摘 要
芝加哥選擇權交易所(CBOE)於1993推出VIX指數，用來衡量選擇權交易人對未來股票市場波動率的預期，可具體描繪投資人心理的變化情形。臺灣期貨交易所於民國90年12月24日推出臺指選擇權，但目前尚未編制VIX指數，無法提供相關的數據作研究，本研究乃針對當前台灣選擇權市場的實際交易情形，提出編制臺指選擇權VIX指數的方法，並詳加說明編制時所面臨的問題與解決方式，以期編制一套符合目前台灣選擇權市場現況的波動率指數，提供選擇權交易人更多的市場資訊，協助其判斷市場的狀況與擬定合宜的交易決策。其次，觀察臺指選擇權VIX指數的特性，研究結果顯示市場波動率與報酬率為正向關係、日內波動率於盤中一路下跌及週內波動率走勢則呈現W形狀，及研究臺指選擇權到期日時對現貨市場的影響，並沒有顯著的價格效果、波動率效果與到期日效果，但有指數反轉的現象。最後，利用波動率的變化與特性作為交易訊號，並將其與交易策略相互結合，採取選擇權交易策略，於開盤時賣出跨式策略而後於收盤時結清部位，無論交易成本是否存在經統計檢定的結果顯示並無法獲得顯著的超額利潤，因此台灣的選擇權市場於研究期間是具有效率。

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第一章 緒論…………………………………………………………………………8
第一節 研究動機與背景………………………………………………………8
第二節 研究目的………………………………………………………………9
第三節 研究限制………………………………………………………………10
第四節 VIX指數的介紹………………………………………………………11
一、VIX的源由…………………………………………………………11
二、隱含波動率…………………………………………………………12
三、Black-Scholes選擇權定價模式…………………………………13
四、二項式模型評價模型………………………………………………15
五、CBOE編制VIX指數的理論基礎……………………………………16
六、VIX指數的編制方法…………………………………………………18
第二章 文獻回顧……………………………………………………………………21
第三章 研究方法……………………………………………………………………29
第一節 資料來源………………………………………………………………29
第二節 臺指選擇權之交易現況………………………………………………29
第三節 臺指選擇權VIX指數之編制…………………………………………33
一、臺指選擇權VIX指數之編制方法…………………………………33
二、編制臺指選擇權之VIX指數所面臨的問題與解決方式……………35
第四節 實證研究方法…………………………………………………………38
第四章 實證結果與分析……………………………………………………………39
第一節 臺指選擇權VIX指數之敘述統計……………………………………39
第二節 VIX指數與市場報酬率的關係………………………………………41
第三節 VIX指數變動之特性…………………………………………………44
一、日內的波動率…………………………………………………………44
二、週內的波動率…………………………………………………………52
三、VIX指數與到期日效果………………………………………………56
第四節 到期日效果……………………………………………………………58
一、價格效果………………………………………………………………58
二、指數反轉………………………………………………………………60
三、價格波動率……………………………………………………………62
四、臺指選擇權的市場波動率……………………………………………63
第五節 檢定台灣選擇權市場之效率………………………………………65
第五章 結論與建議…………………………………………………………………64
第一節 結論……………………………………………………………………69
第二節 建議……………………………………………………………………71
參考文獻……………………………………………………………………………72

圖目錄
圖3-1-1 交易人開戶數統計………………………………………..……………30
圖3-1-2 市場參與券商家數統計………………………………..………………31
圖3-1-3 臺指選擇權月成交量統計……………………………..………………31
圖4-2-1 VIX指數與加權指數的關係……………………………………………43
圖4-3-1每分鐘的平均VIX指數…………………………………………………45
圖4-3-2 每分鐘的平均偏離程度…………………………………………………46
圖4-3-3 股價上漲時VIX指數的變化……………………………………………49
圖4-3-4 股價下跌時VIX指數的變化……………………………………………49
圖4-3-5 買權波動率與賣權波動率之差………………………………..………50
圖4-3-6 週內的平均VIX指數……………………………………………………53

表目錄
表3-1-1 臺指選擇權每日平均交易量統計………………………………………32
表 4-1-1 VIX報價與計算頻率統計………………………………………………39
表 4-1-2 VIX指數之敘述統計……………………………………………………40
表4-3-1 每小時對日內偏離之迴歸分析…………………………………………47
表4-3-2 買權波動率與賣權波動率………………………………………………51
表 4-3-3 市場報酬率與週資料統計……………………………………………52
表4-3-4 週內日偏離之迴歸分析…………………………………………………55
表4-3-5 到期日效果之迴歸分析…………………………………………………56
表4-4-1 價格效果…………………………………………………………………60
表4-4-2 價格反轉…………………………………………………………………61
表4-4-3 波動率效果………………………………………………………………62
表4-4-4 VIX指數之到期日效果…………………………………………………63
表4-5-1 交易模擬損益統計………………………………………………………68

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