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題名 封閉偏斜常態因子模型違約風險估計之研究
Estimating Tail Probability of Credit Loss Distribution with Closed Skew Normal作者 曹立諭
Tsao, Li-Yu貢獻者 劉惠美
Liu, Hui-Mei
曹立諭
Tsao, Li-Yu關鍵詞 信用違約風險
資產投資組合
常態關聯結構
封閉偏斜常態關聯結構
蒙地卡羅法
重要性取樣法
指數轉換
變異數縮減
直尋牛頓法
Normal-Copula
Closed-Skew-Normal-Copula
Asset Portfolio
Credit Default Risk
Monte Carlo Method
Importance Sampling
Exponential Twisting
Variation Reduction
Line Search Newton method日期 2019 上傳時間 7-Aug-2019 16:01:25 (UTC+8) 摘要 投資組合的信用風險常使用常態關聯結構模型進行估計，但模型能調整的參數有限，本篇使用封閉常態關聯結構模型進行推導，其分配擁有常態分配的性質，也具有調整分配偏度及厚尾程度的參數，使其更適合用在解釋投資組合間的相依程度。在衡量投資組合的稀有事件時，其機率值不易模擬，但卻包含著高額資產違約時的重大損失，若僅使用蒙地卡羅法模擬其信用風險，其模擬耗費的時間比一般事件還久且變異較大，我們使用Glasserman and Li (Management Science, 51(11), 1643-1656, 2005)與Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007)各別提出的重要性取樣法(簡稱GIS法與MIS法)進行推導及延伸，在封閉偏斜常態關聯結構模型的投資組合下進行模擬，透過變異數縮減效果衡量兩種方法的模擬效率。數值結果顯示，在單因子模型中，MIS法所花費的時間較GIS法少，其變異數縮減效果顯著；在多因子模型中，GIS法能適用的範圍較廣，透過兩階段重要性取樣法，其變異數縮減效果良好，模擬時間也較蒙地卡羅法縮短。兩種方法都有其適用的模型，也具有良好的估計精準度及模擬穩定性。
The credit risk of the portfolio is often estimated using the Normal Copula model, but the parameters that the model can adjust are limited. This paper uses the Closed Normal Copula model to derive. The CSN distribution has the nature of normal distribution, and also has the adjustment distribution skewness. The degree of parameters make it more suitable for interpreting the degree of dependency between portfolios. When measuring the rare events of a portfolio, the probability value is not easy to simulate, but it contains a large loss in the event of a high-value Asset Default. Using Monte Carlo to simulate its credit risk, the simulation takes longer than usual and varies greatly. We use the importance sampling method proposed by Glasserman and Li (Management Science, 51(11), 1643-1656, 2005) and Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007). Referred to as GIS method and MIS method, it is deduced and extended. The simulation is carried out under the portfolio of Closed Skew Normal Copula model, and the simulation efficiency of the two methods is measured by the reduction effect of variance. The numerical results show that in the single factor model, the MIS method takes less time than the GIS method, and the Variance Reduction effect is significant. In the multi-factor model, the GIS method can be applied to a wide range, through the two-stage importance sampling method. The Variance Reduction effect is good, and the simulation time is shortened compared with the Monte Carlo method. Both methods have their applicable models and also have good estimation accuracy and simulation stability.參考文獻 [1] 邱嬿燁 (2008).“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.[2] 陳家丞 (2016).“極值相依模型下投資組合之重要性取樣法”,國立政治大學統計學系碩士論文.[3] 許文銘 (2016).“異質性投資組合下的改良式重點取樣法”,國立政治大學統計學系碩士論文.[4] Azzalini, A. (1985). “A class of distributions which includes the normal ones.”, Scandinavian Journal of Statistics, 171-178.[5] Azzalini, A. (2005). “The Skew-normal Distribution and Related MultivariateFamilies.”, Scandinavian Journal of Statistics, 32(2), 159-188.[6] Azzalini A. and Dalla-Valle A. (1996). “The multivariate skew-normal distribution.”, Biometrika, 83(4), 715–726.[7] Chiang, M.H., Yueh, M.L., and Hsieh, M.H. (2007). “An Efficient Algorithm forBasket Default Swap Valuation.”, Journal of Derivatives, 15(2), 8-19.[8] Elal-Olivero, D. (2010). “ Alpha-skew-normal distribution. ” Proyecciones(Antofagasta), 29(3), 224-240.[9] Glasserman‚ P. (2004). “Tail Approximations for Portfolio Credit Risk.”‚ Journal of Derivatives, 12(2), 24-42.[10] Glasserman, P. and Li, J. (2005). “Importance Sampling for Portfolio Credit Risk.”, Management Science, 51(11),1643-1656.[11] Glasserman, P., Heidelberger, P. and Shahabuddin, P. (2000). “Variance Reduction Techniques for Estimating Value-at-Risk. ”, Management Science, 46(10), 1349-1364.[12] 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, 126(2), 521-534.[13] González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “Amultivariate skew normal distribution.”, Journal of Multivariate Analysis, 89(1), 181-190.[14] Han, C.H, and Wu, C.T. (2010). “Efficient importance sampling for estimatinglower tail probabilities under Gaussian and Student’s t distributions.”, Preprint.National Tsing-Hua University.[15] Li, D.X. (1999). “On default correlation: a copula function approach.” , Journal of Fixed Income , 9(4), 43-54.[16] Nocedal, J., and M. Wright. (1999). Numerical Optimization. Springer-Verlag, New York.[17] Wilson, T. (1999). “Value at risk. ” Risk Management and Analysis, 1, 61-124. 描述 碩士
國立政治大學
統計學系
106354012資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106354012 資料類型 thesis dc.contributor.advisor 劉惠美 zh_TW dc.contributor.advisor Liu, Hui-Mei en_US dc.contributor.author (Authors) 曹立諭 zh_TW dc.contributor.author (Authors) Tsao, Li-Yu en_US dc.creator (作者) 曹立諭 zh_TW dc.creator (作者) Tsao, Li-Yu en_US dc.date (日期) 2019 en_US dc.date.accessioned 7-Aug-2019 16:01:25 (UTC+8) - dc.date.available 7-Aug-2019 16:01:25 (UTC+8) - dc.date.issued (上傳時間) 7-Aug-2019 16:01:25 (UTC+8) - dc.identifier (Other Identifiers) G0106354012 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/124683 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 106354012 zh_TW dc.description.abstract (摘要) 投資組合的信用風險常使用常態關聯結構模型進行估計，但模型能調整的參數有限，本篇使用封閉常態關聯結構模型進行推導，其分配擁有常態分配的性質，也具有調整分配偏度及厚尾程度的參數，使其更適合用在解釋投資組合間的相依程度。在衡量投資組合的稀有事件時，其機率值不易模擬，但卻包含著高額資產違約時的重大損失，若僅使用蒙地卡羅法模擬其信用風險，其模擬耗費的時間比一般事件還久且變異較大，我們使用Glasserman and Li (Management Science, 51(11), 1643-1656, 2005)與Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007)各別提出的重要性取樣法(簡稱GIS法與MIS法)進行推導及延伸，在封閉偏斜常態關聯結構模型的投資組合下進行模擬，透過變異數縮減效果衡量兩種方法的模擬效率。數值結果顯示，在單因子模型中，MIS法所花費的時間較GIS法少，其變異數縮減效果顯著；在多因子模型中，GIS法能適用的範圍較廣，透過兩階段重要性取樣法，其變異數縮減效果良好，模擬時間也較蒙地卡羅法縮短。兩種方法都有其適用的模型，也具有良好的估計精準度及模擬穩定性。 zh_TW dc.description.abstract (摘要) The credit risk of the portfolio is often estimated using the Normal Copula model, but the parameters that the model can adjust are limited. This paper uses the Closed Normal Copula model to derive. The CSN distribution has the nature of normal distribution, and also has the adjustment distribution skewness. The degree of parameters make it more suitable for interpreting the degree of dependency between portfolios. When measuring the rare events of a portfolio, the probability value is not easy to simulate, but it contains a large loss in the event of a high-value Asset Default. Using Monte Carlo to simulate its credit risk, the simulation takes longer than usual and varies greatly. We use the importance sampling method proposed by Glasserman and Li (Management Science, 51(11), 1643-1656, 2005) and Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007). Referred to as GIS method and MIS method, it is deduced and extended. The simulation is carried out under the portfolio of Closed Skew Normal Copula model, and the simulation efficiency of the two methods is measured by the reduction effect of variance. The numerical results show that in the single factor model, the MIS method takes less time than the GIS method, and the Variance Reduction effect is significant. In the multi-factor model, the GIS method can be applied to a wide range, through the two-stage importance sampling method. The Variance Reduction effect is good, and the simulation time is shortened compared with the Monte Carlo method. Both methods have their applicable models and also have good estimation accuracy and simulation stability. en_US dc.description.tableofcontents 誌謝 I摘要 IIAbstract III目錄 1圖目錄 3表目錄 5第一章 緒論 6第二章 文獻探討 7第三章 封閉偏斜常態分配與因子模型 9第一節 封閉偏斜常態分配之性質與定理 9第二節 封閉偏斜常態關聯結構模型 15第三節 指數轉換應用於CSN分配 18第四章 研究方法 20第一節 模型基本假設 20第二節 重要性取樣法 23第三節 MIS改良式重要性取樣法 25第四節 MIS改良式重要性取樣法推廣 28第五節 GIS改良式重要性取樣法 33第五章 信用違約估計流程 39壹、蒙地卡羅法 (A.單因子模型) 40貳、MIS改良式重要性取樣法 (A.單因子模型) 41參、GIS重要性取樣法 (A.單因子模型) 42肆、蒙地卡羅法 (B.多因子模型) 43伍、MIS改良式重要性取樣法 (B.多因子模型) 44陸、GIS重要性取樣法 (A.多因子模型) 45第六章 估計近似結果分析 46第一節 投資組合模擬結果 47第二節 各方法近似結果分析 63參考文獻 64 zh_TW dc.format.extent 2149706 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106354012 en_US dc.subject (關鍵詞) 信用違約風險 zh_TW dc.subject (關鍵詞) 資產投資組合 zh_TW dc.subject (關鍵詞) 常態關聯結構 zh_TW dc.subject (關鍵詞) 封閉偏斜常態關聯結構 zh_TW dc.subject (關鍵詞) 蒙地卡羅法 zh_TW dc.subject (關鍵詞) 重要性取樣法 zh_TW dc.subject (關鍵詞) 指數轉換 zh_TW dc.subject (關鍵詞) 變異數縮減 zh_TW dc.subject (關鍵詞) 直尋牛頓法 zh_TW dc.subject (關鍵詞) Normal-Copula en_US dc.subject (關鍵詞) Closed-Skew-Normal-Copula en_US dc.subject (關鍵詞) Asset Portfolio en_US dc.subject (關鍵詞) Credit Default Risk en_US dc.subject (關鍵詞) Monte Carlo Method en_US dc.subject (關鍵詞) Importance Sampling en_US dc.subject (關鍵詞) Exponential Twisting en_US dc.subject (關鍵詞) Variation Reduction en_US dc.subject (關鍵詞) Line Search Newton method en_US dc.title (題名) 封閉偏斜常態因子模型違約風險估計之研究 zh_TW dc.title (題名) Estimating Tail Probability of Credit Loss Distribution with Closed Skew Normal en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] 邱嬿燁 (2008).“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.[2] 陳家丞 (2016).“極值相依模型下投資組合之重要性取樣法”,國立政治大學統計學系碩士論文.[3] 許文銘 (2016).“異質性投資組合下的改良式重點取樣法”,國立政治大學統計學系碩士論文.[4] Azzalini, A. (1985). “A class of distributions which includes the normal ones.”, Scandinavian Journal of Statistics, 171-178.[5] Azzalini, A. (2005). “The Skew-normal Distribution and Related MultivariateFamilies.”, Scandinavian Journal of Statistics, 32(2), 159-188.[6] Azzalini A. and Dalla-Valle A. (1996). “The multivariate skew-normal distribution.”, Biometrika, 83(4), 715–726.[7] Chiang, M.H., Yueh, M.L., and Hsieh, M.H. (2007). “An Efficient Algorithm forBasket Default Swap Valuation.”, Journal of Derivatives, 15(2), 8-19.[8] Elal-Olivero, D. (2010). “ Alpha-skew-normal distribution. ” Proyecciones(Antofagasta), 29(3), 224-240.[9] Glasserman‚ P. (2004). “Tail Approximations for Portfolio Credit Risk.”‚ Journal of Derivatives, 12(2), 24-42.[10] Glasserman, P. and Li, J. (2005). “Importance Sampling for Portfolio Credit Risk.”, Management Science, 51(11),1643-1656.[11] Glasserman, P., Heidelberger, P. and Shahabuddin, P. (2000). “Variance Reduction Techniques for Estimating Value-at-Risk. ”, Management Science, 46(10), 1349-1364.[12] 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, 126(2), 521-534.[13] González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “Amultivariate skew normal distribution.”, Journal of Multivariate Analysis, 89(1), 181-190.[14] Han, C.H, and Wu, C.T. (2010). “Efficient importance sampling for estimatinglower tail probabilities under Gaussian and Student’s t distributions.”, Preprint.National Tsing-Hua University.[15] Li, D.X. (1999). “On default correlation: a copula function approach.” , Journal of Fixed Income , 9(4), 43-54.[16] Nocedal, J., and M. Wright. (1999). Numerical Optimization. Springer-Verlag, New York.[17] Wilson, T. (1999). “Value at risk. ” Risk Management and Analysis, 1, 61-124. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU201900228 en_US
