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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/36923


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    題名: 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
    Pricing CDOs with One Factor Double Mixture Distribution Copula Model
    作者: 邱嬿燁
    Chiou, Yan ya
    貢獻者: 劉惠美
    Liu, Hui mei
    邱嬿燁
    Chiou, Yan ya
    關鍵詞: 擔保債權憑證
    單因子關聯結構模式
    多變量封閉常態分配
    複合分配
    collateralized debt obligation
    one factor copula model
    closed skew normal distribution
    mixture distribution
    日期: 2007
    上傳時間: 2009-09-18 20:10:02 (UTC+8)
    摘要: 依據之前的文獻研究，市場上主要是在LHP (Large Homogeneous Portfolio) 假設下利用單因子常態關聯結構模式(One factor double Gaussian copula model) 評價擔保債權憑證 (Collateralized debt obligation, CDO)。但這會造成擔保債權憑證的評價與市場報價的差距過大，且會造成base correlation偏斜的情況。Kalemanova et al. (2007) 提出用Normal inverse Gaussian (NIG) 取代常態分配評價擔保債權憑證，此模型不但計算快速而且可以準確估計權益分券 (equity tranche) 的價格，但是它也過於高估了其它的分券的價格。
    在本文中使用多變量封閉常態分配(Closed skew normal, 簡稱CSN) 分配取代NIG分配作擔保債權憑證分券的評價，CSN分配具有常態分配的性質，其線性組合仍具有封閉性的特質，且具有較多的參數以控制分配的偏態與峰態。但是與單因子常態關聯結構模式相同，多變量封閉常態分配的單因子關聯結構模式仍然無法估計的很準確，僅有在最高等級分券(senior tranche)的評價上有明顯的改進。
    因此在本文中我們使用NIG與CSN複合分配之單因子關聯結構模式評價擔保債權憑證分券，在實例分析時得到極佳的評價結果，並且比單因子常態關聯結構模型具有更多的的參數以使模型更符合實際的需求。
    This article extends the Large Homogeneous Portfolio (LHP) and one factor double Gaussian copula approach for pricing CDOs. In the literature, the one factor double Gaussian copula model under LHP assumption fails to fit the prices of CDO tranches, moreover, it leads to the implied base correlation skew. Some researchers proposed using one factor double NIG copula model to price CDO tranches. It not only economizes on time but also fits the equity tranches exactly, but NIG models do not price other tranches well simultaneously. On the other hand, we substitute the NIG distribution with the Closed Skew normal (CSN) distribution. This family also has properties similar to the normal distribution, which is closure under convolution, and has extra parameters to control the shape. By using this model we get a better fit in the senior tranches, but it seriously overprices subordinate tranches. Thus we consider a mixture distribution of NIG and CSN distributions. The employments of this mixture distribution are comparatively well, and furthermore it brings more flexibility to the dependence structure.
    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. Burtschell, X., Gregory, J. and Laurent, L.-P. (April 2005). A Comparative Analysis of CDO Pricing Models. Working paper.
    7. Cifuentes, A. and O’Connor, G. (December 1996). The Binomial Expectation Method applied to CBO/CLO analysis. Moody’s Special Report.
    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. Embrechts, P., Lindskog, F. and McNeil, A. (September 2001). Modelling Dependence with Copulas and Applications to Risk Management. Working paper.
    11. 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.
    12. 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.
    13. Hull, J. Options, Futures, and Other Derivatives. Pearson International. Sixth Edition.
    14. 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.
    15. Garcia, J., Dwyspelaere, T., Leonard, L. Alderweireld, T. and Van Gestel, T. (January 2005). Comparing BET and Copulas for Cash Flows CDO. Working Paper.
    16. 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.
    17. 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.
    18. Karlis, D. and Papadimitriou, A. (2004). Inference for the Multivariate Normal Inverse Gaussian Model. Working paper.
    19. Li, D.X. (April 2000). On Default Correlation: A Copula Function Approach. Working Paper.
    20. Lüscher, A. (December 2005). Synthetic CDO Pricing Using the Double Normal Inverse Gaussian Copula with Stochastic Factor Loadings. Master’s thesis in Zürich University.
    21. McGinty, L., Ahluwaila, R., Watts, M. and Beinstein, E. (2004). Introducing Base Correlation. JP Morgan Credit Derivatives Strategy.
    22. McGinty, L., Ahluwaila, R., Watts, M. and Beinstein, E. (2004a). Credit Correlation: A Guide. JP Morgan Credit Derivatives Strategy.
    23. Maria, F. (July 2007). Implied Correlation Smile. Master’s thesis in Humboldt University.
    24. Nelsen, R.B. (2005). An Introduction to Copulas. Springer. Second Edition.
    25. O’kane, D., and Livesey, M. (2001). Modeling Credit: Theory and Practice. Quantitative Credit Research, Lehman Brothers.
    26. O’kane, D., and Livesey, M. (2004). Base Correlation Explained. Quantitative Credit Research, Lehman Brothers.
    27. Willemann, S. (2004). An Evaluation of the Base Correlation Framework for Synthetic CDOs. Working Paper.
    28. Torresetti, R., Brigo, D., Pallavicini, A. (November 2006). Implied correlation in CDO tranches: a Paradigm to be handled with care. Working Paper.
    29. Vasicek, O. (2002). “Loan Portfolio Value.” Risk, Vol. 12, pp. 160-162.
    描述: 碩士
    國立政治大學
    統計研究所
    95354007
    96
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0095354007
    資料類型: thesis
    顯示於類別:[統計學系] 學位論文

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