重點重覆抽樣下拔靴法估計風險值-以台泥華碩股票為例

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姓名

黃元貞(Yuan-Chen Huang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

重點重覆抽樣下拔靴法估計風險值-以台泥華碩股票為例

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摘要(中)

近幾年來，在金融界一個重要的議題是風險管理，其中風險值(VaR)
是用以度量且管理市場風險的參考。本文目的在於計算投資組合之風險值，以及風險值之尾端估計機率，再與原始設定之尾端機率作比較。而蒙地卡羅分析到目前為此是最有用的方法之一，其最大的缺點是計算時間較長。在本文中，我們假設風險因子為一個多維常態分配，利用重點抽樣方法，增加尾端機率樣本被抽樣的機率，配合拔靴法，即重點抽樣下的拔靴法估計投資組合之風險值，以及估計風險值之尾端機率。最後使用本文所建議的方法，對台灣兩個股票之投資組合，台泥與華碩，做一個實證的分析。

摘要(英)

Nowadays, risk management is an important issue. A standard benchmark used to measure and to manage market risks is the Value-at-Risk (VaR).To evaluate a portfolio value-at-risk (VaR), Monte Carlo analysis is by far the most powerful method. However, the biggest drawback of this method is its computational time. In this paper, we model the return of risk factors with a multivariate normal and provide an efficient method, a bootstrap algorithm with importance resampling, to estimate portfolio loss probability and portfolio value-at-risk. As an illustration of our proposed methods, we report an empirical study based on two stock index returns in
Taiwan, the Taiwan cement corporation and the ASUS.

關鍵字(中)

★ 重點重覆抽樣
★ 拔靴法
★ 風險值

關鍵字(英)

★ VaR
★ bootstrap
★ importance resampling

論文目次

第一章緒論........................................... 1
第一節研究背景與動機................................. 1
第二節文獻回顧....................................... 2
第三節風險值與投資組合............................... 3
第二章重點重覆抽樣與拔靴演算法....................... 9
第一節拔靴法(Bootstrap).............................. 9
第二節重點重覆抽樣拔靴法............................. 13
第三節一維常態重點重覆抽樣........................... 14
第四節多維常態重點重覆抽樣拔靴法......................16
第五節多維常態重點重覆抽樣拔靴演算法................. 19
第三章實證分析....................................... 21
第一節資料來源....................................... 21
第二節資料分析....................................... 21
第三節相對效率分析................................... 27
第四節回溯測試....................................... 29
第四章結論.......................................... 32
參考文獻. ..............................................33
附錄：................................................ 37

參考文獻

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[6] Fuh, C. D., & Hu, I. (2004). Efficient importance sampling for events of moderate deviations with applications. Biometrika, 91, 471–490.
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[10] Glasserman, P., Heidelberger, P., and Shahabuddin, P. (2002). Portfolio Value-at-Risk with heavy tailed risk factors. Mathematical Finance,12, 239-270.
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[12] Hall, P. (1990a). Asymptotic properties of the bootstrap for heavy-tail distributions. Annals of Probability,18, 1342–1360.
[13] Hall, P. (1990b). Performance of balanced bootstrap resampling in distribution function and quantile problems. Probability. Theory Related Fields, 85, 239–260.
[14] Hall, P. (1991). Bahadur representations for uniform resampling and importance resampling with applications to asymptotic relative efﬁciency. Annals of Statistics, 19, 1062–1072.
[15] Hall, P. (1992). The Bootstrap and Edgeworth Expansion. Springer-Verlag, New York.
[16] Hull, J., & White, A(1998).Incorporating Volatility Updating Into the Historical Simulation Method for Value at Risk. Journal of Risk, 6, 9-19, spring.
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[18] Lin,S.K , Wang,R.H & Fuh,C.D. (2007).Risk Management for Linear and Non-Linear Assets: A Bootstrap Method with Importance Resampling to Evaluate Value-at-Risk. Springer Science+Business Media, LLC

指導教授

傅承德(Cheng-der Fuh)

審核日期

2008-6-25

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