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研究生:朱慧培
研究生(外文):Chu, Hui-Pei
論文名稱:以時變自我迴歸模型預測金融商品之風險值
論文名稱(外文):Predicting Value At Risk Of Financial Products By Time-Varying Autoregressive Model
指導教授:李孟峰李孟峰引用關係
指導教授(外文):Lee, Mong-Hong
口試委員:吳庭斌李美杏李孟峰
口試委員(外文):Wu, Ting-PinLee, Mei-HsingLee, Mong-Hong
口試日期:2012-07-05
學位類別:碩士
校院名稱:國立臺北大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:46
中文關鍵詞:時變自我迴歸GARCH族群模型滾動估計風險值
外文關鍵詞:time-varying autoregressiveGARCH family modelrolling estimationvalue at risk
相關次數:
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  隨著財務工程理論之發展,金融商品不斷推陳出新,資產部位趨於多元與複雜,使得風險隨之增加。風險值主要的目的是用以衡量投資部位在未來所面臨的最大損失,因此,如何有效評估風險實為投資者所關心的重要議題。許多財務金融文獻指出,資產報酬分配具有自我相關性及波動叢聚性(volatility clustering),故常使用自我相關條件異質變異的GARCH族群模型,如:ARMA(p,q) - GARCH(m,n) 模型進行資產報酬之風險值估計。
  本論文主要目的是建立金融商品報酬風險值(VaR)的模型,其概念來自於Tesheng Hsiao(2008) 所提及的時變自我迴歸模型。此模型有別於一般自我迴歸模型,一般自我迴歸模型假設常數項與落遲項的係數均為常數,不會隨著時間而改變,但金融商品報酬風險值通常並不滿足此假設。因此,本研究考慮建立時變自我迴歸模型,建模方式為先以滾動 (rolling) 方式對不同時間點估計其AR模型之常數項r0(t)與落遲項之係數r1(t)、r2(t);GARCH模型之常數項a0(t)與過去變異數項之係數a1(t)、及干擾項之係數b1(t),以建構金融商品報酬風險值 (VaR) 的時變AR-GARCH模型。
  在實證方面,本文以Dow Jones和NASDAQ為例,針對所建立的模型進行實證分析,評估在1%、5%及10%信賴水準下,其模型所計算出來的風險值之特性,並計算其穿透率,即損失超過風險值的比率,來評估VaR的預測能力。

  The fast growing of the theory of financial engineering and well developing of variety financial products in the financial market cause the evaluation of asset positions tends to diversification and complex, and the risk of access is increased as well. The major function of VaR (value at risk) is to measure the maximum loss of investment positions; therefore, how to assess VaR effectively is an important issue concerned by investors. It is already shown on many finance literatures that the distribution of assets return have the properties of autocorrelation and volatility clustering. Hence, models of GARCH (autocorrelation conditional heteroskedasticity) family, such as: ARMA (p, q)-GARCH (m, n) models are suggested to estimate the risk of assets return.
  The purpose of this study is to establish the VaR of assets return of financial products. The major idea of this study is applying time-varying autoregressive model by Tesheng Hsiao (2008). This model differs from general autoregressive model on assuming that the constant term and lag coefficients are fixed and not change over time. This assumption seems inadequate for modeling the VaR of assets return of financial products. The technique of this study obtains time varying coefficients by using rolling estimation to estimate the coefficient of AR-GARCH model and then obtains a time varying model.
  Finally, the Dow Jones and NASDAQ indices are illustrated for empirical analysis. And the penetration rate of 1%, 5% and 10% confidence level are calculated to assess the predictive ability.

目 錄
第1章 緒論 1
1.1研究動機與背景 1
1.2研究目的與方法 2
1.3研究架構與流程 2
第2章 文獻探討 4
2.1風險值之定義 4
2.2 風險值之估計方法 5
2.2.1有母數法 5
2.2.2無母數法 9
2.3時間數列模型 10
第3章 研究方法與模型 15
3.1 時變AR-GARCH模型 15
3.2實證資料介紹 17
3.2.1道瓊工業平均股價指數(DJIA) 17
3.2.2那斯達克綜合指數(NASDAQ) 17
3.3 資料的檢定 18
3.3.1時間序列的常態性檢定 18
3.3.2時間序列之恆定性檢定 19
3.3.3 ARMA(p,q)模型的配適 21
3.3.4 ARCH檢定 22
3.4實證流程 23
第4章 實證分析 24
4.1資料的描述 24
4.2資料檢定 24
4.3 樣本資料的描述統計 26
4.4樣本資料的實證分析 27
4.4.1 股價報酬率之敘述統計 27
4.4.2 恆定性檢定 28
4.4.3 選取ARMA(p,q)模型 29
4.4.4 ARCH檢定 30
4.4.5 選取GARCH(m,n)模型 31
4.4.6 建立VaR時變AR-GARCH模型之步驟流程 34
4.5實證資料之使用限制 37
4.6評估VaR時變AR-GARCH模型 38
第5章 結論及建議 41
參考文獻 42

表目錄

表4-1 DJIA與NASDAQ二股價指數序列ADF單根檢定 25
表4-3 DJIA與NASDAQ二股價指數報酬率序列ADF單根檢定 29
表4-4 DowJones酬報率ARMA(p,q)模型估計結果 29
表4-5 NASDAQ酬報率ARMA(p,q)模型估計結果 30
表4-6 ARCH檢定 30
表4-7 Ljung-Box Q-Statistics 31
表4-8 DowJones酬報率AR(2)-GARCH(m,n)模型估計結果 33
表4-9 NASDAQ酬報率AR(2)-GARCH(m,n)模型估計結果 34
表4-10 以回溯測試法評量DowJones股價指數報酬率風險值之穿越次數 39
表4-11 以回溯測試法評量NASDAQ股價指數報酬率風險值之穿越次數 40

圖目錄

圖1-1 研究流程 3
圖2-1 風險值定義圖 4
圖4-1美國道瓊工業平均股價指數走勢圖 25
圖4-2美國那斯達克綜合指數走勢圖 25
圖4-3美國道瓊工業平均股價指數報酬率走勢圖 26
圖4-4美國那斯達克綜合指數報酬率走勢圖 27
圖4-5 樣本資料處理流程圖 32
圖4-6實證研究流程圖 38



中文文獻
李伶芳 (2001), 應用具有厚尾誤差項的非線性自我迴歸模型計算風險值, 國立
中山大學應用數學系碩士論文。
吳亭穎 (2008), 投資組合風險值估算模型之探討-多變量MAR-GARCH模型,
國立台北大學統計研究所碩士論文。
邱思妤 (2011), 在風險值限制下考量動態波動的最適投資組合, 國立台北大學
統計研究所碩士論文。
陳旭昇 (2009), 時間序列分析:總體經濟與財務金融之應用,第二次修訂版, 東
華書局新月圖書, 台北。
陳景祥 (2012), R軟體:應用統計方法,修訂版, 東華書局新月圖書, 台北。
楊奕農 (2005), 時間序列:經濟與財務上的應用, 第一版, 雙葉書廊, 台北。
劉洪鈞、黃聖志,「從巴塞爾協定探索臺灣外匯市場之風險值估計」。中華國際經貿研究學會年會暨學術研討會,台北:國立政治大學,2007年09月22日。
劉士賢 (2010), GARCH模型探討風險值-以電子五哥為例, 國立中正大學經濟學系國際經濟學碩士論文。
蔡錦昌 (2011), 台、美、中股市報酬率與波動外溢效果之研究, 佛光大學管理學系碩士論文。

英文文獻
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