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題名 探討合成型抵押擔保債券憑證之評價
Pricing the Synthetic CDOs
作者 林聖航
貢獻者 劉惠美
林聖航
關鍵詞 合成型抵押擔保債權憑證
單因子關聯結構模型
NIG分配
CSN分配
synthetic CDOs
one factor copula model
NIG distribution
CSN distribution
日期 2011
上傳時間 30-Oct-2012 10:58:16 (UTC+8)
摘要 根據以往探討評價合成型抵押擔保債券之文獻研究，最廣為使用的方法應用大樣本一致性資產組合(large homogeneous portfolio portfolio ; LHP)假設之單因子常態關聯結構模型來評價，但會造成合成型抵押擔保債券憑證與市場報價間的差異過大，且會造成相關性微笑曲線現象。由文獻顯示，單因子關聯結構模型若能加入厚尾度或偏斜性能夠改善以上問題，且對於分券評價時也會有較好的效果，像是Kalemanova et al. (2007) 提出應用LHP假設之單因子Normal Inverse Gaussian(NIG)關聯結構模型以及邱嬿燁(2007)提出NIG及Closed Skew Normal(CSN)複合分配之單因子關聯結構模型(MIX模型)在實證分析中得到極佳的評價結果。自2008年起，合成型抵押擔保債券商品結構開始出現變化，而以往評價合成型抵押擔保債券價格時，商品結構皆為同一種型式。本文將利用常態分配、NIG分配、CSN分配以及NIG與CSN複合分配作為不同的單因子關聯結構模型，藉由絕對誤差極小化方法，針對不同商品結構的合成型抵押擔保債券評價，並進行模型比較分析。由最後實證分析結果顯示，單因子NIG(2)關聯結構模型優於其他模型，也證明NIG分配的第二個參數 β 能夠帶來改善的評價效果，此項證明與過去文獻結論有所不同，但 MIX模型則為唯一一個符合LHP假設的模型。
Based on the literature of discussing the approach for pricing synthetic CDOs, the most widely used methods used application of Large Homogeneous Portfolio (LHP) assumption of the one factor Gaussian copula model, however , it fails to fit the prices of synthetic CDOs tranches and leads to the implied correlation smile. The literature shows that one factor copula model adding the heavy-tail or skew can improve the above problem, and also has a good effect for pricing tranches such as
Kalemanova et al (2007) proposed the application of LHP assumption of one factor NIG copula model and Qiu Yan Ye (2007) proposed the application of LHP assumption of one factor NIG and CSN copula model. This article found that the structure of synthetic CDOs began to change since 2008. The past of pricing synthetic CDOs, the structure of synthetic CDOs are the same type, so this article will use different one factor copula model for pricing different structure of synthetic CDOs by using the absolute error minimization. This article will observe whether the above model can be applied in the new synthetic CDOs and implement of different type model for comparative analysis. The last empirical analysis shows that one factor NIG (2) copula model is superior to other models, more meeting the actual market demand, also proving the second parameter β of the NIG distribution able to bring about improvements in pricing results. This proving is different for the past literature conclusions. However, the MIX model is the only one in line with the LHP assumptions.
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. (2004 winter). “Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings.” Journal of Credit Risk, Vol. 1, pp. 29-71.
3. Arellano-Valle, R.B., Gómez, H.W. and Quintana, F. A. (2004). “A New Class of Skew-Normal Distributions.” Communications in Statistics-Theory and Methods, Vol. 33, pp.1465-1480.
4. Azzalini, A. (2005). “The Skew-normal Distribution and Related Multivariate Families.” Scandinavian Journal of Statistics, Vol. 32, pp.159-188.
5. Barndorff-Nielsen, O.E. (1997). “Normal Inverse Gaussian Distributions and Stochastic Volatility Modeling.” Scandinavian Journal of Statistics, Vol. 24, pp.1-13.
6. Black, Fischer and John C. Cox, "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions", Journal of Finance, Vol. 31, No. 2, (May 1976), pp. 351-367
7. Burtschell, X., Gregory, J. and Laurent, L.-P. (April 2005). A Comparative Analysis of CDO Pricing Models. Working paper.
8. Dezhong, W. Rachev S.T., Fabozzi F.J. (October 2006). Pricing Tranches of a CDO and a CDS Index: Resent Advances and Future Research. Working paper.
9. Dezhong W., Rachev S.T., Fabozzi F.J. (November 2006). Pricing of Credit Default Index Swap Tranches with One-Factor Heavy-Tailed Copula Models. Working paper.
10. González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “Additive properties of skew normal random vectors.” Journal of Statistical Planning and Inference, Vol. 126, pp. 521-534.
11. González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “A multivariate skew normal distribution.” Journal of Multivariate Analysis, Vol. 89, pp.181-190.
12. Hull, J. and White, A. (winter 2004) “Valuation of a CDO and an n-th to Default CDS without Monte Carlo Simulation.” The Journal of Derivatives, Vol. 12, pp. 8-23.
13. Garcia, J., Dwyspelaere, T., Leonard, L. Alderweireld, T. and Van Gestel, T. (January 2005). Comparing BET and Copulas for Cash Flows CDO. Working Paper.
14. Garcia, J., Gielens, G., Leonard, L. and Van Gestel, T. (June 2003). Pricing Baskets Using Gaussian Copula and BET Methodology: A Market Test. Working Paper.
15. Kalemanove, 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.
16. Karlis, D. and Papadimitriou, A. (2004). Inference for the Multivariate Normal Inverse Gaussian Model. Working paper.
17. Karlis. D. (2000). An EM type algorithm for maximum likelihood estimation of
the normal–inverse Gaussian distribution. Statistic & Probability Letters , 57, 43-52.
18. Li, D.X. (April 2000). On Default Correlation: A Copula Function Approach. Working Paper.
19. Lüscher, A. (December 2005). Synthetic CDO Pricing Using the Double Normal Inverse Gaussian Copula with Stochastic Factor Loadings. Master’s thesis in Zürich University.
20. McGinty, L., Ahluwaila, R., Watts, M. and Beinstein, E. (2004). Introducing Base Correlation. JP Morgan Credit Derivatives Strategy.
21. McGinty, L., Ahluwaila, R., Watts, M. and Beinstein, E. (2004a). Credit Correlation: A Guide.a JP Morgan Credit Derivatives Strategy.
22. Merton, R. C (1974) . On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, 29, pp. 449-470.
23. McGinty, L., R. Ahluwalia, M. Watts, and E. Beinstein (2004). Introducing Base Correlation. JP Morgan Credit Derivatives Strategy.
24. Nelsen, R.B. (2005). An Introduction to Copulas. Springer. Second Edition.
25. D. O’Kane and L. Schloegl., M. (2001). Modeling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
26. D. O’Kane and L. Schloegl., M. (2004). Base Correlation Explained. Quantitative Credit Research, Lehman Brothers.
27. O.E. Barndor®-Nielsen. (1978). Hyperbolic distributions and distributions on hyperbolae. Scandinavian. Journal of statistics, 5, 151-157.
28. O.E. Barndor®-Nielsen. (1997.) Normal Inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of statistics, 24, 1-13.
29. Willemann, S. (2004). An Evaluation of the Base Correlation Framework for Synthetic CDOs. Working Paper.
30. Torresetti, R., Brigo, D., Pallavicini, A. (November 2006). Implied correlation in CDO tranches: a Paradigm to be handled with care. Working Paper.
31. Vasicek, O. (2002). “Loan Portfolio Value.” Risk, Vol. 12, pp. 160-162.
32. 陳松男 (民98)。固定收益證券與衍生產品 。台北市：新陸書局。
33. 邱嬿燁 (民97) 。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 。國立政治大學統計學系碩士論文，台北市。
描述 碩士
國立政治大學
統計研究所
99354002
100
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099354002
資料類型 thesis
dc.contributor.advisor 劉惠美zh_TW
dc.contributor.author (Authors) 林聖航zh_TW
dc.creator (作者) 林聖航zh_TW
dc.date (日期) 2011en_US
dc.date.accessioned 30-Oct-2012 10:58:16 (UTC+8)-
dc.date.available 30-Oct-2012 10:58:16 (UTC+8)-
dc.date.issued (上傳時間) 30-Oct-2012 10:58:16 (UTC+8)-
dc.identifier (Other Identifiers) G0099354002en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54406-
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) 99354002zh_TW
dc.description (描述) 100zh_TW
dc.description.abstract (摘要) 根據以往探討評價合成型抵押擔保債券之文獻研究，最廣為使用的方法應用大樣本一致性資產組合(large homogeneous portfolio portfolio ; LHP)假設之單因子常態關聯結構模型來評價，但會造成合成型抵押擔保債券憑證與市場報價間的差異過大，且會造成相關性微笑曲線現象。由文獻顯示，單因子關聯結構模型若能加入厚尾度或偏斜性能夠改善以上問題，且對於分券評價時也會有較好的效果，像是Kalemanova et al. (2007) 提出應用LHP假設之單因子Normal Inverse Gaussian(NIG)關聯結構模型以及邱嬿燁(2007)提出NIG及Closed Skew Normal(CSN)複合分配之單因子關聯結構模型(MIX模型)在實證分析中得到極佳的評價結果。自2008年起，合成型抵押擔保債券商品結構開始出現變化，而以往評價合成型抵押擔保債券價格時，商品結構皆為同一種型式。本文將利用常態分配、NIG分配、CSN分配以及NIG與CSN複合分配作為不同的單因子關聯結構模型，藉由絕對誤差極小化方法，針對不同商品結構的合成型抵押擔保債券評價，並進行模型比較分析。由最後實證分析結果顯示，單因子NIG(2)關聯結構模型優於其他模型，也證明NIG分配的第二個參數 β 能夠帶來改善的評價效果，此項證明與過去文獻結論有所不同，但 MIX模型則為唯一一個符合LHP假設的模型。zh_TW
dc.description.abstract (摘要) Based on the literature of discussing the approach for pricing synthetic CDOs, the most widely used methods used application of Large Homogeneous Portfolio (LHP) assumption of the one factor Gaussian copula model, however , it fails to fit the prices of synthetic CDOs tranches and leads to the implied correlation smile. The literature shows that one factor copula model adding the heavy-tail or skew can improve the above problem, and also has a good effect for pricing tranches such as
Kalemanova et al (2007) proposed the application of LHP assumption of one factor NIG copula model and Qiu Yan Ye (2007) proposed the application of LHP assumption of one factor NIG and CSN copula model. This article found that the structure of synthetic CDOs began to change since 2008. The past of pricing synthetic CDOs, the structure of synthetic CDOs are the same type, so this article will use different one factor copula model for pricing different structure of synthetic CDOs by using the absolute error minimization. This article will observe whether the above model can be applied in the new synthetic CDOs and implement of different type model for comparative analysis. The last empirical analysis shows that one factor NIG (2) copula model is superior to other models, more meeting the actual market demand, also proving the second parameter β of the NIG distribution able to bring about improvements in pricing results. This proving is different for the past literature conclusions. However, the MIX model is the only one in line with the LHP assumptions.		en_US
dc.description.tableofcontents 謝辭 I
摘要 II
Abstract III
表目錄 VI
圖目錄 VII
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 抵押擔保債券(Collateralized Debt Obligation ,CDO) 3
第四節 合成型抵押擔保債券(Synthetic CDOs ) 4
第五節 信用違約交換(Credit Default Swaps ,CDS) 5
第六節 信用違約指數（Credit Default Indexes） 6
第七節 本文架構 9
第二章 文獻回顧 10
第一節 關聯結構模型(Copula Model) 10
第二節 單因子關聯結構模型(One Factor Copula Model) 11
第三節 Normal Inverse Gaussian Distribution(NIG) 17
第四節 Closed Skew Normal Distribution(CSN) 18
第三章 合成型CDO之評價方法與單因子關聯結構模型 19
第一節 合成型抵押擔保債權憑證之評價方法 19
第二節 應用LHP假設之單因子高斯關聯結構模型 23
第三節 NIG分配性質及定義 28
第四節 應用LHP假設之單因子NIG關聯結構模型 31
第四章 單因子CSN與NIG混合分配之關聯結構模型 35
第一節 CSN分配之性質與定理 35
第二節 應用LHP假設之單因子CSN關聯結構模型 40
第三節 單因子CSN與NIG混合分配之關聯結構模型 46
第五章 實證分析：評價DJ iTraxx 51
第一節 比較各模型在不同時期DJ iTraxx之分券評價 53
第二節 觀察各模型在不同時期DJ iTraxx之隱含相關性 58
第六章 結論與建議 60
參考文獻 64
附錄一 67
附錄二 71
附錄三 73
附錄四 77		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099354002en_US
dc.subject (關鍵詞) 合成型抵押擔保債權憑證zh_TW
dc.subject (關鍵詞) 單因子關聯結構模型zh_TW
dc.subject (關鍵詞) NIG分配zh_TW
dc.subject (關鍵詞) CSN分配zh_TW
dc.subject (關鍵詞) synthetic CDOsen_US
dc.subject (關鍵詞) one factor copula modelen_US
dc.subject (關鍵詞) NIG distributionen_US
dc.subject (關鍵詞) CSN distributionen_US
dc.title (題名) 探討合成型抵押擔保債券憑證之評價zh_TW
dc.title (題名) Pricing the Synthetic CDOsen_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. (2004 winter). “Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings.” Journal of Credit Risk, Vol. 1, pp. 29-71.
3. Arellano-Valle, R.B., Gómez, H.W. and Quintana, F. A. (2004). “A New Class of Skew-Normal Distributions.” Communications in Statistics-Theory and Methods, Vol. 33, pp.1465-1480.
4. Azzalini, A. (2005). “The Skew-normal Distribution and Related Multivariate Families.” Scandinavian Journal of Statistics, Vol. 32, pp.159-188.
5. Barndorff-Nielsen, O.E. (1997). “Normal Inverse Gaussian Distributions and Stochastic Volatility Modeling.” Scandinavian Journal of Statistics, Vol. 24, pp.1-13.
6. Black, Fischer and John C. Cox, "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions", Journal of Finance, Vol. 31, No. 2, (May 1976), pp. 351-367
7. Burtschell, X., Gregory, J. and Laurent, L.-P. (April 2005). A Comparative Analysis of CDO Pricing Models. Working paper.
8. Dezhong, W. Rachev S.T., Fabozzi F.J. (October 2006). Pricing Tranches of a CDO and a CDS Index: Resent Advances and Future Research. Working paper.
9. Dezhong W., Rachev S.T., Fabozzi F.J. (November 2006). Pricing of Credit Default Index Swap Tranches with One-Factor Heavy-Tailed Copula Models. Working paper.
10. González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “Additive properties of skew normal random vectors.” Journal of Statistical Planning and Inference, Vol. 126, pp. 521-534.
11. González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “A multivariate skew normal distribution.” Journal of Multivariate Analysis, Vol. 89, pp.181-190.
12. Hull, J. and White, A. (winter 2004) “Valuation of a CDO and an n-th to Default CDS without Monte Carlo Simulation.” The Journal of Derivatives, Vol. 12, pp. 8-23.
13. Garcia, J., Dwyspelaere, T., Leonard, L. Alderweireld, T. and Van Gestel, T. (January 2005). Comparing BET and Copulas for Cash Flows CDO. Working Paper.
14. Garcia, J., Gielens, G., Leonard, L. and Van Gestel, T. (June 2003). Pricing Baskets Using Gaussian Copula and BET Methodology: A Market Test. Working Paper.
15. Kalemanove, 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.
16. Karlis, D. and Papadimitriou, A. (2004). Inference for the Multivariate Normal Inverse Gaussian Model. Working paper.
17. Karlis. D. (2000). An EM type algorithm for maximum likelihood estimation of
the normal–inverse Gaussian distribution. Statistic & Probability Letters , 57, 43-52.
18. Li, D.X. (April 2000). On Default Correlation: A Copula Function Approach. Working Paper.
19. Lüscher, A. (December 2005). Synthetic CDO Pricing Using the Double Normal Inverse Gaussian Copula with Stochastic Factor Loadings. Master’s thesis in Zürich University.
20. McGinty, L., Ahluwaila, R., Watts, M. and Beinstein, E. (2004). Introducing Base Correlation. JP Morgan Credit Derivatives Strategy.
21. McGinty, L., Ahluwaila, R., Watts, M. and Beinstein, E. (2004a). Credit Correlation: A Guide.a JP Morgan Credit Derivatives Strategy.
22. Merton, R. C (1974) . On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, 29, pp. 449-470.
23. McGinty, L., R. Ahluwalia, M. Watts, and E. Beinstein (2004). Introducing Base Correlation. JP Morgan Credit Derivatives Strategy.
24. Nelsen, R.B. (2005). An Introduction to Copulas. Springer. Second Edition.
25. D. O’Kane and L. Schloegl., M. (2001). Modeling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
26. D. O’Kane and L. Schloegl., M. (2004). Base Correlation Explained. Quantitative Credit Research, Lehman Brothers.
27. O.E. Barndor®-Nielsen. (1978). Hyperbolic distributions and distributions on hyperbolae. Scandinavian. Journal of statistics, 5, 151-157.
28. O.E. Barndor®-Nielsen. (1997.) Normal Inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of statistics, 24, 1-13.
29. Willemann, S. (2004). An Evaluation of the Base Correlation Framework for Synthetic CDOs. Working Paper.
30. Torresetti, R., Brigo, D., Pallavicini, A. (November 2006). Implied correlation in CDO tranches: a Paradigm to be handled with care. Working Paper.
31. Vasicek, O. (2002). “Loan Portfolio Value.” Risk, Vol. 12, pp. 160-162.
32. 陳松男 (民98)。固定收益證券與衍生產品 。台北市：新陸書局。
33. 邱嬿燁 (民97) 。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 。國立政治大學統計學系碩士論文，台北市。		zh_TW