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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 Mei en_US dc.contributor.author (Authors) 黃于騰 zh_TW dc.contributor.author (Authors) Huang, Yu Teng en_US dc.creator (作者) 黃于騰 zh_TW dc.creator (作者) Huang, Yu Teng en_US dc.date (日期) 2012 en_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) G0100354020 en_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) 100354020 zh_TW dc.description (描述) 101 zh_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/#G0100354020 en_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 obligation en_US dc.subject (關鍵詞) one factor copula model en_US dc.subject (關鍵詞) standardized skew student-t distribution en_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 Model en_US dc.type (資料類型) thesis en 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
