本研究旨在探討台股加權指數與選擇權間之關聯性。本文選取2002年至2005年之間加權指數日內資料以及各該交易日價平選擇權收盤資料，分別計算加權指數報酬之歷史波動率、價平買權與賣權隱含波動率。藉由單根檢定檢視三者在時間序列上是否為定態之資料產生過程（DGP , Data Generation Process）；建立2002年至2004年間之向量自我迴歸模型，以探討歷史波動率與隱含波動率之領先─落後關係；並進一步利用衝擊反應函數與預測誤差變異分解來了解兩個波動率間相互影響程度。此外，根據所建立之向量自我迴歸模型來預測2005年間各交易日收盤時價平買權與賣權之隱含波動率，進行買低賣高之交易策略。
歸納本研究之結果如下：就加權指數報酬之歷史波動率與價平買權、賣權隱含波動率三者在時間序列上的特性而言，三者之資料產生過程皆屬定態；而就領先─落後關係以及相互影響的程度與期間觀之，加權指數報酬歷史波動率與價平買權隱含波動率兩者互有領先，但價平賣權隱含波動率對於加權指數報酬之歷史波動率僅具有單項領先效果；大致而言，隱含波動率受其自身自發性衝擊影響最大，且該衝擊均屬短期效果；而加權指數報酬歷史波動率對於自身與隱含波動率之衝擊所呈現的反應程度將會漸趨一致。
就買低賣高交易策略而言，在考量交易成本後，不論是買進隱含波動率低估之價平買權、賣出隱含波動率高估之價平賣權，或是買進隱含波動率低估之價平賣權、賣出隱含波動率高估之價平買權，平均而言仍有正向報酬，顯示價平選擇權之隱含波動率具有均數迴歸特性，也符合其隱含波動率之時間序列為定態之檢定結果。

This research investigates the relationship between Taiwan stock index and Taiwan stock index options. The historical volatility of the return on Taiwan stock index and the implied volatility of the at-the-money call and put are measured based on the intraday data of Taiwan stock index and the close data of the at-the-money call and put corresponding to each trading day which are selected from 2002 to 2005. This research applies unit root test to see if the data generation processes of the three volatilities are stationary and vector auto-regression models to establish the lead-lag relationship between the historical and implied volatility. Impulse response function and forecast error variance decomposition , then , are used to explore the degree of the impacts by the two volatility have on each other . In addition, this research simulates two trading strategy: buying the call／put that the implied volatility is under-valued while selling the put／call that is over-valued, according to the closing implied volatility of the at-the-money call and put through 2005 forecasted by the VAR models described above.
The empirical results are as follow: the data generation processes of the historical volatility of the return on Taiwan stock index and the implied volatilities of the at-the-money call and put are stationary; contemporaneous relationship exists between the historical volatility of the return on Taiwan stock index and the implied volatility of the at-the-money call while the implied volatility of the at-the-money put lead the historical volatility. Generally speaking, implied volatility is affected by its own shock which has only short-term effect while the historical volatility of the return on Taiwan stock index will response to the shock by its own and the implied volatility gradually equally .
For the trading strategies under the consideration of trading cost, we still earn a positive profit on average no matter buying the call that the implied volatility is under-valued and selling the put that is over-valued or vice versa. The result means that the implied volatility of the at-the-money option has the property of mean reverse, according with the stationary data generation process of it.

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