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研究生:張沛德
研究生(外文):Pei-te Chang
論文名稱:不對稱拉普拉斯分配之風險值計算
論文名稱(外文):Value-at-Risk of Asymmetric Laplace Distribution
指導教授:張揖平, 洪明欽
指導教授(外文):Yi-ping Chang, Hung, M.
學位類別:碩士
校院名稱:東吳大學
系所名稱:商用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:39
中文關鍵詞:風險值AL分配GH分配蒙地卡羅模擬法
外文關鍵詞:VaRAL distributionGH distributionMonte Carlo simulation
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由於金融資產報酬率分配皆具有高峰厚尾的特性,以往常用的常態分配已漸漸被淘汰,改採用較能描述厚尾現象的t分配配適報酬率之資料,有些金融資產報酬率甚至會出現偏斜的情形,而屬於對稱分佈的t分配也無法描述偏斜的資料型態,因此本文提出以AL分配配適高峰、厚尾、甚至是偏斜的資料,並以最大概似估計法估計AL分配之參數,進而估算風險值,經由蒙地卡羅模擬法的結果顯示,具有偏斜的資料型態以AL分配配適所計算出的風險值最為準確。實證部分是採用美國股市的三大指數週報酬率,以AL分配配適之,推估其風險值,並利用移動視窗的方式計算穿透次數、穿透率,最後在配合統計的檢定。結果顯示AL分配可以有效地捕捉到報酬率資料高峰、厚尾及偏斜的特性,並能有效地估計風險值。
Because of the characteristic of leptokurtosis and heavy tail of the financial asset return, the method we used to fit financial asset return by normal distribution was weeded out gradually. Now, we use the distribution which can describe the phenomenon of heavy tail such as Student’s t distribution to fit financial asset return. But some financial asset return may appear the situation of skewness, so the Student’s t distribution which belongs to symmetric distribution cannot describe skewed financial asset return. In this paper, we use AL distribution to fit the leptokurtosis, heavy tail, even skewed financial asset return, and estimate three parameters of AL distribution by maximum likelihood estimation, and then estimate value at risk. The results through Monte Carlo simulation show that the skewed data which fitted by AL distribution are most accurate. In empirical, we adopt weekly return of three indices of American, fit them by AL distribution, estimate their VaR, use the method of moving window to calculate violation rate, and test by statistical tools finally. The results show that AL distribution can catch the characteristic of leptokurtosis, heavy tail, and skewness, and estimate VaR efficiently.
目錄...........................................................................1
圖目錄.........................................................................2
表目錄.........................................................................3
中文摘要.......................................................................4
英文摘要.......................................................................5
1. 前言........................................................................6
2. 研究方法...................................................................10
2.1 參數估計..................................................................10
2.2 風險值之計算方式..........................................................12
2.3 風險值評比準則............................................................12
a. 回顧測試法(Back Testing)...................................................12
b. 二項分配檢定法(binomial test)、非條件涵蓋檢定法(unconditional coverage test).........................................................................13
c. 條件涵蓋檢定法(conditional coverage test)..................................13
3. 模擬.......................................................................15
3.1 模擬方法..................................................................15
3.2 模擬結果..................................................................17
4. 實證研究...................................................................28
4.1 資料選取..................................................................28
4.2 三大指數週報酬率資料......................................................28
5. 結論.......................................................................38
參考文獻......................................................................39
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5. Kotz, S., Kozubowski, T. J. and Podgórski, K., (2002). Maximum likelihood estimation of asymmetric Laplace parameters, Annals of the Institute of Statistical Mathematics, 54, 4, 816-826.

6. Kotz, S., Kozubowski, T. J. and Podgórski, K., (2002). The Laplace Distribution and Generations:A Revisit with Applications to Communications, Economics, Engineering, and Finance, Birkhäuser Boston.

7. Kozubowski, T. J. and Podgórski, K., (2000). Asymmetric Laplace distributions, Mathematical Scientist, 25, 37-46.

8. Kozubowski, T. J. and Podgórski, K., (2001). Asymmetric Laplace laws and modeling financial data, Mathematical and Computer Modeling, 34, 1003-1021.

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10. Prause, K., (1999). The generalized hyperbolic model:estimation, financial derivatives, and risk measures, Dissertation University of Freiburg (http://www.uni-freiburg.de/).

11. 許智淵(2004),「使用EM演算法探討GH分配之風險值計算」,私立東吳大學商用數學研究所碩士論文。
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