價
Pricing Basket Default Swap with Spectral Decomposition
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
31
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2006-07-01
繳交日期
Date of Submission
2007-06-01
關鍵字
Keywords
光譜分解、關聯結構、一籃子違約交換
Spectral Decomposition, Copula, Basket Default Swap
統計
Statistics
本論文已被瀏覽 5757 次,被下載 12
The thesis/dissertation has been browsed 5757 times, has been downloaded 12 times.
中文摘要
Cholesky Decomposition是處理多資產相關性時一個常用的技巧,但是其有相關係數矩陣所有特徵值不得小於0的限制條件。因此利用Spectral Decomposition的方法可以在相關係數矩陣為非正定矩陣時,計算出一個半正定的代替矩陣,因此在處理這種多資產相關性時,建議可以先使用Spectral Decomposition的方法來調整原始相關係數矩陣。惟當資產個數增加時,利用Spectral Decomposition所得到的新的半正定矩陣與原始矩陣的差異亦越來越大,使用者應斟酌契約中標的資產的個數來決定是否使用此方法。
Abstract
Cholesky Decomposition is usually used to deal with the correlation problem among a financial product's underlying assets. However, Cholesky Decomposition inherently suffers from the requirement that all eigenvalues must be positive. Therefore, Cholesky Decomposition can't work very well when the number of the underlying assets is high. The report takes a diffrent approach called spectral Decomposition in attempt to solve the problem. But it turns out that although Spectral Decomposition can meet the requirement of all-positive eigenvalue, the decomposision error will be larger as the number of underlying asset getting larger. Thus, although Spectral Decomposition does offer some help, it works better when the number of underlying assets is not very large.
目次 Table of Contents
目錄
第一章 緒論……………………………………………1
研究動機與背景………………………………………1
第二章 相關文獻探討…………………………………3
信用風險模型之探討…………………………………3
Spectral Decomposition分解法……………………4
第三章Basket Default Swaps之介紹與評價………5
First-to-default………………………………………5
First-x-to-default及評價方式…………………………6
第四章 研究方法………………………………………9
Copula方法介紹………………………………………9
Basket Default Swaps 之評價數值模擬步驟……...11
Spectral Decomposition法…………………………15
第五章 模擬分析………………………………………17
模擬之假設與結果……………………….……………17
敏感度分析……………………………….……………19
第六章 結論與建議……………………………………22
參考文獻………………………………………………23
附錄……………………………………………………25
表目錄
圖一…………………………………………………5
圖二…………………………………………………6
表一…………………………………………………6
表二…………………………………………………7
表三…………………………………………………19
表四…………………………………………………19
表五…………………………………………………20
表六…………………………………………………20
表七…………………………………………………21
表八…………………………………………………21
參考文獻 References
中文部份
1.儲蓉,2004,金融資產證券化:理論與案例分析, 金融研訓院出版
2.儲蓉,2005,進入信用衍生性金融商品殿堂,金融研訓院出版
3.陳松男,2006,信用連結商品個案之分析與評價,新陸書局經銷
4.蔡麗君,2004,隨機違約強度模型下CDO之評價與分析-Copula方法,國立政治大學金融研究所碩士論文
5.林晚容,2004,單一分券違約信用交換與單一分券擔保債權憑證之評價-Copula方法,國立政治大學經濟研究所碩士論文
6.葉倍宏, 2006 MATLAB 7 程式設計-應用篇,全華科技
英文部分
1. Brigo, D. and Mercurio, F. (2001), “Interest rate models theory and practice” Springer Finance
2. Chen, Z. and Glasserman, P. (2006), “Fast pricing of basket default swaps”, Columbia University Financial Engineering Reports
3. Duffie, D. (1998), “First-to-default vailuation“, Stanford University Working Paper
4. Duffie, D.and Singleton, K. (1999), “Simulating correlated defaults“, Working paper, Graduate School of Business, Stanford University
5. Esposito, M. (2002), “Basic Insights in Pricing Basket Credit Derivatives”, Economic Notes Volume 31
6. Laurent, J.P. & Gregory, J. (2002), “Basket Default Swaps, CDOs and one-factor copulas”, Available from http://www.maths.univ-evry.fr/mathfi/JPLaurent.pdf, September 2003
7. Lee, C.W. (2004), ”Pricing collateralized Debt Obligation: A model of common shock for loss functions”, Volume 6, Number 3, Nov-2004風險管理學報
8. Leo, S. (2002), “Linear algebra with applications”, New York : Macmillan Pub. Co
9. Li, D.X. (2000), “On default correlation: A copula approach”, Journal of Fixed Income
10. Marrison, C. (2002), The fundamentals of risk measurement, New York: McGraw-Hill
11. Thompson, J. (2000), “Simulation : a modeler's approach” New York : Wiley.
12. Rebonato, R. & Jackel, P. (1999) “The most general methodology to create a valid correlation matrix for risk management and option pricing purposes”, Quantitative Research Centre of the NatWest Group
13. Skora, R. (1998), “The credit default swap”
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