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中文論文名稱 DCC多變量GARCH模型之風險值計算-G7及臺灣等八國股市投資組合之實證研究
英文論文名稱 Application of DCC Multivariate GARCH Model at VaR-Evidence from G7 and Taiwan's Stock Markets
校院名稱 淡江大學
系所名稱(中) 財務金融學系碩士班
系所名稱(英) Department of Banking and Finance
學年度 93
學期 2
出版年 94
研究生中文姓名 黃小菁
研究生英文姓名 Hsiao-Chin Huang
學號 791490146
學位類別 碩士
語文別 中文
口試日期 2005-05-28
論文頁數 73頁
口試委員 指導教授-李命志
委員-邱建良
委員-邱哲修
委員-林卓民
中文關鍵字 風險值  動態條件相關  多變量GARCH  股票投資組合 
英文關鍵字 Value-at-Risk  DCC  Multivariate GARCH  Equity Portfolio 
學科別分類 學科別社會科學商學
中文摘要 本文的目的在於探討國際投資組合之風險值預測模型。有鑑於過去由多種資產組成之投資組合,因資產數量的限制,在實務上往往發生風險值估計上的困難。本文應用Engle(2002)所提出的DCC-GARCH模型推估而得的變異數共變異數矩陣,用以預測投資組合未來的市場風險值,並比較簡單移動平均法(SMA)及實務上常用的指數權數移動法(EWMA)二種變異數預測模型之預測結果。經由以七大工業國G7與台灣股價指數組成之資產組合而得之實證研究發現,利用DCC-GARCH模型所預測出的資產組合風險值比起其他變異數模型所預測出的結果,顯然具有更高的有效性及正確性。而DCC-GARCH模型中,一般而言,在通過Kupiec PF-test之情況下,t分配模型較Normal分配模型之RMSE低,故DCC-GARCH(1,1)-t模型將是估算風險值的更好選擇。另各模型皆顯示,八國股市報酬率間相關係數與變異數呈現正向關係,亦即各國股市間之波動性高時相關性會隨之上升,此亦說明八國股市報酬率為動態之共變異數及相關係數時間序列。
英文摘要 The purpose of this study is to find a more effective model to forecast Value-at-Risk (VaR). Due to a portfolio usually holds numerous assets, it would be difficult to estimate the very large covariance matrix that is required to caculate VaR. In this paper, we apply the Dynamic Conditional Correlation (DCC) multivariate GARCH model, proposed by Engle (2002), to estimate the future market risk. We also use two other variance-covariance forecast models, such as SMA and EWMA to compare the results. Through a portfolio composed of eight indices from the G7 (America, Canada, UK, France, Germany, Italy, Japan) and Taiwan stock markets, the findings imply that the VaR calculated from DCC multivariate GARCH model has better accuracy and efficiency. Moreover, among DCC models which pass the Kupiec PF test in backtesting, we examine RMSE for capital efficiency and find that t distribution performs better than normal distribution. Thus this study recommends DCC- GARCH(1,1)-t model to be the best option in computing VaR on equity portfolio. In addition, all the results indicate that the correlation and covariance of returns move in the same direction. That is correlations increase during times when the volatility of market is large.
論文目次 目 錄
第一章 緒論..................................1
第一節 研究動機..............................1
第二節 研究目的..............................3
第三節 研究架構..............................4
第四節 研究流程..............................6
第二章 理論基礎與文獻回顧....................7
第一節 風險值的意義及概念....................7
第二節 風險值之估算方法......................9
第三節 國外相關文獻.........................11
第四節 國內相關文獻.........................15
第三章 研究方法.............................19
第一節 單根檢定.............................19
第二節 ARCH效果檢定.........................23
第三節 波動性預測計量模型...................25
第四節 風險值的評價方式與預測績效...........37
第四章 實證結果與實證分析...................40
第一節 資料來源與處理.......................40
第二節 八國股價指數基本統計量分析...........41
第三節 單根檢定.............................44
第四節 ARCH效果檢定.........................47
第五節 固定相關係數檢定.....................48
第六節 風險值之估計.........................49
第七節 投資組合共變異數及相關係數分析.......58
第五章 結論.................................68
參考文獻....................................69
表 目 錄
【表3-4-1】 Kupiec(1995)檢定法之臨界值 38
【表4-2-1】八國股價指數基本統計量 43
【表4-2-2】八國股價指數報酬率基本統計量 43
【表4-3-1】八國股價指數時間序列資料之單根檢定(水準項) 45
【表4-3-2】八國股價指數日報酬率時間序列資料之之單根檢定(差分項) 46
【表4-4-1】八國報酬率ARCH效果檢定 47
【表4-5-1】八國報酬率模型殘差項之固定相關係數矩陣 48
【表4-5-2】八國報酬率殘差項之固定相關係數檢定 49
【表4-6-1】多頭部位估計1天之風險值穿透情形及RMSE比較表 51
【表4-6-2】空頭部位估計1天之風險值穿透情形及RMSE比較表 51
【表4-6-3】多頭部位估計10天之風險值穿透情形及RMSE比較表 54
【表4-6-4】空頭部位估計10天之風險值穿透情形及RMSE比較表 54
【表4-7-1】三模型(SMA、EWMA及DCC-GARCH)之投資組合波動度比較表 59
【表4-7-2】八國報酬率SMA模型之相關係數矩陣的平均值與標準差 60
【表4-7-3】八國報酬率EWMA模型之相關係數矩陣的平均值與標準差 62
【表4-7-4】八國報酬率DCC-GARCH(1,1)模型之相關係數矩陣的平均值與標準差 63
【表4-7-5】投資組合中八國股市報酬率間最大及最小相關係數 65
【表4-7-6】八國股市報酬率間相關係數平均值與標準差之關係 65
【表4-7-7】八國股市報酬率間相關係數與變異數之關係 66

圖 目 錄
【圖4-2-1】 各國股價指數時間序列圖 42
【圖4-6-1】 SMA模型之風險值(預測一天)模型 52
【圖4-6-2】 EWMA模型之風險值(預測一天)模型 52
【圖4-6-3】 DCC-GARCH模型之風險值(預測一天)模型 53
【圖4-6-4】 SMA模型之風險值(預測十天)模型 55
【圖4-6-5】 EWMA模型之風險值(預測十天)模型 55
【圖4-6-6】 DCC-GARCH模型之風險值(預測十天)模型 56
【圖4-7-1】 三模型(SMA、EWMA及DCC-GARCH)之投資組合波動度 58
【圖4-7-2】 法國與義大利股價指數日報酬率之走勢圖(相關係數最高者) 60
【圖4-7-3】 臺灣與美國股價指數日報酬率之走勢圖(相關係數最低者) 61
【圖4-7-4】 八國報酬率SMA模型之最大及最小相關係數圖 61
【圖4-7-5】 八國報酬率EWMA模型之最大及最小相關係數圖 62
【圖4-7-6】八國報酬率DCC-GARCH(1,1)模型之最大及最小相關係數圖 63
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