本研究應用Engle（2002）提出之動態條件相關（Dynamic Conditional Correlation，DCC）多變量GARCH模型去估計八國貨幣（歐元、英鎊、日圓、加拿大元、新台幣、韓元、新加坡元及澳元）所組成外匯投資組合的風險值。比較SMA、EWMA、CCC-GARCH及DCC-GARCH等四種模型在風險值之預測能力，在回溯測試採用Kupiec PF 檢定與RMSE資金運用效率之評估準則下，實證結果發現DCC-GARCH(1,1)-t模型因較能捕捉厚尾及波動群聚現象，其風險管理績效較為優異，故為估算外匯投資組合風險值的較佳選擇。
另八國匯率報酬率拒絕固定條件相關（Constant Conditional Correlation）之虛無假設，顯示國際匯率報酬率相關性並非固定，應適用動態相關係數之模型。本文亦發現八國匯市間之相關性及風險值會隨著波動性之提高而上升，說明國際匯市之波動性及相關係數為動態之時間序列，此可做為資產管理及投資組合分散風險之良好參考。

In this study, we apply the Dynamic Conditional Correlation (DCC) multivariate GARCH model, proposed by Engle (2002), to estimate Value-at-Risk (VaR) on foreign exchange portfolio composed of eight currencies including Euro, British pound, Japanese yen, Canadian dollar, Taiwan dollar, South Korea won, Singapore dollar and Australian dollar. By comparing the performance based on the Kupiec PF test in backtesting and RMSE for capital efficiency among SMA, EWMA, CCC-GARCH and DCC-GARCH models, we conclude that the DCC-GARCH(1,1)-t model, which accounts for characteristics of fat-tail and volatility clustering, is the better choice to compute VaR on foreign exchange portfolio.
In addition, the returns of eight currencies lead to reject the null hypothesis of a constant conditional correlation, which reveals that the dynamic correlation model should be adopted. We also find that the correlation and VaR rise in periods when the conditional volatility of markets increases, implying that the volatility and correlation in international currency markets are dynamic time series. We could use such criterions as a good reference to allocate assets and diversify portfolio risk.

目 錄
第一章 緒論................................. 1
第一節 研究動機............................. 1
第二節 研究目的............................. 4
第三節 研究架構............................. 5
第四節 研究流程............................. 7
第二章 理論基礎與文獻回顧................... 8
第一節 風險值的意義及概念................... 8
第二節 風險值之估算方法.....................11
第三節 國外相關文獻.........................14
第四節 國內相關文獻.........................17
第三章 研究方法.............................20
第一節 投資組合風險值之計算.................20
第二節 模型參數之估計.......................24
第三節 風險值的評價方式與預測績效...........44
第四章 實證結果與實證分析...................47
第一節 資料來源與處理.......................47
第二節 基本統計量分析.......................48
第三節 單根檢定.............................53
第四節 ARCH效果檢定.........................56
第五節 固定相關係數檢定.....................57
第六節 投資組合風險值之估計.................58
第七節 投資組合共變異數及相關係數分析.......65
第五章 結論.................................76
參考文獻....................................78
表 目 錄
【表2-2-1】三種估算風險值方法優缺點比較表.......................................................13
【表3-2-1】多變量GARCH 模型之比較...................................................................44
【表3-3-1】Kupiec（1995）檢定法之臨界值...........................................................45
【表4-1-1】八國貨幣占全球貿易交易量之比率（2005 年2 月3 日）..................47
【表4-2-1】八國匯率基本統計量...............................................................................52
【表4-2-2】八國匯率報酬率基本統計量...................................................................52
【表4-3-1】八國匯率時間序列資料之單根檢定（水準項）...................................54
【表4-3-2】八國匯率日報酬率時間序列資料之之單根檢定（差分項）...............55
【表4-4-1】八國匯率報酬率ARCH 效果檢定..........................................................56
【表4-5-1】八國匯率報酬率標準化殘差之固定相關係數矩陣R ...........................57
【表4-5-2】八國匯率報酬率標準化殘差之固定相關係數檢定...............................58
【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......................62
【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.......................63
【表4-7-1】三模型（SMA、EWMA 及DCC-GARCH）之投資組合波動度比較表..68
【表4-7-2】八國匯率報酬率間相關係數平均值與標準差之關係...........................69
【表4-7-3】八國匯率報酬率DCC-GARCH 模型之相關係數矩陣平均值及標準差.......70
【表4-7-4】八國匯率報酬率間共變異數平均值與標準差之關係...........................73
【表4-7-5】八國匯率報酬率間相關係數與共變異數之關係...................................74
圖 目 錄
【圖4-2-1】八國匯率走勢圖.......................................................................................49
【圖4-2-2】八國匯率報酬率走勢圖...........................................................................50
【圖4-6-1】估計期間（500 天）與預估1 天之移動視窗方法................................59
【圖4-6-2】各模型預測一天之VaR 圖形..................................................................64
【圖4-7-1】三模型（SMA、EWMA 及DCC-GARCH）之投資組合波動度........66
【圖4-7-2】三模型（SMA、EWMA 及DCC-GARCH）之風險值........................67
【圖4-7-3】八國匯率報酬率DCC-GARCH 模型之最大及最小相關係數圖.........71
【圖4-7-4】歐元與其他七國匯率報酬率相關係數圖...............................................72

一、國內文獻
1.沈大白、柯瓊鳳、鄒武哲，(1998)，「風險值衡量模式之探討－以台灣上市公司權益證券為例」，東吳經濟商學學報，第二十二期，頁57-76。
2.周業熙，(2002)，GARCH-type模型在VaR之應用，東吳大學經濟學系碩士論文。
3.洪瑞成，(2002)，風險值之探討-對稱與不對稱波動GARCH模型之應用，淡江大學財務金融研究所碩士論文。
4.殷惠緡，(2001)，股價與匯價關聯性分析-多變量GARCH模式運用，淡江大學財務金融所碩士論文。
5.許傑翔，(2004)，多變量財務時間數列模型之風險值計算，東吳大學商用數學系碩士論文。
6.張維敉，(2002)，金融危機與風險外溢-DCC模型之應用，國立中央大學財務金融研究所碩士論文。
7.郭憲鍾，(2004)，國際股市之動態關連，暨南國際大學國際企業學系碩士論文。
8.謝家和，(1999)，風險值之衡量-多元變數GARCH模型之應用，暨南國際大學國際企業學系碩士論文。
9.聶瑋瑩，(2004)，台灣電子產業海外存託憑證報酬率之匯率風險，國立政治大學國際貿易研究所碩士論文。

二、國外文獻：
1.Alexander, C. O. and C. T. Leigh, (1997), “On the Covariance Matrices Used in Value at Risk Models,” Journal of Derivatives, Vol. 4, pp.50-62.
2.Bautista, C. C., (2003), “Interest rate-exchange rate dynamics in the Philippines: a DCC analysis,” Applied Economics Letters, Vol. 10(2), pp.107-111.
3.Billio, M. and L. Pelizzon, (2000), “Value-at-Risk: a multivariate switching regime approach,” Journal of Empirical Finance, Vol. 7, pp.531-554.
4.Bollerslev, T., (1986), “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, Vol. 31, pp.307-327.
5.Bollerslev, T., R. F. Engle, and J. M. Wooldridge, (1988), “A Capital- Asset Pricing Model with Time-Varying Covariances,” Journal of Political Economy, Vol. 96, pp.116-131.
8.Bollerslev, T., (1990), “Modeling the Coherence in Short-Run Nominal Exchange Rates Generalized ARCH,” Review of Economics and Statistics, Vol. 70, pp.498-505.
9.Bredin, D. and S. Hyde, (2004), “FOREX Risk: Measurement and Evaluation using Value-at-Risk,” Journal of Business Finance and Accounting, Vol. 31, pp.1389-1417.
10.Christoffersen, P. and F. Diebold, (2000), “How relevant is volatility forecasting for financial risk management?,” Review of Economics and Statistics, Vol. 82, pp.1–11.
11.Colm, K. and A. J. Patton, (2000), “Multivariate GARCH Modeling of Exchange Volatility Transmission in the European Monetary System,” The Financial Review, Vol. 41, pp.29-48.
12.Dickey, D. A. and W. A. Fuller, (1981), “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica, Vol. 49(4), pp.1057-1072.
13.Engle, R. F., (1982), “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation,” Econometirca, Vol. 50, pp.987-1008.
14.Engle, R. F. and K. F. Kroner, (1995), “Multivariate simultaneous generalized ARCH,” Econometric Theory, Vol. 11, pp.122-150.
15.Engle, R. F. and S. Manganelli, (2000), “CAVaR: Conditional Autoregressive Value at Risk by Regression Quantiles,” Working paper, NBER.
16.Engle, R. F. and K. Sheppard, (2001), “Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH,” discussion paper, University of California, San Diego.
17.Engle, R. F., (2002), “Dynamic conditional correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models,” Journal of Business and Economic Statistics, Vol. 20(3), pp.339-350.
18.Fama, E. F., (1965), “The Behavior of Stock Market Prices,” Journal of Business, Vol. 38, pp.34-105.
19.Giot, P. and S. Laurent, (2003), “Value-at-Risk for long and short trading positions,” Applied Econometrics, Vol. 18, pp.641-663.
20.Goorbergh, R.V. D. and P. Vlaar, (1999), “Value-at-Risk Analysis of Stock Returns Historical Simulation, Variance Techniques or Tail Index Estimation,” DNB Staff Reports 40, Netherlands Central Bank.
21.Granger, C. W. J. and P. Newbold, (1974), “Superious Regressions in Econometrics,” Journal of Econometrics, Vol. 12, pp.111-120.
22.Hendricks, D., (1996), “Evaluation of ‘Value-at-Risk’ Models Using Historical Data,” Economic Policy Review, Federal Reserve Bank of New York, 2, April, pp.39-69.
23.Jorion, P., (2000), Value-at-Risk, 2nd edition, McGraw-Hill, N.Y.
24.J. P. Morgan and Reuters, (1996), RiskMetrics-Technical Document, 4th ed., J.P. Morgan.
25.Kupiec, P. H., (1995), “Techniques for Verifying the Accuracy of Risk Measurement Models,” Journal of Derivatives, Vol. 3, pp.73-84.
26.Longin, F. and B. Solnik, (1995), “Is the Correlation in International Equity Returns Constant：1960–1990?,” Journal of International Money and Finance, Vol. 14(1), pp.3-26.
27.Mandelbrot, B., (1963), “The variation of certain speculative prices,” Journal of Business, Vol. 36, pp.394-419.
28.Mandelbrot, B., (1967), “The Variation of Some Other Speculative Prices,” Journal of Business, Vol. 40, pp.393-413.
29.Schwert, G. W. and P. J. Seguin, (1990), “Herteroscedasticity in Stock Returns,” Journal of Finance, Vol. 45, pp.1129-1155.
30.Tse, Y. K., (2000), “A test for constant correlations in a multivariate garch model,” Journal of Econometrics, Vol. 98, pp.107-127.
31.Tsui, A. K. and Q. Yu, (1999),“Constant conditional correlation in a bivariate garch model: Evidence from the stock market in China,” Mathematics and Computers in Simulation, Vol. 48, pp.503-509.
32.Wang, P. and P. Wang, (2001),“Equilibrium Adjustment, Basis Risk and Risk Transmission in Spot and Forward Foreign Exchange Markets,” Applied Financial Economics, Vol. 11, pp.127-136.