臺灣博碩士論文加值系統

2011年歐債風暴不斷影響全球的經濟與股市，一連串風暴的中心點來自於歐洲其中五個國家：葡萄牙(Portugal)、義大利(Italy)、愛爾蘭(Ireland) 希臘(Greece) 、西班牙(Spain)，將五國的英文字母縮寫即為PIIGS，至今，歐債仍然對全世界的經濟有著極大的影響。極值理論模型(Extreme Value Theory Model)主要應用描述尾部特性，不需對整個分配做假設，減少模型的選擇風險。本文將以PIIGS五國的股價指數做為資料，將股價指數取過對數後的一階差分來計算股價指數報酬率，使用Ljung-Box統計量檢定發現資料具有序列相關。因此，根據McNeil and Frey(2000)所提出的方法，先以GARCH模型來過濾股價指數資料，得到非常態分配與iid之標準化殘差，再以極值理論模型來估計GARCH標準化殘差的分配尾部。本文使用Hill估計式與GPD分配，在三種信賴水準之下，以三種不同的門檻值分別估算PIIGS五國的形狀參數、規模參數、理論穿透次數、實際穿透次數、預期損失與Kupiec(1995)的概似比統計量(LR-test)。由形狀參數來看，除了愛爾蘭為薄尾分配的情況，其餘四國為厚尾的分配。在模型的相互比較之下，由實證結果中的LR-test顯示Hill估計式與GPD分配，在信賴水準99.5%且門檻值為5%的情況下，兩種模型表現最好，表示模型預測能力良好。本文將表現最好的模型假設之下，進一步估算兩種模型風險值，並以去年義大利與希臘債務事件做為爆發點，將兩個國家的實際報酬率與模型風險值做比較。然而，實證結果再度顯示Hill估計式與GPD分配，兩種模型的預測能力結果良好。

Europe's debt crisis continue to affect the global economy and the stock market in 2011, the center of the series of storms from Europe and five European countries: Portugal, Italy, Ireland, Greece , Spain, English initials of the five countries is the PIIGS, so far, the European debt still has a great influence on the world economy. Extreme value theory model applications describe the tail characteristics, assumptions, without the entire allocation to reduce the risk of model selection. This article will be the PIIGS five stock index as the data, take off the stock index stock index returns to calculate the number of first-order differential rate, find the data with serial correlation using the Ljung-Box statistic test. Thus, McNeil and Frey (2000), uesd the GARCH model to filter the stock price index data, non-normal distribution with iid standardized residuals, then the extreme value theory model to estimate the distribution of the tail of the GARCH standardized residuals. Hill estimator and GPD distribution used in this article, under the three confidence level in three different threshold values to estimate the shape parameter of the PIIGS, the scale parameter, the number of theoretical violation, actual violation of the number of expected shortfall and Kupiec (1995), the likelihood ratio statistic (LR-test).Shape parameters from the point of view, in addition to the Irish thin tail distribution of the remaining four thick tail distribution. LR-test the empirical results show Hill estimator formula in the model compared with the GPD distribution. In the case of the 99.5% confidence level and the threshold value of 5%, the two models performed the best, said the model predictive ability is good. This article will show the best model assumes that under further estimate the risk value of the two models, and the debt event in Italy and Greece last year as a flashpoint, the actual rate of return of the two countries with the model value at risk to compare. However, empirical results show once again Hill estimator and GPD distribution, the predictive
ability of the two models with good results.

中文摘要 ...........................................i
英文摘要 ..........................................ii
誌謝 .............................................iii
表目錄 ............................................iv
一、緒論 ...........................................1
1.1研究背景與動機 ...............................1
1.2研究目的 ....................................4
1.3研究架構 ....................................6
二、文獻回顧 ........................................7
三、研究方法 .......................................10
3.1風險值 .....................................10
3.2極值理論（Extreme Value Theory）.............11
3.3極值理論之風險值與預期損失估計 ................13
四、實證結果 .......................................15
4.1資料分析 ....................................15
4.2全樣本條件極值估計結果 ........................16
4.3樣本外回溯測試 ...............................20
五、結論與建議 ......................................27
參考文獻 ...........................................28

1.江明珠，李政峰，欉清全，2011，台灣不動產市場的下方風險-以台灣四個縣市
為例，住宅學報，第二十卷 第二期，頁1-14，6月。
2.江明珠，李政峰，廖四郎，徐守德，2009，短期利率條件分配之尾部差異性檢
定與風險值，中山管理評論，第十七卷 第二期，頁517-554，6月。
3.許菁旂，2009，巨災影響台灣產業之風險值估計-極值理論之應用，國立高雄應
用科技大學商務經營研究所，碩士論文。
4.廖怡能，2006，利率極端分配風險之衡量-極值理論模型與copulas模型之應用，
國立高雄應用科技大學金融資訊研究所，碩士論文。
5.Balkema, A.A. and de Haan, L., 1974, “Residual Life Time at Great Age,” Annals of
Probability, Vol. 2, No.5, 792-804.
6.Dimitrakopoulos, D.N., Kavussanos, M.G. and Spyrou, S.I.(2010), “Value at risk
models for volatile emerging markets equity portfolios” The Quarterly Review of
Economics and Finance, 50, 515–526.
7.Embrechts, P. (1999), “Extreme Value Theory: Potential and Limitations as an
Integrated Risk Management Tool,” Journal of Empirical Finance, Preprint.
8.Embrechts, P., Kluppelberg, C., and Mikosch, T., 2003, Modelling Extremal Events
for Insurance and Finance, London: Springer-Verlag.
9.Gençay, R. , Selçuk, F. and Ulugülyaˇgci, A.(2003),“High volatility, thick tails and
extreme value theory in value-at-risk estimation” Insurance: Mathematics and
Economics , 33 , 337–356.
10.Gilli, M. and Këllezi, E. (2000), “Extreme Value Theory for Tail-Related Risk
Measure,” Computation Finance 2000 Conference, 9-11.
11.Hall, P., 1990, “Using Bootstrap to Estimate Mean Square Error and Select
Smoothing Parameters in Non-parametric Problems,” Journal of Multivariate
Analysis, Vol. 32, No. 2, 177-203.
12.Jorion, P. (1996), “Risk: Measuring the Risk in Value at Risk,” Financial Analysts
Journal,vol. 52, No. 6, pp. 47-56.
13.Kupiec. P. H (1995), “Tehniques for Verifying the Accuracy of Risk Measurement
Models,” Journal of Derivatives, Winter, pp.73-84.
14.Longin, F. M. (2000), “From Value at Risk to Stress Testing: the Extreme value
Approach,”Journal of Baking and Finance, vol. 24, pp. 1097-1130.4.
15.Mcneil, A. J. (1997), “Estimating the tails of loss severity distributions using
ExtremeValue Theory,” Astin Bulletin, 27, No.1, 117-137.
16.Mcneil, A. J. (1999) “Extreme Value Theory for Risk Managers.” Internal Modeling
and CAD II, Risk books. London, UK, 193-118.
17.McNeil, A. 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.
18.Neftci, S. N., 2000, “Value at Risk Calculations , Extreme Events, and Tail
Estimation,” Journal of Derivatives, Vol. 7, No. 3, 1-15.
19.Philippe Jorion, Zhu Liu, Charles Shi, “Informational effects of regulation FD:
evidence from rating agencies.” Journal of Financial Economics, Vol.76,
309-330
20.Pickands, J., 1975, “Statistical Inference using Extreme Order Statistics,” Annals of
Statistics, Vol. 3, No. 1, 119-131.