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題名 厚尾、偏態與壓力測試：混合分配模型的應用
作者 林子慶
貢獻者 杜化宇
林子慶
關鍵詞 壓力測試
厚尾
偏態
混合分配
一般化偏態t分配
日期 2011
上傳時間 30-Oct-2012 10:13:59 (UTC+8)
摘要 本文使用混合分配方法發展一個可處理厚尾,偏態(報酬分配不對稱)的壓力 測試模型。在資料上,我們以希臘國債與 S&P500 指數作為核心資產,臺灣市場 的標的資產作為邊緣資產。在與資料的配適能力上,本文發展的模型確實優於過 去假設常態分配的壓力測試模型。在實際執行壓力測試中,本研究比較了本文使 用的混合分配模型與過去模型的差異,我們發現壓力測試結果的差異相當大,因 此肯定了能抓住厚尾及偏態現象模型的重要性。
參考文獻 1. Azzalini, A., (1985) “A Class of Distributions Which Includes the Normal Ones,” Scandinavian Journal of Statistics, 12, 171-178.
     
     2. Azzalini, A., (1986) “Further Results on a Class of Distributions Which Includes the Normal Ones,” Statistica, 46, 199-208.
     
     3. Azzalini, A. and A. Capitaino, (2003) “Distributions Generated by Perturbation of Symmetry With Emphasis on a Multivariate Skew t-Distribution,” Journal of the Royal Statistical Society. Ser.B, 65, 367-389.
     
     4. Basso R. M., V.H. Lachos, C.R. Cabral, P. Ghosh, (2009) “Robust mixture modeling based on scale mixtures of skew-normal distributions,” Computational Statistics & Data Analysis, 12, 2926-2941.
     
     5. Bauwens L, Laurent S., (2005) “A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models, ” Journal of Business and Economic Statistics, 23:3, 346-354.
     
     6. Beber, A., M. W. Brandt, and K. A. Kavajecz (2009) “Flight-to-Quality or Flight-to-Liquidity? Evidence from the Euro-Area Bond Market.” Review of Financial Studies, 22, 925–957.
     
     7. Bollerslev, T., (1987) “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 31, 307-327.
     
     8. Carol, A. and E. Sheedy, (2008) "Developing a stress testing framework based on market risk models," Journal of Banking & Finance, 32, 2220-2236
     
     9. Fernandez, C. and M. F. J. Steel (1998), “On Bayesian Modelling of Fat Tails and Skewness.” Journal of the American Statistical Association, 93, 359–371.
     
     10. Fraley, C. and A. E. Raftery, (2002) “Model-Based Clustering, Discriminant Analysis, and Density Estimation,” Journal of the American Statistical Association, 97, 611-631.
     
     11. Gregor, J., (1969) "An algorithm for the decomposition of a distribution into Gaussian components," Biornetrics, 26, 79-93.
     
     12. Hamilton, J. (1991), “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions,” Journal of Business and Economic Statistics, 9, 1779-1801.
     
     13. Hewitt, C. C. Jr. and B. Lefkowitz, (1979) "Methods for Fitting Distributions to Insurance Loss Data," Proceedings of the Casualty Actuarial Society, LXVI, 139-160.
     
     14. Jones, M. C. and M. J. Faddy, (2003) “A skew extension of the t distribution, with applications,” Statist. Soc B, 65, 159–174.
     
     15. Jorion, P., (1995) “Predicting Volatility in the Foreign Exchange Market.” Journal of Finance, 2, 507-528
     
     16. Kim, J. and C. Finger (2000), “A stress test to incorporate correlation breakdown,” Journal of Risk, 2, 5-19.
     
     17. Lin, T. I., J. C., Lee, and H. F., Ni, (2004) “Bayesian Analysis of Mixture Modeling Using the Multivariate t Distribution,” Statistics and Computing, 14, 119-130.
     
     18. Lin, T. I., J. C., Lee, and S.Y., Yen, (2007) “Finite mixture modeling using the skew normal distribution,” Statistica Sinica, 17, 909-927.
     
     19. Markowitz, H., (1952) "Portfolio selection," Journal of Finance, 7, 77-91.
     
     20. McLachlan, G. J. and K. E. Basord, (1988) Mixture Models: Inference and
     Application to Clustering, Marcel Dekker, New York.
     
     21. McLachlan, G. J. and D. Peel, (2000) Finite Mixture Models, Wiely, New York.
     
     22. McLachlan, G. J. and D. Peel, (2000) “Robust Mixture Modeling Using the t
     Distribution,” Statistics and Computing, 10, 339-348.
     
     23. Mendenhall, W. and R.J. Hader, (1958) "Estimation of parameters of mixed
     exponentially distributed failure time distributions from censored life test data," Biometrika, 45, 504–520.
     
     24. Shoham, S., (2002) “Robust Clustering by Deterministic Agglomeration EM of Mixtures of Multivariate t-Distributions,” Pattern Recognition, 35, 1127-1142.
     
     25. Shoham, S., M. R., Fellows, and R. A. Normann, (2003) “Robust, Automatic Spike Sorting Using Mixtures of Multivariate t-Distributions,” Journal of
     Neuroscience Methods, 127, 111-122.
     
     26. Titterington, D. M., A. F. M. Smith, and U. E. Markov, (1985) Statistical
     Analysis of Finite Mixture Distributions, Wiely, New York.
     
     27. Venkataraman, S., (1997), “Value at risk for a mixture of normal distributions: the use of quasi-Bayesian estimation techniques,” Economic Perspective, Federal Reserve Bank of Chicago, 2—13.
     
     28. Wang, H. X., Q. B. Zhang, B. Luo, and S. Wei, (2004) “Robust Mixture Mod-
     elling Using Multivariate t Distribution With Missing Information”, Pattern
     Recognition Letter, 25, 701-710.
     
     29. Zangari, P.,(1996) “A VaR methodology for portfolios that include options,” RiskMetrics Monitor, 4–12.
描述 碩士
國立政治大學
財務管理研究所
99357001
100
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099357001
資料類型 thesis
dc.contributor.advisor 杜化宇zh_TW
dc.contributor.author (Authors) 林子慶zh_TW
dc.creator (作者) 林子慶zh_TW
dc.date (日期) 2011en_US
dc.date.accessioned 30-Oct-2012 10:13:59 (UTC+8)-
dc.date.available 30-Oct-2012 10:13:59 (UTC+8)-
dc.date.issued (上傳時間) 30-Oct-2012 10:13:59 (UTC+8)-
dc.identifier (Other Identifiers) G0099357001en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54175-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 財務管理研究所zh_TW
dc.description (描述) 99357001zh_TW
dc.description (描述) 100zh_TW
dc.description.abstract (摘要) 本文使用混合分配方法發展一個可處理厚尾,偏態(報酬分配不對稱)的壓力 測試模型。在資料上,我們以希臘國債與 S&P500 指數作為核心資產,臺灣市場 的標的資產作為邊緣資產。在與資料的配適能力上,本文發展的模型確實優於過 去假設常態分配的壓力測試模型。在實際執行壓力測試中,本研究比較了本文使 用的混合分配模型與過去模型的差異,我們發現壓力測試結果的差異相當大,因 此肯定了能抓住厚尾及偏態現象模型的重要性。zh_TW
dc.description.tableofcontents 1. 前言 ..................................................................................... 7
     2. 理論回顧暨研究方法 ............................................................. 10
      2-1 一般化 Student-t 分配 ................................................... 10
      2-2 混合分配模型 ................................................................. 12
      2-3 EM 演算法(Expectation Maximization algorithm) ............16
      2-4 模型配適 ....................................................................... 18
      2-5 條件相關係數 ................................................................. 19
      2-6 Broken Arrow 壓力測試法介紹 .........................................20
     3. 實證分析 ............................................................................. 22
      3-1 資料來源與處理 .............................................................. 22
      3-2 模型配適 ....................................................................... 22
      3-3 條件相關係數 ................................................................. 24
      3-4 執行壓力測試 ................................................................. 27
     4. 結論 ................................................................................... 28
     5. 參考文獻 ............................................................................. 29		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099357001en_US
dc.subject (關鍵詞) 壓力測試zh_TW
dc.subject (關鍵詞) 厚尾zh_TW
dc.subject (關鍵詞) 偏態zh_TW
dc.subject (關鍵詞) 混合分配zh_TW
dc.subject (關鍵詞) 一般化偏態t分配zh_TW
dc.title (題名) 厚尾、偏態與壓力測試：混合分配模型的應用zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Azzalini, A., (1985) “A Class of Distributions Which Includes the Normal Ones,” Scandinavian Journal of Statistics, 12, 171-178.
     
     2. Azzalini, A., (1986) “Further Results on a Class of Distributions Which Includes the Normal Ones,” Statistica, 46, 199-208.
     
     3. Azzalini, A. and A. Capitaino, (2003) “Distributions Generated by Perturbation of Symmetry With Emphasis on a Multivariate Skew t-Distribution,” Journal of the Royal Statistical Society. Ser.B, 65, 367-389.
     
     4. Basso R. M., V.H. Lachos, C.R. Cabral, P. Ghosh, (2009) “Robust mixture modeling based on scale mixtures of skew-normal distributions,” Computational Statistics & Data Analysis, 12, 2926-2941.
     
     5. Bauwens L, Laurent S., (2005) “A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models, ” Journal of Business and Economic Statistics, 23:3, 346-354.
     
     6. Beber, A., M. W. Brandt, and K. A. Kavajecz (2009) “Flight-to-Quality or Flight-to-Liquidity? Evidence from the Euro-Area Bond Market.” Review of Financial Studies, 22, 925–957.
     
     7. Bollerslev, T., (1987) “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 31, 307-327.
     
     8. Carol, A. and E. Sheedy, (2008) "Developing a stress testing framework based on market risk models," Journal of Banking & Finance, 32, 2220-2236
     
     9. Fernandez, C. and M. F. J. Steel (1998), “On Bayesian Modelling of Fat Tails and Skewness.” Journal of the American Statistical Association, 93, 359–371.
     
     10. Fraley, C. and A. E. Raftery, (2002) “Model-Based Clustering, Discriminant Analysis, and Density Estimation,” Journal of the American Statistical Association, 97, 611-631.
     
     11. Gregor, J., (1969) "An algorithm for the decomposition of a distribution into Gaussian components," Biornetrics, 26, 79-93.
     
     12. Hamilton, J. (1991), “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions,” Journal of Business and Economic Statistics, 9, 1779-1801.
     
     13. Hewitt, C. C. Jr. and B. Lefkowitz, (1979) "Methods for Fitting Distributions to Insurance Loss Data," Proceedings of the Casualty Actuarial Society, LXVI, 139-160.
     
     14. Jones, M. C. and M. J. Faddy, (2003) “A skew extension of the t distribution, with applications,” Statist. Soc B, 65, 159–174.
     
     15. Jorion, P., (1995) “Predicting Volatility in the Foreign Exchange Market.” Journal of Finance, 2, 507-528
     
     16. Kim, J. and C. Finger (2000), “A stress test to incorporate correlation breakdown,” Journal of Risk, 2, 5-19.
     
     17. Lin, T. I., J. C., Lee, and H. F., Ni, (2004) “Bayesian Analysis of Mixture Modeling Using the Multivariate t Distribution,” Statistics and Computing, 14, 119-130.
     
     18. Lin, T. I., J. C., Lee, and S.Y., Yen, (2007) “Finite mixture modeling using the skew normal distribution,” Statistica Sinica, 17, 909-927.
     
     19. Markowitz, H., (1952) "Portfolio selection," Journal of Finance, 7, 77-91.
     
     20. McLachlan, G. J. and K. E. Basord, (1988) Mixture Models: Inference and
     Application to Clustering, Marcel Dekker, New York.
     
     21. McLachlan, G. J. and D. Peel, (2000) Finite Mixture Models, Wiely, New York.
     
     22. McLachlan, G. J. and D. Peel, (2000) “Robust Mixture Modeling Using the t
     Distribution,” Statistics and Computing, 10, 339-348.
     
     23. Mendenhall, W. and R.J. Hader, (1958) "Estimation of parameters of mixed
     exponentially distributed failure time distributions from censored life test data," Biometrika, 45, 504–520.
     
     24. Shoham, S., (2002) “Robust Clustering by Deterministic Agglomeration EM of Mixtures of Multivariate t-Distributions,” Pattern Recognition, 35, 1127-1142.
     
     25. Shoham, S., M. R., Fellows, and R. A. Normann, (2003) “Robust, Automatic Spike Sorting Using Mixtures of Multivariate t-Distributions,” Journal of
     Neuroscience Methods, 127, 111-122.
     
     26. Titterington, D. M., A. F. M. Smith, and U. E. Markov, (1985) Statistical
     Analysis of Finite Mixture Distributions, Wiely, New York.
     
     27. Venkataraman, S., (1997), “Value at risk for a mixture of normal distributions: the use of quasi-Bayesian estimation techniques,” Economic Perspective, Federal Reserve Bank of Chicago, 2—13.
     
     28. Wang, H. X., Q. B. Zhang, B. Luo, and S. Wei, (2004) “Robust Mixture Mod-
     elling Using Multivariate t Distribution With Missing Information”, Pattern
     Recognition Letter, 25, 701-710.
     
     29. Zangari, P.,(1996) “A VaR methodology for portfolios that include options,” RiskMetrics Monitor, 4–12.		zh_TW