臺灣博碩士論文加值系統

本文透過GARCH模式修正外匯選擇權模式中波動率為常數的假設，並且加入介入模式修正，發現透過介入模式的修正確實可以降低評價誤差，並且透過以B-S為基礎的卡曼濾波器設計，得到優於只考慮GARCH波動性選擇權模式的結果，而文中所有的模型買權、賣權使用同一波動率與利率，其隱含條件為買賣平權等式成立。
本文分析的外匯選擇權報價為2007/3/19至2008/3/20的NYSE Euronext Liffe發行的美元兌歐元選擇權。此分析區間出現五個相加型態的離群值 (AO) ，經由修正離群值後的模型可以提高評價績效，若是放寬無風險利率為非給定的資料並利用卡曼濾波器估計，可以得到更為優異的評價績效。

一、緒論---------------------------------------------------------1
1.1研究動機----------------------------------------------------1
1.2研究目的----------------------------------------------------2
1.3本文架構----------------------------------------------------3
二、文獻回顧----------------------------------------------------5
2.1 選擇權文獻-------------------------------------------------5
2.2卡曼濾波器文獻---------------------------------------------6
2.3 波動率文獻-------------------------------------------------7
三、研究方法----------------------------------------------------8
3.1 外匯選擇權評價模式----------------------------------------8
3.2 卡曼濾波器------------------------------------------------10
3.2.1 擴展卡曼濾波器-------------------------------------11
3.2.2 無軌跡卡曼濾波器-----------------------------------12
3.3波動性估計模型--------------------------------------------14
3.4介入模式---------------------------------------------------15
3.5績效評估---------------------------------------------------19
四、實證分析及結果--------------------------------------------20
4.1資料處理與資料分析----------------------------------------20
4.2 GARCH波動性模型估計--------------------------------------21
4.2.1 GARCH模型搭配B-S模型-----------------------------22
4.2.2 加入介入模式的GARCH模型搭配B-S模型------------23
4.3卡曼濾波器即時預測----------------------------------------25
4.3.1 擴展卡曼濾波器-------------------------------------26
4.3.2 無軌跡卡曼濾波器-----------------------------------26
4.4濾波器下的狀態變數走勢-----------------------------------27
4.5小結--------------------------------------------------------29
五、結論與建議-------------------------------------------------30
5.1結論--------------------------------------------------------30
5.2後續研究建議-----------------------------------------------32
參考文獻--------------------------------------------------------33








圖表索引
表目錄
(表01) GARCH估計係數--------------------------------------------22
(表02) GARCH績效評估--------------------------------------------23
(表03) ARIMA階次選取---------------------------------------------24
(表04) 離群值偵測表-----------------------------------------------24
(表05) 加入介入模式GARCH估計係數--------------------------------24
(表06) 加入介入模式績效比較表-------------------------------------25
(表07) 擴展卡曼濾波器的績效---------------------------------------26
(表08) 無軌跡卡曼濾波器績效---------------------------------------27
(表09) 加入介入模式與卡曼濾波器績效比較表-------------------------28
圖目錄
(圖1) EKF利率比較圖-----------------------------------------------27
(圖2) Call在價平下的表現--------------------------------------------29
(圖3) 履約價128下的資料結果---------------------------------------36
(圖4) 履約價128狀態變數的預估-------------------------------------38
(圖5) 履約價134下的資料結果---------------------------------------39
(圖6) 履約價134狀態變數的預估-------------------------------------41
(圖7) 履約價136 下的資料結果---------------------------------------42
(圖8) 履約價136狀態變數的預估-------------------------------------44
(圖9) 接近價平下的資料分析-----------------------------------------45
(圖10) 接近價平狀態變數的預估--------------------------------------47

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1. 謝盈弘，2002,馬可夫鏈蒙地卡羅法在外匯選擇權定價的應用，政治大學統計學系碩士論文。
2. 蘇鼎宇，2003,隨機利率下外匯選擇權評價模型之實證研究，世新大學財務金融學研究所碩士論文。
3. 林慧芳，2004,結構性改變下Black-Scholes 與 Hull-White 評價模型之應用–以台灣股價選擇權為例，東海大學經濟學系碩士論文。
4. 任紀為，2004,外匯選擇權的定價與馬可夫鏈蒙地卡羅法的應用，風險管理學報 第七卷 第三期 2005 年11 月,237-277，
5. 王鈺淩，2007,外匯期貨選擇權定價-VG與FFT方法，國立中正大學財務金融所碩士論文。
6. 陳裕文，2007,台指選擇權是否存在衝擊遞延效果以介入模式與狀態空間模型分析，東海大學經濟學系碩士論文。