本研究仿效CBOE先後公佈二套波動率指數編制方法，編制臺指選擇權之VXO與VIX，希望能建立一套有效指標為投資者帶來更適切的資訊。研究期間為2002年4月1日至2006年3月31日，共計997個交易日之日資料作為樣本，主要針對波動率指數對未來真實波動率之預測能力及波動率指數與指數報酬之間的關係作為研究的二大主題，最後再輔以穩定度分析，使結論更具可靠性，本研究結論歸納如下： 一、以三種波動率模型(HV、VXO及VIX) 來預測未來真實波動率，透過迴歸分析，各時期下均以VXO預測能力最佳，且隨著真實波動率計算期間增長預測能力逐漸增加；於迴歸模型中加入交易量變數，亦可增加預測能力。另外利用MAE與RMSE分析，大致以VXO與真實波動率間的誤差為最小。 二、VXO與VIX的變動對同期股價指數報酬皆有顯著負向關係，同時注意到VXO變動和報酬呈現負向不對稱關係，而VIX不對稱關係不顯著。進一步以多空頭市場來研究，空頭市場下加強了VXO不對稱效果，而在多頭市場下VXO無不對稱效果；VIX在多空頭市場下皆無不對稱效果。 三、VXO及VIX在預期未來指數報酬方面皆只有對未來10日、20日及60日有顯著負向關係存在，並以VXO解釋能力較佳，若加入交易量結果亦為VXO最佳。 四、將歷年樣本依高低波動率排序，發現VXO與VIX在低波動率時未來持有期間報酬多為負值，在高波動率時報酬多為正值，隨著持有期間拉長報酬會有相反變化。 五、將樣本依照市場交易情形劃分二階段，加以檢驗VXO與VIX預測真實波動率與預測未來指數報酬，結果均以VXO表現較佳，與全樣本時期結果一致。 就二種波動率指數在臺灣選擇權市場應用來看，以VXO指標在臺灣市場較能提供較多的資訊內容及預測能力，期待臺灣未來也能建構適合市場的波動率指數。 This article makes a description of the market volatility indices (VXO and VIX) which were introduced by CBOE in 1993 and 2003. We apply the two formulas of volatility indices to calculate volatility indices of TXO. The research period is from April 1, 2002 to March 31, 2006.The main topic of this research is to test the ability of the volatility index to forecast realized volatility and test the relationship between volatility index and stock index return. Finally, the research is also supplemented with robustness analysis to make the conclusion more credible. The major empirical results are shown as follows. 1. Three models are used to forecast realized volatility. By regression analysis, VXO has the best forecasting ability among all volatility models and the forecasting ability increases with the increase of calculation period of realized volatility. If options trading volume is added to the regression model, the forecasting performance increases as well. Besides, VXO has the lowest error from MAE and RMSE analysis. 2. There is a negative relationship between the changes in the stock index return and volatility indices. For VXO, the relationship is asymmetric. The extent of this asymmetric effect depends on the market trend. The bear market enhances VXO's asymmetric effect while there is no significant asymmetric effect in the bull market. For VIX, there is no asymmetric effect in either market. 3. As for the VXO and VIX to forecast the stock index return, there is significant negative relationship only for 10, 20 and 60 days. VXO has the better power to forecast the stock index return. VXO also has the better forecasting power when options trading volume is added. 4. If the volitility is sorted, the low volatility from VXO and VIX is accompanied by negative return while the high volatility is accompanied by the positive return. 5. If the sample is divided into two stages according to the trading environment to test the ability of VXO and VIX to predict the volatility and stock index return, VXO is the best estimator. This result is consistent with that of the whole sample period. For the application in Taiwan option market, VXO is able to provide more information and ability to forecast. It is hoped that Taiwan market can establish the appropriate volatility index.
