本文以台灣股價指數選擇權上市後之資料估計VIX(volatility index)指數波動性與30、60、90天期之無模型(Model-free)隱含波動性與Black-Scholes模型之價平隱含波動性等三種，來對台指選擇權之平均隱含波動性與台指選擇權標的物進行預測。預測模型我們使用包含式迴歸(emcompassing regression)，並加入非同時期的預測變數來對台指選擇權標的物波動性與隱含波動性進行一天前的預測；最後，我們採樣本內與樣本外的預測誤差來比較使用何種波動性之預測能力較佳。 比較樣本內、外結果發現，單一變數預測模型以價平的B-S隱含波動性與VIX波動性指數預測較佳；雙變數模型則無一致結果；而以VIX指數波動性、60天期的Model-Free隱含波動性與60天期價平的B-S隱含波動性之三變數包含式迴歸預測能力最佳。且本文使用預測模型的變數皆為隱含波動性，實證發現模型對台指選擇權隱含波動性的預測效果優於對台指選擇權標的物的波動性預測。 This paper use the data of TXO to compute VIX(volatility index), 30-day, 60-day, and 90-day Model-Free implied volatility and at-the-money Black–Scholes (B–S) implied volatility, forecasting the average implied volatility and underlying of TXO. In addition, we employ encompassing regressions and use asynchronous predictive variables to forecast the volatility and implied volatility of the underlying of TXO. Furthermore, we use both in-the-sample and out-of-the-sample forecasting error to compare the predictive performance. The empirical shows that for single variable forecasting model ,at-the-money B-S implied volatility and VIX are preferred, for multi variable forecasting model ,there is no consistent conclusion, but the volatility of VIX、60 day Model-Free implied volatility and at-the-money B-S implied volatility seem to dominate. Besides, we use implied volatility as the variable of forecasting models, and we find that forecasting models predict the volatility of TXO perform better than the volatility of the underlying of TXO.
