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題名 不對稱分配於風險值之應用 - 以台灣股市為例
An application of asymmetric distribution in value at risk - taking Taiwan stock market as an example
作者 沈之元
Shen,Chih-Yuan
貢獻者 毛維凌
Mao,Wei-Ling
沈之元
Shen,Chih-Yuan
關鍵詞 風險值
極值理論
skew-t 分配
回溯測試
Value at Risk
Extreme Value Theory
asymmetric exponential power distribution
Back-testing
日期 2008
上傳時間 9-Dec-2010 14:45:25 (UTC+8)
摘要 本文以台灣股價加權指數，使用 AR(3)-GJR-GRACH(1,1) 模型，白噪音假設為 Normal 、 Skew-Normal 、 Student t 、 skew-t 、 EPD 、 SEPD 、與 AEPD 等七種分配。著重於兩個部份，(一) Student t 分配一族與 EPD 分配一族在模型配適與風險值估計的比較；(二) 預測風險值區分為低震盪與高震盪兩個區間，比較不同分配在兩區間預測風險值的差異。

實證分析顯示， t 分配一族與 EPD 分配一族配適的結果，無論是只考慮峰態 ( t 分配與 EPD 分配) ，或者加入影響偏態的參數 ( skew-t 分配與 SEPD 分配) ， t 分配一族的配適程度都較 EPD 分配一族為佳。更進一步考慮分配兩尾厚度不同的 AEPD 分配，配適結果為七種分配中最佳。

風險值的估計在低震盪的區間，常態分配與其他厚尾分配皆能通過回溯測試，採用厚尾分配效果不大；在高震盪的區間，左尾風險值回溯測試結果，常態分配與其他厚尾分配皆無法全數通過，但仍以 AEPD 分配為最佳。最後比較損失函數，左尾風險值估計以 AEPD 分配為最佳，右尾風險值則無一致的結果。因此我們認為 AEPD 分配可作為風險管理有用的工具。
參考文獻 Angelidis, T. , A. Benos and S. Degiannakis (2007), ”A robust VaR model under different time periods and weighting schemes.” Review of Quantitative Finance and Accounting, Springer, 28(2), 187-201.
Blanco, C. and G. Ihle (1999), ”How good is Your VaR? Using Backtesting to Assess System Performance.” Financial Engineering News , August , 11 , 1-4.
Bollerslev, T. (1986), ”Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 31 , 307-327.
Christoffersen, P. (1998), ”Evaluating Interval Forecasts.” International Economic Review, 39, 841-862.
Engle, R. F. (1982), ”Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation.” Econometrica, 50 , 987-1008.
Ghorbel, A. and A. Trabelsi (2007), ”Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation.” MPRA Working Paper.
Gilli, M. and E. Kellezi (2006), ”An application of extreme value theory for measuring financial risk.”, Computational Economics, 27, 1-23.
Glosten L. R., R. Jagannathan and D. E. Runkle (1993), ”On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48, No.5, 1779-801.
Hansen, B. E. (1994), ”Autoregressive Conditional Density Estimation.” International Economic Review, 35 , 705-730.
Hendricks, D. (1996), ”Evaluation of value-at-risk models using historical data.” Economic Police Review, 2, 39-70.
Hull, J. and A. White (1998), ”Incorporating volatility updating for value-at-risk.” Journal of Risk, 1 , 5-19.
Jondeau, E. , S. H. Poon and M. Rockinger (2007), ”Financial Modeling Under Non-Gaussian Distributions.” , Springer Finance
Kupiec, P. (1995), ”Techniques for Verifying the Accuracy of Risk Management Models.” Journal of Derivatives, 3, 73-84.
Lopez, J.A. (1999), ”Methods for Evaluating Value-at-Risk Estimates.” , Federal Reserve Bank of San Francisco Economic Review, 2, 3-17.
Marimoutou, V. ,B. Raggad, and A. Trabelsi (2006), ”Extreme value theory and value at risk: application to oil market.” GREQAM Working Paper 2006-38
McNeil, A.J, and R. Frey (2000), ”Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach.” Journal of Empirical Finance , 7 , 271-300.
Theodossiou, P. (2000), ”Skewed Generalized Error Distribution of Financial Assets and Option Pricing.” SSRN Working Paper
Tsay, R. S. (2005), ”Analysis of Financial Time Series.”, 2nd ,Wiley.
Zhu, D. and V. Zinde-Walsh (2009), ”Properties and estimation of asymmetric exponential power distribution.” Journal of Econometrics, 148 , 86-99.
描述 碩士
國立政治大學
經濟研究所
96258009
97
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096258009
資料類型 thesis
dc.contributor.advisor 毛維凌zh_TW
dc.contributor.advisor Mao,Wei-Lingen_US
dc.contributor.author (Authors) 沈之元zh_TW
dc.contributor.author (Authors) Shen,Chih-Yuanen_US
dc.creator (作者) 沈之元zh_TW
dc.creator (作者) Shen,Chih-Yuanen_US
dc.date (日期) 2008en_US
dc.date.accessioned 9-Dec-2010 14:45:25 (UTC+8)-
dc.date.available 9-Dec-2010 14:45:25 (UTC+8)-
dc.date.issued (上傳時間) 9-Dec-2010 14:45:25 (UTC+8)-
dc.identifier (Other Identifiers) G0096258009en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49959-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 經濟研究所zh_TW
dc.description (描述) 96258009zh_TW
dc.description (描述) 97zh_TW
dc.description.abstract (摘要) 本文以台灣股價加權指數，使用 AR(3)-GJR-GRACH(1,1) 模型，白噪音假設為 Normal 、 Skew-Normal 、 Student t 、 skew-t 、 EPD 、 SEPD 、與 AEPD 等七種分配。著重於兩個部份，(一) Student t 分配一族與 EPD 分配一族在模型配適與風險值估計的比較；(二) 預測風險值區分為低震盪與高震盪兩個區間，比較不同分配在兩區間預測風險值的差異。

實證分析顯示， t 分配一族與 EPD 分配一族配適的結果，無論是只考慮峰態 ( t 分配與 EPD 分配) ，或者加入影響偏態的參數 ( skew-t 分配與 SEPD 分配) ， t 分配一族的配適程度都較 EPD 分配一族為佳。更進一步考慮分配兩尾厚度不同的 AEPD 分配，配適結果為七種分配中最佳。

風險值的估計在低震盪的區間，常態分配與其他厚尾分配皆能通過回溯測試，採用厚尾分配效果不大；在高震盪的區間，左尾風險值回溯測試結果，常態分配與其他厚尾分配皆無法全數通過，但仍以 AEPD 分配為最佳。最後比較損失函數，左尾風險值估計以 AEPD 分配為最佳，右尾風險值則無一致的結果。因此我們認為 AEPD 分配可作為風險管理有用的工具。		zh_TW
dc.description.tableofcontents 1 前言 1
2 風險衡量與相關文獻 4
2.1 風險值 4
2.2 歷史模擬法(Historical Simulation) 4
2.3 極值理論(Extreme Value Theory) 5
2.4 GARCH Model 10
2.5 動態歷史模擬法(Filtered Historical Simulation) 11
2.6 動態極值理論(Conditional Extreme Value Theory) 11
3 研究方法 12
3.1 AR-GJR-GARCH 13
3.2 白噪音設定 13
3.3 模型配適 19
3.4 回溯測試(Back-testing) 21
3.5 損失函數(Loss Function) 23
4 實證分析 24
4.1 資料 24
4.2 樣本內估計 26
4.3 樣本外預測 31
4.4 動態極值理論與動態歷史模擬法 35
4.5 損失函數 42
4.6 小結 46
5 結論 47
附錄 50		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096258009en_US
dc.subject (關鍵詞) 風險值zh_TW
dc.subject (關鍵詞) 極值理論zh_TW
dc.subject (關鍵詞) skew-t 分配zh_TW
dc.subject (關鍵詞) 回溯測試zh_TW
dc.subject (關鍵詞) Value at Risken_US
dc.subject (關鍵詞) Extreme Value Theoryen_US
dc.subject (關鍵詞) asymmetric exponential power distributionen_US
dc.subject (關鍵詞) Back-testingen_US
dc.title (題名) 不對稱分配於風險值之應用 - 以台灣股市為例zh_TW
dc.title (題名) An application of asymmetric distribution in value at risk - taking Taiwan stock market as an exampleen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Angelidis, T. , A. Benos and S. Degiannakis (2007), ”A robust VaR model under different time periods and weighting schemes.” Review of Quantitative Finance and Accounting, Springer, 28(2), 187-201.zh_TW
dc.relation.reference (參考文獻) Blanco, C. and G. Ihle (1999), ”How good is Your VaR? Using Backtesting to Assess System Performance.” Financial Engineering News , August , 11 , 1-4.zh_TW
dc.relation.reference (參考文獻) Bollerslev, T. (1986), ”Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 31 , 307-327.zh_TW
dc.relation.reference (參考文獻) Christoffersen, P. (1998), ”Evaluating Interval Forecasts.” International Economic Review, 39, 841-862.zh_TW
dc.relation.reference (參考文獻) Engle, R. F. (1982), ”Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation.” Econometrica, 50 , 987-1008.zh_TW
dc.relation.reference (參考文獻) Ghorbel, A. and A. Trabelsi (2007), ”Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation.” MPRA Working Paper.zh_TW
dc.relation.reference (參考文獻) Gilli, M. and E. Kellezi (2006), ”An application of extreme value theory for measuring financial risk.”, Computational Economics, 27, 1-23.zh_TW
dc.relation.reference (參考文獻) Glosten L. R., R. Jagannathan and D. E. Runkle (1993), ”On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48, No.5, 1779-801.zh_TW
dc.relation.reference (參考文獻) Hansen, B. E. (1994), ”Autoregressive Conditional Density Estimation.” International Economic Review, 35 , 705-730.zh_TW
dc.relation.reference (參考文獻) Hendricks, D. (1996), ”Evaluation of value-at-risk models using historical data.” Economic Police Review, 2, 39-70.zh_TW
dc.relation.reference (參考文獻) Hull, J. and A. White (1998), ”Incorporating volatility updating for value-at-risk.” Journal of Risk, 1 , 5-19.zh_TW
dc.relation.reference (參考文獻) Jondeau, E. , S. H. Poon and M. Rockinger (2007), ”Financial Modeling Under Non-Gaussian Distributions.” , Springer Financezh_TW
dc.relation.reference (參考文獻) Kupiec, P. (1995), ”Techniques for Verifying the Accuracy of Risk Management Models.” Journal of Derivatives, 3, 73-84.zh_TW
dc.relation.reference (參考文獻) Lopez, J.A. (1999), ”Methods for Evaluating Value-at-Risk Estimates.” , Federal Reserve Bank of San Francisco Economic Review, 2, 3-17.zh_TW
dc.relation.reference (參考文獻) Marimoutou, V. ,B. Raggad, and A. Trabelsi (2006), ”Extreme value theory and value at risk: application to oil market.” GREQAM Working Paper 2006-38zh_TW
dc.relation.reference (參考文獻) McNeil, A.J, and R. Frey (2000), ”Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach.” Journal of Empirical Finance , 7 , 271-300.zh_TW
dc.relation.reference (參考文獻) Theodossiou, P. (2000), ”Skewed Generalized Error Distribution of Financial Assets and Option Pricing.” SSRN Working Paperzh_TW
dc.relation.reference (參考文獻) Tsay, R. S. (2005), ”Analysis of Financial Time Series.”, 2nd ,Wiley.zh_TW
dc.relation.reference (參考文獻) Zhu, D. and V. Zinde-Walsh (2009), ”Properties and estimation of asymmetric exponential power distribution.” Journal of Econometrics, 148 , 86-99.zh_TW