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題名 單因子關聯結構模型與時間數列模型應用於合成型擔保債權憑證之評價
The One-factor Copula Model and the Time Series Model for Synthetic CDO Pricing作者 劉釋璟
Liu, Shih Ching貢獻者 劉惠美<br>陳麗霞
劉釋璟
Liu, Shih Ching關鍵詞 合成型擔保債權憑證
單因子關聯結構模型
單因子NIG關聯結構模型
AR(1)
synthetic CDO
one-factor copula model
one-factor NIG copula model
AR(1)日期 2015 上傳時間 27-七月-2015 11:21:55 (UTC+8) 摘要 Lamb、Perraudin和 Landschoot (2009)提出市場共同因子具有時間數列特性AR(p)的單因子關聯結構模型，評價合成型擔保債權憑證，其最佳模型為市場共同因子具備AR(1)，且使用兩個高斯分配組合之混合分配，結果顯示除了權益分券外，其他分券均有不錯的配適結果。本文僅討論市場共同因子具備AR(1)之高斯關聯結構模型，針對CDX.NA.IG.指數Series 9 五年期之週資料，以極小化各分券總絕對誤差，來比較不同評價模型的估計結果，分成三組進行，分別為(1)單因子高斯關聯結構模型(期數固定)v.s.單因子NIG關聯結構模型(期數固定)(2)單因子高斯關聯結構模型(期數遞減)v.s.單因子NIG關聯結構模型(期數遞減)(3)單因子高斯關聯結構模型(期數固定)v.s.單因子NIG關聯結構模型(期數固定)v.s.市場共同因子具備AR(1)之高斯關聯結構模型。觀察市場共同因子具備AR(1)之高斯關聯結構模型中的每週參數，可以發現相關係數長期來看呈現穩定，約介於0.7至0.9之間，與Lamb等(2009)觀察到的現象一致，表示造成各分券市場報價波動的主要原因並非相關係數的波動，而與市場共同因子前一期的水準有關。
Lamb, Perraudin, Landschoot (2009) proposed the one-factor copula model with the common factor under the assumption of AR(p) for pricing synthetic CDO. Their best model was the mixture model with AR(1). Additionally, there were good fits on different tranches, except the equity tranch. This paper applies the one-factor Gaussian copula model with the common factor under the assumption of AR(1) to the pricing of CDX.NA.IG. Series 9 weekly data (5-year maturity). We minimize the total absolute error on different tranches to obtain the parameters of different models. We compare three sets of models: (1) The one-factor Gaussian copula model (fixed maturity) v.s. the one-factor NIG copula model (fixed maturity). (2) The one-factor Gaussian copula model (declined maturity) v.s. the one-factor NIG copula model (declined maturity). (3) The one-factor Gaussian copula model (fixed maturity) v.s. the one-factor NIG copula model (fixed maturity) v.s. the one-factor Gaussian copula model with the common factor under the assumption of AR(1). In the one-factor Gaussian copula model with the common factor under the assumption of AR(1), we find the correlation parameter is stable through the observed period, ranging from 0.7 to 0.9. The same fact was observed in Lamb et al.,2009. This means that the market spreads are driven considerably by the level of one factor lag, not the default correlations.參考文獻 Casey, O. “The CDS Big Bang” The Markit Magazine, Spring 2009. Chaplin, G. Credit Derivatives: Trading, Investing and Risk Management. 2nd ed. John Wiley & Sons, Ltd, 2010. Das, S. R., D. Duffie, N. Kapadia, and L. Saita “Common Failings: How Corporate Defaults are Correlated” Journal of Finance, 2007, 62(1), 93-117. Duffie, D. and N. Garleanu “Risk and Valuation of Collateralized Debt Obligations” Financial Analysts Journal, 2001, 57, 41-59. Hull, J. and A.White “Valuing Credit Default Swaps I: No Counterparty Default Risk” Working Paper, April 2000. Hull, J. and A.White “Valuation of a CDO and nth to Default CDS Without Monte Carlo Simulation” The Journal of Derivatives, 2004, 12(2), 8-23. Kalemanova, A., B. Schmid, and R. Werner “The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing” The Journal of Derivatives, Spring 2007, Vol. 14, pp. 80-93. Lamb, R., and W. Perraudin “Dynamic Loan Distributions: Estimation and Implications” Working Paper, August 2006. Lamb, R., W. Perraudin, and A.V. Landschoot “Dynamic Pricing of Synthetic Collateralized Debt Obligations” SSRN Electronic Journal, February 2009. Li, D.X. “On Default Correlation: A Copula Function Approach” The Journal of Fixed Income, March 2000, Vol. 9,No. 4: pp. 43-54. O’ Kane D. Modelling Single-name and Multi-name Credit Derivatives. John Wiley & Sons, Ltd, 2008. Vasicek, O. “Probability of Loss on Loan Portfolio” Memo, KMV Corporation, February 1987. Vasicek, O. “Limiting Loan Loss Probability Distribution” Memo, KMV Corporation, August 1991. 林聖航「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。(民101) 描述 碩士
國立政治大學
統計研究所
102354014資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102354014 資料類型 thesis dc.contributor.advisor 劉惠美<br>陳麗霞 zh_TW dc.contributor.author (作者) 劉釋璟 zh_TW dc.contributor.author (作者) Liu, Shih Ching en_US dc.creator (作者) 劉釋璟 zh_TW dc.creator (作者) Liu, Shih Ching en_US dc.date (日期) 2015 en_US dc.date.accessioned 27-七月-2015 11:21:55 (UTC+8) - dc.date.available 27-七月-2015 11:21:55 (UTC+8) - dc.date.issued (上傳時間) 27-七月-2015 11:21:55 (UTC+8) - dc.identifier (其他 識別碼) G0102354014 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/76861 - 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) 102354014 zh_TW dc.description.abstract (摘要) Lamb、Perraudin和 Landschoot (2009)提出市場共同因子具有時間數列特性AR(p)的單因子關聯結構模型，評價合成型擔保債權憑證，其最佳模型為市場共同因子具備AR(1)，且使用兩個高斯分配組合之混合分配，結果顯示除了權益分券外，其他分券均有不錯的配適結果。本文僅討論市場共同因子具備AR(1)之高斯關聯結構模型，針對CDX.NA.IG.指數Series 9 五年期之週資料，以極小化各分券總絕對誤差，來比較不同評價模型的估計結果，分成三組進行，分別為(1)單因子高斯關聯結構模型(期數固定)v.s.單因子NIG關聯結構模型(期數固定)(2)單因子高斯關聯結構模型(期數遞減)v.s.單因子NIG關聯結構模型(期數遞減)(3)單因子高斯關聯結構模型(期數固定)v.s.單因子NIG關聯結構模型(期數固定)v.s.市場共同因子具備AR(1)之高斯關聯結構模型。觀察市場共同因子具備AR(1)之高斯關聯結構模型中的每週參數，可以發現相關係數長期來看呈現穩定，約介於0.7至0.9之間，與Lamb等(2009)觀察到的現象一致，表示造成各分券市場報價波動的主要原因並非相關係數的波動，而與市場共同因子前一期的水準有關。 zh_TW dc.description.abstract (摘要) Lamb, Perraudin, Landschoot (2009) proposed the one-factor copula model with the common factor under the assumption of AR(p) for pricing synthetic CDO. Their best model was the mixture model with AR(1). Additionally, there were good fits on different tranches, except the equity tranch. This paper applies the one-factor Gaussian copula model with the common factor under the assumption of AR(1) to the pricing of CDX.NA.IG. Series 9 weekly data (5-year maturity). We minimize the total absolute error on different tranches to obtain the parameters of different models. We compare three sets of models: (1) The one-factor Gaussian copula model (fixed maturity) v.s. the one-factor NIG copula model (fixed maturity). (2) The one-factor Gaussian copula model (declined maturity) v.s. the one-factor NIG copula model (declined maturity). (3) The one-factor Gaussian copula model (fixed maturity) v.s. the one-factor NIG copula model (fixed maturity) v.s. the one-factor Gaussian copula model with the common factor under the assumption of AR(1). In the one-factor Gaussian copula model with the common factor under the assumption of AR(1), we find the correlation parameter is stable through the observed period, ranging from 0.7 to 0.9. The same fact was observed in Lamb et al.,2009. This means that the market spreads are driven considerably by the level of one factor lag, not the default correlations. en_US dc.description.tableofcontents 謝辭 I 摘要 II Abstract III 表目次 VI 圖目次 VII 第一章 緒論 - 1 - 第一節 研究動機 - 1 - 第二節 研究目的 - 2 - 第三節 擔保債權憑證 - 3 - 第四節 合成型擔保債權憑證 - 4 - 第五節 信用違約交換指數 - 6 - 第六節 本文架構 - 7 - 第二章 文獻回顧 - 8 - 第一節 單因子關聯結構模型 - 8 - 第二節 動態模型 - 10 - 第三章 合成型擔保債權憑證之評價 - 12 - 第一節 合成型擔保債權憑證之評價 - 12 - 第二節 LHP假設下之單因子高斯關聯結構模型 - 17 - 第三節 LHP假設下之單因子NIG關聯結構模型 - 21 - 第四章 假設市場共同因子具備AR(1)之高斯關聯結構模型 - 25 - 第一節 假設市場共同因子具備AR(1)之高斯關聯結構模型 - 25 - 第二節 參數校準 - 30 - 第五章 CDX.NA.IG Series 9之評價 - 34 - 第一節 資料型態 - 34 - 第二節 不同模型在各分券之比較 - 35 - 第六章 結論與建議 - 61 - 參考文獻 - 63 - zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102354014 en_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) 單因子NIG關聯結構模型 zh_TW dc.subject (關鍵詞) AR(1) zh_TW dc.subject (關鍵詞) synthetic CDO en_US dc.subject (關鍵詞) one-factor copula model en_US dc.subject (關鍵詞) one-factor NIG copula model en_US dc.subject (關鍵詞) AR(1) en_US dc.title (題名) 單因子關聯結構模型與時間數列模型應用於合成型擔保債權憑證之評價 zh_TW dc.title (題名) The One-factor Copula Model and the Time Series Model for Synthetic CDO Pricing en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Casey, O. “The CDS Big Bang” The Markit Magazine, Spring 2009. Chaplin, G. Credit Derivatives: Trading, Investing and Risk Management. 2nd ed. John Wiley & Sons, Ltd, 2010. Das, S. R., D. Duffie, N. Kapadia, and L. Saita “Common Failings: How Corporate Defaults are Correlated” Journal of Finance, 2007, 62(1), 93-117. Duffie, D. and N. Garleanu “Risk and Valuation of Collateralized Debt Obligations” Financial Analysts Journal, 2001, 57, 41-59. Hull, J. and A.White “Valuing Credit Default Swaps I: No Counterparty Default Risk” Working Paper, April 2000. Hull, J. and A.White “Valuation of a CDO and nth to Default CDS Without Monte Carlo Simulation” The Journal of Derivatives, 2004, 12(2), 8-23. Kalemanova, A., B. Schmid, and R. Werner “The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing” The Journal of Derivatives, Spring 2007, Vol. 14, pp. 80-93. Lamb, R., and W. Perraudin “Dynamic Loan Distributions: Estimation and Implications” Working Paper, August 2006. Lamb, R., W. Perraudin, and A.V. Landschoot “Dynamic Pricing of Synthetic Collateralized Debt Obligations” SSRN Electronic Journal, February 2009. Li, D.X. “On Default Correlation: A Copula Function Approach” The Journal of Fixed Income, March 2000, Vol. 9,No. 4: pp. 43-54. O’ Kane D. Modelling Single-name and Multi-name Credit Derivatives. John Wiley & Sons, Ltd, 2008. Vasicek, O. “Probability of Loss on Loan Portfolio” Memo, KMV Corporation, February 1987. Vasicek, O. “Limiting Loan Loss Probability Distribution” Memo, KMV Corporation, August 1991. 林聖航「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。(民101) zh_TW
