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題名 單因子動態模型對合成型擔保債劵憑證之評價與預測
One Factor Dynamic Model pricing and forecast of Synthetic CDOs
作者 蔡慶龍
Tsai, Ching Lung
貢獻者 劉惠美
蔡慶龍
Tsai, Ching Lung
關鍵詞 合成型擔保債權憑證
單因子關聯結構模型
NIG分配
動態模型
synthetic CDOs
one factor copula model
NIG distribution
dynamic model
日期 2015
上傳時間 13-Jul-2015 11:06:46 (UTC+8)
摘要 應用大樣本一致性資產組合(large homogeneous portfolio portfolio ; LHP)假設之單因子關聯結構模型(One Factor Copula Model)為以往評價合成型擔保債權憑證最廣為使用的方法。最早是由O’Kane and Schloegl (2001)所提出的應用LHP假設之單因子常態關聯結構模型,而其針對各分卷的評價結果僅有在權益分券(equity tranch)得到好的配適。Kalemanova et al. (2007) 提出應用LHP假設之單因子NIG關聯結構模型,其評價結果遠優於常態分配,但在中間順位(Mezzanine)層級以上的分券還是高估。以上的單因子模型皆是對2008年以前的擔保債權憑證做評價,且僅挑選特定幾天做分析,因此本文針對2008年三月到2013年三月做完整的長期分析,比較不同模型對於擔保債權憑證之評價結果。本文利用了單因子常態關聯結構模型、單因子NIG關聯結構模型以及單因子動態模型來做討論。在常態與NIG的單因子關聯結構模型中,最後實證結果分析顯示,期數n隨著時間遞減的話將能夠大幅改善評價結果;而在動態模型的部分,由於參數估計的方法不夠完善,因此得到的評價結果不符合預期。
The most widely used methods used application of Large Homogeneous Portfolio (LHP) assumption of the one factor copula model for pricing synthetic CDOs. The one factor Gaussian copula model was first used by O`Kane and Schloegl (2001) proposed, however, only in equity tranches get a good evaluation of the results of the fit for each tranches. Kalemanova et al (2007) proposed the application of LHP assumption of one factor NIG copula model. The one factor copula model of NIG distribution evaluation results are far better than normal distribution, but overestimated above mezzanine tranches. The above models are all pricing of Synthetic CDOs before 2008, and select only certain days for analysis. Therefore, this paper in March 2008 to March 2013 to do a complete long-term analysis, comparison of different models for pricing of Synthetic CDOs results. In this paper, one factor Gaussian copula model, one factor NIG copula model and one factor dynamic model do discussion. In Gaussian and NIG one factor copula model, the empirical results of the final analysis, diminishing over time periods n, then will be able to significantly improve the results of Synthetic CDOs pricing. In the part of the one factor dynamic model, since the parameter estimation method is not perfect, so the results of Synthetic CDOs pricing are not in line with expectations.
參考文獻 1. Andersen, L., and Sidenius, J. (2004 winter). “Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings.” Journal of Credit Risk,
2. ANNA KALEMANOVA, BERND SCHMID, AND RALFWERNER. (2007). The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing
3. D. O’Kane and L. Schloegl., M. (2001). Modeling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
4. D. O’Kane and L. Schloegl., M. (2001). Modeling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
5. D. O’Kane and L. Schloegl., M. (2004). Base Correlation Explained. Quantitative Credit Research, Lehman Brothers.
6. 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.
7. Hull, J., and A. White,(2000). VALUING CREDIT DEFAULT SWAPS I: NO COUNTERPARTY DEFAULT RISK.
8. Hull, J., and A. White, (2004), “Valuation of a CDO and an nth to Default CDS without Monte Carlo Simulation”
9. 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.
10. Li, D.X. (April 2000). On Default Correlation: A Copula Function Approach. Working Paper.
11. Mark Dais and Violet Lo.(1999). Infectious Defaults
12. Oldrich Vasicek. (1991). ” LIMITING LOAN LOSS PROBABILITY DISTRIBUTION”
13. O.E. Barndor®-Nielsen. (1997.) Normal Inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of statistics, 24, 1-13.
14. Roger B. Nelsen.(1999). Properties and applications of copulas: A brief survey
15. R¨udiger Frey, Alexander J. McNeil(2001). Copulas and credit models
16. Robert Lamb and William Perraudin. (2006). DYNAMIC LOAN LOSS DISTRIBUTIONS:ESTIMATION AND IMPLICATIONS
17. Robert Lamb, William Perraudin and Astrid Van Landschoot. (2009). DYNAMIC PRICING OF SYNTHETIC COLLATERALIZED DEBT OBLIGATIONS
18. Vasicek, O. (2002). “Loan Portfolio Value.” Risk, Vol. 12

19. 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。
20. 林聖航 (民101) 。探討合成型抵押擔保債券憑證之評價 。國立政治大學統計學系碩士論文,台北市。
21. 張蕾 (民101)。信用違約互換優缺點分析。現代商業.2011年15期
描述 碩士
國立政治大學
統計研究所
102354024
103
資料來源 http://thesis.lib.nccu.edu.tw/record/#G1023540241
資料類型 thesis
dc.contributor.advisor 劉惠美zh_TW
dc.contributor.author (Authors) 蔡慶龍zh_TW
dc.contributor.author (Authors) Tsai, Ching Lungen_US
dc.creator (作者) 蔡慶龍zh_TW
dc.creator (作者) Tsai, Ching Lungen_US
dc.date (日期) 2015en_US
dc.date.accessioned 13-Jul-2015 11:06:46 (UTC+8)-
dc.date.available 13-Jul-2015 11:06:46 (UTC+8)-
dc.date.issued (上傳時間) 13-Jul-2015 11:06:46 (UTC+8)-
dc.identifier (Other Identifiers) G1023540241en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/76421-
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) 102354024zh_TW
dc.description (描述) 103zh_TW
dc.description.abstract (摘要) 應用大樣本一致性資產組合(large homogeneous portfolio portfolio ; LHP)假設之單因子關聯結構模型(One Factor Copula Model)為以往評價合成型擔保債權憑證最廣為使用的方法。最早是由O’Kane and Schloegl (2001)所提出的應用LHP假設之單因子常態關聯結構模型,而其針對各分卷的評價結果僅有在權益分券(equity tranch)得到好的配適。Kalemanova et al. (2007) 提出應用LHP假設之單因子NIG關聯結構模型,其評價結果遠優於常態分配,但在中間順位(Mezzanine)層級以上的分券還是高估。以上的單因子模型皆是對2008年以前的擔保債權憑證做評價,且僅挑選特定幾天做分析,因此本文針對2008年三月到2013年三月做完整的長期分析,比較不同模型對於擔保債權憑證之評價結果。本文利用了單因子常態關聯結構模型、單因子NIG關聯結構模型以及單因子動態模型來做討論。在常態與NIG的單因子關聯結構模型中,最後實證結果分析顯示,期數n隨著時間遞減的話將能夠大幅改善評價結果;而在動態模型的部分,由於參數估計的方法不夠完善,因此得到的評價結果不符合預期。zh_TW
dc.description.abstract (摘要) The most widely used methods used application of Large Homogeneous Portfolio (LHP) assumption of the one factor copula model for pricing synthetic CDOs. The one factor Gaussian copula model was first used by O`Kane and Schloegl (2001) proposed, however, only in equity tranches get a good evaluation of the results of the fit for each tranches. Kalemanova et al (2007) proposed the application of LHP assumption of one factor NIG copula model. The one factor copula model of NIG distribution evaluation results are far better than normal distribution, but overestimated above mezzanine tranches. The above models are all pricing of Synthetic CDOs before 2008, and select only certain days for analysis. Therefore, this paper in March 2008 to March 2013 to do a complete long-term analysis, comparison of different models for pricing of Synthetic CDOs results. In this paper, one factor Gaussian copula model, one factor NIG copula model and one factor dynamic model do discussion. In Gaussian and NIG one factor copula model, the empirical results of the final analysis, diminishing over time periods n, then will be able to significantly improve the results of Synthetic CDOs pricing. In the part of the one factor dynamic model, since the parameter estimation method is not perfect, so the results of Synthetic CDOs pricing are not in line with expectations.en_US
dc.description.tableofcontents 謝辭 I
摘要 II
Abstract II
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 3
第三節 擔保債權憑證(Collateralized Debt Obligation ,CDO) 3
第四節 合成型擔保債權憑證(Synthetic CDOs ) 5
第五節 信用違約交換(Credit Default Swaps ,CDS) 6
第六節 信用違約指數(Credit Default Indexes) 7
第七節 本文架構 11
第二章 文獻回顧 12
第一節 關聯結構模型(Copula Model) 12
第二節 單因子關聯結構模型(One Factor Copula Model) 13
第三節 單因子關聯結構之動態模型 18
第三章 合成型CDO之評價方法與單因子關聯結構模型 20
第一節 單因子高斯關聯結構模型 20
第二節 NIG分配性質及定義 25
第三節 單因子NIG關聯結構模型 28
第四節 合成型擔保債權憑證之評價 31
第四章 合成型擔保債權憑證之動態評價方法 38
第一節 動態損失分配的建構 38
第二節 合成型擔保債權憑證之動態評價 45
第五章 實證分析 48
第一節 單因子關聯結構模型對DJ iTraxx之分券評價 50
第二節 動態模型對DJ iTraxx之分券評價 75
第三節 比較各模型對於DJ iTraxx之評價結果 82
第四節 利用時間序列模型預測DJ iTraxx之市場報價 100
第六章 結論與建議 110
參考文獻 114
zh_TW
dc.format.extent 2302652 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1023540241en_US
dc.subject (關鍵詞) 合成型擔保債權憑證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) 動態模型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) dynamic modelen_US
dc.title (題名) 單因子動態模型對合成型擔保債劵憑證之評價與預測zh_TW
dc.title (題名) One Factor Dynamic Model pricing and forecast of Synthetic CDOsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Andersen, L., and Sidenius, J. (2004 winter). “Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings.” Journal of Credit Risk,
2. ANNA KALEMANOVA, BERND SCHMID, AND RALFWERNER. (2007). The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing
3. D. O’Kane and L. Schloegl., M. (2001). Modeling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
4. D. O’Kane and L. Schloegl., M. (2001). Modeling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
5. D. O’Kane and L. Schloegl., M. (2004). Base Correlation Explained. Quantitative Credit Research, Lehman Brothers.
6. 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.
7. Hull, J., and A. White,(2000). VALUING CREDIT DEFAULT SWAPS I: NO COUNTERPARTY DEFAULT RISK.
8. Hull, J., and A. White, (2004), “Valuation of a CDO and an nth to Default CDS without Monte Carlo Simulation”
9. 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.
10. Li, D.X. (April 2000). On Default Correlation: A Copula Function Approach. Working Paper.
11. Mark Dais and Violet Lo.(1999). Infectious Defaults
12. Oldrich Vasicek. (1991). ” LIMITING LOAN LOSS PROBABILITY DISTRIBUTION”
13. O.E. Barndor®-Nielsen. (1997.) Normal Inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of statistics, 24, 1-13.
14. Roger B. Nelsen.(1999). Properties and applications of copulas: A brief survey
15. R¨udiger Frey, Alexander J. McNeil(2001). Copulas and credit models
16. Robert Lamb and William Perraudin. (2006). DYNAMIC LOAN LOSS DISTRIBUTIONS:ESTIMATION AND IMPLICATIONS
17. Robert Lamb, William Perraudin and Astrid Van Landschoot. (2009). DYNAMIC PRICING OF SYNTHETIC COLLATERALIZED DEBT OBLIGATIONS
18. Vasicek, O. (2002). “Loan Portfolio Value.” Risk, Vol. 12

19. 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。
20. 林聖航 (民101) 。探討合成型抵押擔保債券憑證之評價 。國立政治大學統計學系碩士論文,台北市。
21. 張蕾 (民101)。信用違約互換優缺點分析。現代商業.2011年15期
zh_TW