臺灣博碩士論文加值系統

在財務領域上，指數加權移動平均(EWMA)是一種常見的方法，此方法能夠將近期的觀測值賦予較大的權重，越後期的觀測值權重較小並呈現指數遞減，降低因趨勢出現的結構變異，使模型能夠有最佳的預測效果。往後的學者對EWMA進行改良，提出廣泛指數加權移動平均(GWMA)，GWMA與EWMA的相異之處在於GWMA比EWMA多了一個調整參數α，使得在偵測小變化時更為敏感，並且在實務應用上也較EWMA廣泛，並且利用數值最佳解的方法找出GWMA與EWMA的最佳參數。
本研究以美金/新台幣與美金/日圓兩種外匯做交叉避險，運用歷史法、GWMA、EWMA與GARCH家族模型估計避險比率，並使用不同滾動期比較在不同統計模型下的避險效果，以尋求最適的避險模型與策略提供投資客參考。實證結果顯示，GWMA的避險效果相較於其他模型具有優越性。

Exponentially weighted moving average (EWMA) is one of the most used commonly models in the field of finance. One of the major advantages of EWMA is that it gives more weight to the recent returns while calculating the returns. More and more papers suggest that generally weighted moving average (GWMA) is more extensively applicable because of its sensitivity over micro measurements.
In this study I examine the effectiveness of cross hedging the USD/TWD exchange rate changes with USD/JPY. We take advantage of Historical model, EWMA, GWMA and Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH model) to estimate optimal hedge ratio and compare these methods in different rolling data in this thesis. Moreover, we find out the optimal parameters in GWMA and EWMA by using numerical method.
The empirical results suggest that GWMA model is a powerful model for hedging and should be recognized as a useful hedging strategy.

目錄
摘要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 viii
第一章 緒論 1
第一節 研究背景 1
第二節 研究動機 2
第三節 研究目的 2
第四節 研究架構 3
第二章 文獻探討 4
第一節 避險 4
第二節 GARCH 4
第三節 指數加權移動平均模型(EWMA) 5
第四節 廣泛加權移動平均模型(GWMA) 6
第五節 最佳化方法 6
第三章 研究方法 7
第一節 對數報酬率 7
第二節 最適避險比率 7
第三節 歷史法 8
第四節 天真法 (Naïve) 8
第五節 隨機漫步 8
第六節 指數加權移動平均法(EWMA) 9
第七節 廣泛加權移動平均法(GWMA) 10
第八節 交叉匯率波動 12
第九節 GARCH 13
第十節 GARCH (1, 1) 13
第十一節 EGARCH (1, 1) 14
第十二節 GJR - GARCH (1, 1) 14
第十三節 GARCH(1,1)-t 15
第十四節 滾動法(Rolling window) 16
第十五節 避險績效衡量 17
第十六節 避險績效指數 17
第十七節 研究流程 18
第四章 實證結果與分析 19
第一節 資料來源 19
第二節 敘述統計 19
第三節 實證結果 22
實證結果-資料期間為一年 22
實證結果-資料期間為六個月 27
實證結果-資料期間為三個月 32
實證結果-資料期間為一個月 37
第五章 結論與建議 41
第一節 結論 41
第二節 建議 41
參考文獻 42
附錄 44
資料期間為一年 44
資料期間為六個月 49
資料期間為三個月 54
資料期間為一個月 59

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