本篇論文使用馬可夫移轉變異數模型探討台指選擇權之買權的波動性。馬可夫移轉變異數模型將條件變異設定為可隨時間變動而改變，甚至移轉到不同區間上。樣本在不同區間下的平滑機率估計值有助於捕捉資料特性，實證結果顯示當樣本落在高波動率區間上時，會對應著重大事件的發生，例如2004年台灣319槍擊案、2006年全球股災、2008年金融海嘯等。當樣本落在低波動率區間上時，會對應著投資人傾向將台股指數的上漲或下跌視為超漲或超跌，而賦予台指選擇權之買權負的時間價值。 / This paper investigates the volatility of TAIEX Call Options using Markov-switching variance model. The Markov-switching variance model allows the conditional disturbances to change as time passes and even switch between different regimes. The estimation of smoothed probabilities under different regimes facilitates to capture the characteristics of data. The empirical result shows that the high volatility regime is related to extraordinary events, such as 319 shooting incident in 2004, the global stock market crash in 2006, and the Financial Crisis in 2008. When in low volatility regime, investors tend to treat rise or fall in TAIEX as overreactions and give TAIEX Call Options turning points of time values.

由選擇權價格反推求算出的隱含波動率，可表示市場對未來波動的預期，亦間接反映出該選擇權的價值高低，成為投資者在制定交易策略時重要的依據。經由實證研究發現，CBOE VXO及VIX都可反應投資人的恐慌心理，因此能作為標的走勢的逆向指標，所以又稱為「投資人恐慌指標」。而台指市場並沒有波動率的指標可供投資人參考，所以本研究的目的，是依照臺灣指數選擇權之市場特性，修改多種隱含波動率的估計方法。依照下列比較基準，找出適合台指市場的波動率指數。 1. 報酬反向指標： 分析波動率指數變動與市場報酬之間的關係，觀察「反向非對稱變動行為」，以Vega指數的表現最明顯。 2. 週期行為： 所有波動率指數，在日內行為的偏離幅度都很有限，且週內行為並沒有異常的週期性。分析到期日效果，只有ATM指數在到期日前二日及交易當日顯著下降，顯示台指報酬在到期日前並沒有大幅的異常波動。 3. 預測能力： 比較各波動指數的預測能力優劣。使用避免假性迴歸的模型、每分鐘報價來計算實際波動率，以VIX指數的解釋能力最佳。 綜觀以上分析結果，發現無法找出單一最佳的台指波動率指標。所以若需要最佳的「投資人恐慌指標」，必須使用Vega指數；若想做預測分析，則必須使用VIX指數。

Straddles and strangles are common trading strategies introduced in a lot of textbooks and are widely used for option market participants. However, to our knowledge, we might not know how these trades should be designed, which trades are preferable, and how they are constructed in practice. Thus, we want to apply and discuss straddles and strangles as our trading strategies to the practical market. In our research paper, focusing on the time value and finding some profitable strategies are the two important concepts of our straddles and strangles. Being a sell side to earn the time value is our main goal. Although we may take higher risk, time value decay is helpful for us. The research focuses on straddles and strangles by using historical data of TAIEX futures and options. We use the closing price and settlement price as our trading price from data period January 2005 to December 2010. We also compare two different situations, holding positions to maturity and early offset condition, to our straddles and strangles. The findings show that the straddle strategies have positive earnings by holding positions to maturity, and 3 out of 4 strangle strategies have the same results. We can indeed earn the time value as a seller because time value decays quickly for the last seven days of the options contracts. After considering the early offset condition, the profitability of the ATM straddle and strangles become worse. We might easily fall into a trap in which the index futures price fluctuates greatly for a few days and comes back to the normal level on the settlement date. Therefore, we encounter loss due to selling low and buying high so that the trading performance is poor compared with the positions held to the end. Key words: Straddle Strategy, Strangle Strategy, Time Value, Settlement, Early Offset, TAIEX Options, TAIEX Futures