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題名 探討標準化偏斜Student-t分配關聯結構模型之抵押債務債券之評價
Pricing CDOs with Standardized Skew Student-t Distribution Copula Model
作者 黃于騰
Huang, Yu Teng
貢獻者 劉惠美
Liu, Hui Mei
黃于騰
Huang, Yu Teng
關鍵詞 抵押債務債券
單因子關聯結構模型
標準化偏斜Student-t分配
collateralized debt obligation
one factor copula model
standardized skew student-t distribution
日期 2012
上傳時間 2-Sep-2013 15:36:54 (UTC+8)
摘要 在市場上最常被用來評價抵押債務債券(Collateralized Debt Obligation, CDO)的分析方法即為應用大樣本同質性資產組合(Large Homogeneous Portfolio, LHP)假設之單因子關聯結構模型(One Factor Copula Model)。由過去文獻指出，自2008年起，抵押債務債券的商品結構已漸漸出現改變，而目前所延伸之各種單因子關聯結構模型在新型商品的評價結果中皆仍有改善空間。
     在本文中使用標準化偏斜Student-t分配(Standardized Skew Student-t distribution, SSTD)取代傳統的高斯分配進行抵押債務債券之分券的評價，此分配擁有控制分配偏態與峰態的參數。但是與Student-t分配相同，SSTD同樣不具備穩定的摺積(convolution)性質，因此在評價過程中會額外消耗部分時間。而在實證分析中，以單因子SSTD關聯結構模型評價擔保債務債券新型商品之分券時得到了較佳的結果，並且比單因子高斯關聯結構模型擁有更多參數以符合實際需求。
The most widely used method for pricing collateralized debt obligation(CDO) is the one factor copula model with Large Homogeneous Portfolio assumption. Based on the literature of discussing, the structure of CDO had been changed gradually since 2008. The effects for pricing new type CDO tranches in the current extended one factor copula models are still improvable.
     In this article, we substitute the Gaussian distribution with the Standardized Skew Student-t distribution(SSTD) for pricing CDO tranches, and it has the features of heavy-tail and skewness. However, similar to the Student-t distribution, the SSTD is not stable under convolution as well. For this reason, it takes extra time in the pricing process. The empirical analysis shows that the one factor SSTD copula model has a good effect for pricing new type CDO tranches, and furthermore it brings more flexibility to the one factor Gaussian copula model.
參考文獻 1. Amato, J.D. and Gyntelberg, J. (March 2005). CDS Index Tranches and The pricing of Credit Risk Correlations. BIS Quarterly Review.
     2. Andersen, L. and Sidenius, J. (Winter 2004). Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings. Journal of Credit Risk, Vol. 1, pp. 29-71.
     3. Burtschell, X., Gregory, J. and Laurent, L.-P. (April 2005). A Comparative Analysis of CDO Pricing Models. Working Paper.
     4. Dezhong, W., Rachev, S.T. and Fabozzi, F.J. (October 2006). Pricing Tranches of a CDO and a CDS Index: Resent Advances and Future Research. Working Paper.
     5. Dezhong, W., Rachev, S.T. and Fabozzi, F.J. (November 2006). Pricing if Credit Default Index Swap Tranches with One-Factor Heavy-Tailed Copula Models. Working Paper.
     6. Fernández, C. and Steel, M.F.J. (1998). On Bayesian modeling of fat tails and skewness. Journal of the American Statistical Association, 93(441), pp.359–371.
     7. Giot, P. and S. Laurent (2003). Value-at-Risk for Long and Short Trading Positions. Journal of Applied Econometrics, 18, pp. 641-664.
     8. Hansen, B.E. (1994). Autoregressive Conditional Density Estimation. International Economic Review, 35, pp. 705-730.
     9. Hull, J. and White, A. (Winter 2004). Valuation of a CDO and an n-th to Default CDS without a Monte Carlo Simulation. Journal of Derivatives, Vol. 12, No. 2, pp. 8-23.
     10. Kalemanova, A., Schmid, B. and Werner, R. (Spring 2007). The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing. The Journal of Derivatives, Vol. 14, pp. 80-93.
     11. Lambert, P. and Laurent, S. (2001). Modelling financial time series using GARCH-type models with a skewed Student distribution for the innovations. Discussion Paper 01-25, Institut de Statistique, Université catholique de Louvain, Louvain-la-Neuve, Belgium.
     12. Li, D.X. (April 2000). On Default Correlation: A Copula Function Approach. Journal of Fixed Income, 9(4), pp. 43-54.
     13. Nelsen, R.B. (2005). An Introduction to Copulas. Springer. Second Edition.
     14. O`Kane, D. and Livasey, M. (2004). Base Correlation Explained. Technical report, Quantitative Credit Research, Lehman Brothers.
     15. O`Kane, D. and Schlögl, L. (February 2001). Modelling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
     16. Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l`Institut de Statistique de L`Université de Paris 8, pp. 229-231.
     17. Torresetti, R., Brigo, D. and Pallavicini, A. (November 2006). Implied correlation in CDO tranches: a Paradigm to be handled with care. Working Paper.
     18. Vasicek, O. (2002). Loan PortfoUo Value. Risk, Vol. 12, pp. 160-162.
     19. Willemann, S. (2004). An Evaluation of the Base Correlation FrameWork for Synthetic CDOs. Working Paper.
     20. 林聖航(2012) 探討合成型抵押擔保債券憑證之評價，碩士學位論文
     21. 邱嬿燁(2007) 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，碩士學位論文
描述 碩士
國立政治大學
統計研究所
100354020
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100354020
資料類型 thesis
dc.contributor.advisor 劉惠美zh_TW
dc.contributor.advisor Liu, Hui Meien_US
dc.contributor.author (Authors) 黃于騰zh_TW
dc.contributor.author (Authors) Huang, Yu Tengen_US
dc.creator (作者) 黃于騰zh_TW
dc.creator (作者) Huang, Yu Tengen_US
dc.date (日期) 2012en_US
dc.date.accessioned 2-Sep-2013 15:36:54 (UTC+8)-
dc.date.available 2-Sep-2013 15:36:54 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2013 15:36:54 (UTC+8)-
dc.identifier (Other Identifiers) G0100354020en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/59288-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 100354020zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 在市場上最常被用來評價抵押債務債券(Collateralized Debt Obligation, CDO)的分析方法即為應用大樣本同質性資產組合(Large Homogeneous Portfolio, LHP)假設之單因子關聯結構模型(One Factor Copula Model)。由過去文獻指出，自2008年起，抵押債務債券的商品結構已漸漸出現改變，而目前所延伸之各種單因子關聯結構模型在新型商品的評價結果中皆仍有改善空間。
     在本文中使用標準化偏斜Student-t分配(Standardized Skew Student-t distribution, SSTD)取代傳統的高斯分配進行抵押債務債券之分券的評價，此分配擁有控制分配偏態與峰態的參數。但是與Student-t分配相同，SSTD同樣不具備穩定的摺積(convolution)性質，因此在評價過程中會額外消耗部分時間。而在實證分析中，以單因子SSTD關聯結構模型評價擔保債務債券新型商品之分券時得到了較佳的結果，並且比單因子高斯關聯結構模型擁有更多參數以符合實際需求。		zh_TW
dc.description.abstract (摘要) The most widely used method for pricing collateralized debt obligation(CDO) is the one factor copula model with Large Homogeneous Portfolio assumption. Based on the literature of discussing, the structure of CDO had been changed gradually since 2008. The effects for pricing new type CDO tranches in the current extended one factor copula models are still improvable.
     In this article, we substitute the Gaussian distribution with the Standardized Skew Student-t distribution(SSTD) for pricing CDO tranches, and it has the features of heavy-tail and skewness. However, similar to the Student-t distribution, the SSTD is not stable under convolution as well. For this reason, it takes extra time in the pricing process. The empirical analysis shows that the one factor SSTD copula model has a good effect for pricing new type CDO tranches, and furthermore it brings more flexibility to the one factor Gaussian copula model.		en_US
dc.description.tableofcontents 目錄
     摘要 I
     Abstract II
     表目錄 IV
     圖目錄 IV
     第一章 緒論 1
     第一節 研究背景與動機 1
     第二節 研究目的 2
     第三節 信用違約交換(Credit Default Swap, CDS) 2
     第四節 抵押債務債券(Collateralized Debt Obligation, CDO) 3
     第五節 合成型抵押債務債券(Synthetic CDOs) 4
     第六節 信用違約交換指數(Credit Default Swap Index) 5
     第七節 本文架構 6
     第二章 文獻回顧 7
     第一節 關聯結構模型(Copula Model) 7
     第二節 單因子關聯結構模型(One Factor Copula Model) 8
     第三節 Standardized Skew Student-t Distribution(SSTD) 9
     第三章 評價方法與應用LHP之單因子SSTD關聯結構模型 11
     第一節 合成型CDO的評價方法 11
     第二節 應用LHP之單因子高斯關聯結構模型 14
     第三節 SSTD定義與性質 15
     第四節 應用LHP之單因子SSTD關聯結構模型 17
     第四章 實證分析：評價DJ iTraxx信用違約交換指數 23
     第一節 評價商品介紹 23
     第二節 DJ iTraxx之分券評價結果 25
     第五章 結論與建議 28
     參考文獻 29
     
      
     表目錄
     表 4 1 DJ iTraxx Europe Series 9與DJ iTraxx Europe Series 15的市場報價 24
     表 4 2 DJ iTraxx Europe Series 9之市場報價與配適結果 25
     表 4-3 林聖航(2012)於DJ iTraxx Europe Series 9不同模型之評價結果 25
     表 4 4 DJ iTraxx Europe Series 15之市場報價與配適結果 26
     表 4-5林聖航(2012)於DJ iTraxx Europe Series 15不同模型之評價結果 26
     
     圖目錄
     圖 1 1 CDO流程架構 2
     圖 1 2合成型CDO流程架構 3
     圖 3 1參數v與參數ξ對SSTD機率密度函數之影響 15
     圖 3 2固定ρi下其他參數對Ω分配機率密度函數之影響 17
     圖 3 3固定各參數之下改變ρi對Ω分配機率密度函數之影響 18		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100354020en_US
dc.subject (關鍵詞) 抵押債務債券zh_TW
dc.subject (關鍵詞) 單因子關聯結構模型zh_TW
dc.subject (關鍵詞) 標準化偏斜Student-t分配zh_TW
dc.subject (關鍵詞) collateralized debt obligationen_US
dc.subject (關鍵詞) one factor copula modelen_US
dc.subject (關鍵詞) standardized skew student-t distributionen_US
dc.title (題名) 探討標準化偏斜Student-t分配關聯結構模型之抵押債務債券之評價zh_TW
dc.title (題名) Pricing CDOs with Standardized Skew Student-t Distribution Copula Modelen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Amato, J.D. and Gyntelberg, J. (March 2005). CDS Index Tranches and The pricing of Credit Risk Correlations. BIS Quarterly Review.
     2. Andersen, L. and Sidenius, J. (Winter 2004). Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings. Journal of Credit Risk, Vol. 1, pp. 29-71.
     3. Burtschell, X., Gregory, J. and Laurent, L.-P. (April 2005). A Comparative Analysis of CDO Pricing Models. Working Paper.
     4. Dezhong, W., Rachev, S.T. and Fabozzi, F.J. (October 2006). Pricing Tranches of a CDO and a CDS Index: Resent Advances and Future Research. Working Paper.
     5. Dezhong, W., Rachev, S.T. and Fabozzi, F.J. (November 2006). Pricing if Credit Default Index Swap Tranches with One-Factor Heavy-Tailed Copula Models. Working Paper.
     6. Fernández, C. and Steel, M.F.J. (1998). On Bayesian modeling of fat tails and skewness. Journal of the American Statistical Association, 93(441), pp.359–371.
     7. Giot, P. and S. Laurent (2003). Value-at-Risk for Long and Short Trading Positions. Journal of Applied Econometrics, 18, pp. 641-664.
     8. Hansen, B.E. (1994). Autoregressive Conditional Density Estimation. International Economic Review, 35, pp. 705-730.
     9. Hull, J. and White, A. (Winter 2004). Valuation of a CDO and an n-th to Default CDS without a Monte Carlo Simulation. Journal of Derivatives, Vol. 12, No. 2, pp. 8-23.
     10. Kalemanova, A., Schmid, B. and Werner, R. (Spring 2007). The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing. The Journal of Derivatives, Vol. 14, pp. 80-93.
     11. Lambert, P. and Laurent, S. (2001). Modelling financial time series using GARCH-type models with a skewed Student distribution for the innovations. Discussion Paper 01-25, Institut de Statistique, Université catholique de Louvain, Louvain-la-Neuve, Belgium.
     12. Li, D.X. (April 2000). On Default Correlation: A Copula Function Approach. Journal of Fixed Income, 9(4), pp. 43-54.
     13. Nelsen, R.B. (2005). An Introduction to Copulas. Springer. Second Edition.
     14. O`Kane, D. and Livasey, M. (2004). Base Correlation Explained. Technical report, Quantitative Credit Research, Lehman Brothers.
     15. O`Kane, D. and Schlögl, L. (February 2001). Modelling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
     16. Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l`Institut de Statistique de L`Université de Paris 8, pp. 229-231.
     17. Torresetti, R., Brigo, D. and Pallavicini, A. (November 2006). Implied correlation in CDO tranches: a Paradigm to be handled with care. Working Paper.
     18. Vasicek, O. (2002). Loan PortfoUo Value. Risk, Vol. 12, pp. 160-162.
     19. Willemann, S. (2004). An Evaluation of the Base Correlation FrameWork for Synthetic CDOs. Working Paper.
     20. 林聖航(2012) 探討合成型抵押擔保債券憑證之評價，碩士學位論文
     21. 邱嬿燁(2007) 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，碩士學位論文		zh_TW