An Empirical Study of Currency Exchange Rates via the VaR Models

匯率在國際貿易活動中扮演相當重要的角色，如何做好匯率風險管理是金融機構、企業甚至投資人重要的課題。本研究之主要目的是將風險值的觀念運用在匯率上，以國際間主要貨幣兌換台幣，包括美元兌台幣、英鎊兌台幣、歐元兌台幣、加幣兌台幣、日幣兌台幣與澳幣兌台幣等即期匯率為實證資料，運用變異數－共變異數法、歷史模擬法和蒙地卡羅模擬法來衡量匯率波動所產生的風險，其中變異數－共變異數法包含均等加權移動平均法、指數加權移動平均法、GARCH模型。此外，運用平均值、均方根誤差、回溯測試、失敗比率及失敗率檢定來評估不同風險值模型的適用性，同時比較不同幣別的風險值。文主要結論如下：、持有外幣的風險值以美元最低。、持有外幣的風險值以澳幣最高。、指數加權移動平均法估計之風險值多數情況為最小的，因此效 率性也較佳。、資料結構無明顯變化的情況下，均等加權移動平均法與歷史模 擬法亦是值得參考的模型。、GARCH模型在99%的信賴水準下相較於指數加權移動平均法在準 確性上有較好的表現。、效率性與準確性之間存在抵換關係。、歷史模擬法與蒙地卡羅模擬法在準確性的表現較佳；指數加權 移動平均法與GARCH模型則在效率性的表現較好。Exchange rates play an important role in the international trade, so how to manage the exchange rate risk well is an essential topic to financial institutes, enterprises and even the investors. The main purpose of this study is to apply the concept of VaR to exchange rates, we use historical simulation method, Monte Carlo simulation method and variance-covariance method containing equally weighted moving average approach, exponential weighted moving average approach and GARCH model to measure the risk from the exchange fluctuations and take Taiwanese Dollars against major currencies, such as U.S. Dollars, British Pounds, European Euros, Canadian Dollars, Japanese Yen and Australian Dollars as our empirical data. Moreover, we use some methods including mean, root mean squared error, back-testing, proportion of failure and proportion of failure test to evaluate the applicability of different models, meanwhile, compare the VaR of different currencies.he following are the conclusions of this study:.The VaR of U.S. dollars is the highest..The VaR of Australian dollars is the lowest..Exponential weighted moving average approach produces the lowest VaR estimates in most cases, so it is more efficient than other models. .If the structure of data has no significant change, equally weighted moving average approach and historical simulation method are worth to consider..At 95% confident level, GARCH model is more accurate than exponential weighted moving average approach..There is a trade-off relationship between efficiency and accuracy..Historical simulation method and Monte Carlo simulation method have comparatively fine performance of accuracy while GARCH model and exponential weighted moving average approach have relatively good performance of efficiency.謝辭 i文摘要 iibstract iii錄 v目錄 vi目錄 vii一章 緒論 1.1 研究背景與動機 1.2 研究目的與方法 4.3 研究流程與架構 4二章 文獻回顧 7.1 風險值之介紹 7.2 風險值之估計方法 11.3 風險值之績效比較 15.4 國內外相關文獻回顧 17三章 研究方法 21.1 變異數－共變異數法 21.2 歷史模擬法 28.3 蒙地卡羅模擬法 29.4 模型績效檢測 31四章 實證結果 35.1 資料選取與說明 35.2 美元的實證 36.3 英鎊的實證 39.4 歐元的實證 41.5 加幣的實證 44.6 日圓的實證 47.7 澳幣的實證 50.8 小結 52五章 結論與建議 55.1 研究結論 55.2 研究建議 57考文獻 59錄 6