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| 研究生： |
黃繼緯 Huang, Chi Wei |
|---|---|
| 論文名稱： |
不同單因子結構模型下合成型擔保債權憑證定價之研究 Comparison between different one-factor copula models of synthetic CDOs pricing |
| 指導教授： | 劉惠美 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2013 |
| 畢業學年度： | 101 |
| 語文別： | 中文 |
| 論文頁數： | 30 |
| 中文關鍵詞： | 合成型擔保債權憑證 、單因子結構模型 |
| 外文關鍵詞： | synthetic CDOs, one-factor copula model |
| 相關次數： | 點閱：81 下載：5 |
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1990年代中期信用衍生信商品開始發展，隨著時代變遷，演化出信用違約交換(Credit Default Swaps, CDS)、擔保債權憑證(Collateralized Debt Obligation, CDO)、合成型擔保債權憑證(Synthetic CDO)等商品，其可以分散風險的特性廣受歡迎，並且成為完備金融市場中重要的一環。在2007年金融海嘯中，信用衍生性商品扮演相當關鍵的角色，所以如何合理定價各類信用衍生性商品就變成相當重要的議題
以往在定價合成型擔保債權憑證時，多採取單因子結構模型來做為報酬函數的主要架構，並假設模型分配為常態分配、t分配、NIG分配等，但單因子結構模型的隱含相關係數具有波動性微笑現象，所以容易造成定價偏誤。
為了解決此問題，本文將引用常態分配假設與NIG分配假設下的隨機風險因子負荷模型(Random Factor Loading Model)，觀察隨機風險因子負荷模型是否對於定價偏誤較其他模型有所改善，並且比較各模型在最佳化參數與定價時的效率，藉此歸納出較佳的合成型擔保債權憑證定價模型。
During the mid-1990s, credit-derivatives began to be popular and evolved into credit default swaps (CDS), collateralized debt obligation (CDO), and synthetic collateralized debt obligation (Synthetic CDO). Because of the feature of risk sharing, credit-derivatives became an important part of financial market and played the key role in the financial crisis of 2007. So how to price credit-derivatives is a very important issue.
When pricing Synthetic CDO, most people use the one-factor coupla model as the structure of reward function, and suppose the distribution of model is Normal distribution, t- distribution or Normal Inverse Gaussian distribution(NIG). But the volatility smile of implied volatility always causes the pricing inaccurate.
For solving the problem, I use the random factor loading model under Normal distribution and NIG distribution in this study to test whether the random factor loading model is better than one-factor coupla model in pricing, and compare the efficience of optimization parameters. In conclusion, I will induct the best model of Synthetic CDO pricing.
摘要...................................................... .I
Abstract...................................................II
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.........................................2
第四節 信用違約交換與CDS Index..............................3
第五節 合成型擔保債權憑證...................................4
第六節 論文架構............................ ................5
第二章 文獻回顧.............................................6
第一節 單因子關聯結構................................ .....6
第二節 隨機風險因子負荷模型.......................... ......8
第三節 Normal Inverse Gaussian Distribution.................9
第三章 研究方法............................................10
第一節 合成型擔保債權憑證定價方式..........................10
第二節 單因子結構模型與LHP近似計算.........................13
第三節 NIG分配的特性與單因子結構NIG分配模型................17
第四節 單因子RFL結構模型...................................20
第四章 實證分析............................................23
第一節 DJ iTraxx Europe指數................................23
第二節 合成型CDO各分券定價.................................24
第五章 結論與建議..........................................38
參考文獻...................................................30
[1] Chunfa Wang and Dingwei Huang. (2009). “Double Normal Inverse Gaussian Copula with Random Factor Loadings Model for Synthetic CDO Pricing.” Management and Service Science, 2009. MASS '09. International Conference on.
[2] Li. David X. (2000). “On Default Correlation: A Copula Function Approach.”
Journal of Fixed Income, Vol. 9, Issue 4, pages 43–54.
[3] Hull, J. and White, A. (2004). “Valuation of a CDO and an n-th to Default CDS Without Monte Carlo Simulation.” Journal of Derivatives, Vol. 12, No. 2, pp. 8–23.
[4] Kalemanova, A., Schmid, B. Werner, R. (2007). “The normal inverse gaussian distribution for synthetic CDO pricing.” Journal of derivatives, Vol 14, pp. 80-93.
[5] Barndorff-Nielsen O. E. (1987). “Hyperbolic distributions and distributions on hyperbolae.” Scandinavian Journal of Statistics 5, pp. 151-157.
[6] O'kane, D., and Livesey, M. (2001). “Modeling Credit: Theory and Practice.”
Quantitative Credit Research, Lehman Brothers.
[7] Vasicek , O. (2002). “Loan Portfolio Value.” Risk, Vol. 12, pp.160-162
[8]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,國立政治大學博士學位論文
[9]林聖航 (2012) 探討合成型抵押擔保債券憑證之評價, 國立政治大學碩士學位論文
