| dc.contributor.advisor | 劉惠美 | zh_TW |
| dc.contributor.author (作者) | 許文銘 | zh_TW |
| dc.creator (作者) | 許文銘 | zh_TW |
| dc.date (日期) | 2016 | en_US |
| dc.date.accessioned | 1-七月-2016 14:57:13 (UTC+8) | - |
| dc.date.available | 1-七月-2016 14:57:13 (UTC+8) | - |
| dc.date.issued (上傳時間) | 1-七月-2016 14:57:13 (UTC+8) | - |
| dc.identifier (其他 識別碼) | G1033540101 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/98555 | - |
| 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) | 103354010 | zh_TW |
| dc.description.abstract (摘要) | 衡量投資組合的稀有事件時，即使稀有事件違約的機率極低，但是卻隱含著高額資產違約時所帶來的重大損失，所以我們必須要精準地評估稀有事件的信用風險。本研究係在估計信用損失分配的尾端機率，模擬的模型包含同質模型與異質模型；然而蒙地卡羅法雖然在風險管理的計算上相當實用，但是估計機率極小的尾端機率時模擬不夠穩定，因此為增進模擬的效率，我們利用Glasserman and Li (Management Science, 51(11),2005)提出的重點取樣法，以及根據Chiang et al. (Joural of Derivatives, 15(2),2007)重點取樣法為基礎做延伸的改良式重點取樣法，兩種方法來對不同的投資組合做模擬，更是將改良式重點取樣法推廣至異質模型做討論，本文亦透過變異數縮減效果來衡量兩種方法的模擬效率。數值結果顯示，比起傳統的蒙地卡羅法，此兩種方法皆能達到變異數縮減，其中在同質模型下的改良式重點取樣法有很好的表現，模擬時間相當省時，而異質模型下的重點取樣法也具有良好的估計效率及模擬的穩定性。 | zh_TW |
| dc.description.abstract (摘要) | When measuring portfolio credit risk of rare-event, even though its default probabilities are low, it causes significant losses resulting from a large number of default. Therefore, we have to measure portfolio credit risk of rare-event accurately. In particular, our goal is estimating the tail of loss distribution. Models we simulate are including homogeneous models and heterogeneous models. However, Monte Carlo simulation is useful and widely used computational tool in risk management, but it is unstable especially estimating small tail probabilities. Hence, in order to improve the efficiency of simulation, we use importance sampling proposed by Glasserman and Li (Management Science, 51(11),2005) and modified importance sampling based on importance sampling which proposed by Chiang et al. (2007 Joural of Derivatives, 15(2),). Simulate different portfolios by these two of simulations. On top of that, we extend and discuss the modified importance sampling simulation to heterogeneous model. In this article, we measure efficiency of two simulations by variance reduction. Numerical results show that proposed methods are better than Monte Carlo and achieve variance reduction. In homogeneous model, modified importance sampling has excellent efficiency of estimating and saves time. In heterogeneous model, importance sampling also has great efficiency of estimating and stability. | en_US |
| dc.description.tableofcontents | 第一章 緒論 1第二章 文獻探討 4第三章 研究方法 6第一節 模型基本假設 6第二節 重點取樣法 8第三節 改良式重點取樣法 12第四節 推廣改良式重點取樣法 133-4-1 二因子同質模型 143-4-2 多因子同質模型 143-4-3 二因子異質模型 14 3-4-4 三因子異質模型 17 第五節 模型之模擬流程 19 3-5-1 單因子同質模型之模擬流程 193-5-2 二因子同質模型之模擬流程 21 3-5-3 多因子同質模型之模擬流程 233-5-4 二因子異質模型之模擬流程 253-5-5 三因子異質模型之模擬流程 27第四章 數值呈現與模擬比較分析 30第一節 同質模型模擬結果 304-1-1單因子同質模型 304-1-2二因子同質模型 374-1-3多因子同質模型 44第二節 異質模型模擬結果 464-2-1二因子異質模型 464-2-2三因子異質模型 47第五章 結論 49附錄 50參考文獻 60 | zh_TW |
| dc.format.extent | 2250338 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G1033540101 | en_US |
| dc.subject (關鍵詞) | 投資組合 | zh_TW |
| dc.subject (關鍵詞) | 信用風險 | zh_TW |
| dc.subject (關鍵詞) | 尾端機率 | zh_TW |
| dc.subject (關鍵詞) | 蒙地卡羅法 | zh_TW |
| dc.subject (關鍵詞) | 重點取樣法 | zh_TW |
| dc.subject (關鍵詞) | 改良式重點取樣法 | zh_TW |
| dc.subject (關鍵詞) | 變異數縮減 | zh_TW |
| dc.subject (關鍵詞) | Portfolio credit risk | en_US |
| dc.subject (關鍵詞) | Tail probability | en_US |
| dc.subject (關鍵詞) | Monte Carlo | en_US |
| dc.subject (關鍵詞) | Importance sampling | en_US |
| dc.subject (關鍵詞) | Modified importance sampling | en_US |
| dc.subject (關鍵詞) | Variance reduction | en_US |
| dc.title (題名) | 異質性投資組合下的改良式重點取樣法 | zh_TW |
| dc.title (題名) | Modified Importance Sampling for Heterogeneous Portfolio | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | 1. Bassamboo, A.,Juneja, S.and Zeevi, A. (2008) , “Portfolio Credit Risk with 2. Extremal Dependence: Asymptotic Analysis and Efficient Simulation” , Operations Research, 56(3), 593-6062. Chiang, M.H., Yueh, M.L., and Hsieh, M.H. (2007), “An Efficient Algorithm for Basket Default Swap Valuation”, Joural of Derivatives, 15(2), 8-193. Fuh, C.D., Teng, H.W., and Wang, R.H. (2013), “Efficient Importance Sampling for Rare Event Simulation with Applications”, Technical Report.4. Glasserman, P. (2004), “Tail Approximations for Portfolio Credit Risk”, Journal of Derivatives, 12, 24-425. Glasserman, P. and Li, J. (2005), “Importance Sampling for Portfolio Credit Risk”, Management Science, 51(11), 1643-16566. Han,C.H. ,Wu,C.T. (2010), “Efficient Importance Sampling for Estimating Lower Tail Probabilities under Gaussian and Student’s t Distributions”, Preprint. National Tsing-Hua University. 20107. Li, D.X. (2000), “On Default Correlation: A Coupla Function Approach”, Journal of Fixed Income, 9, 43-548. Nocedal, J. and M. Wright (1999), “Numerical Optimization”. New York: Springer-Verlag | zh_TW |
