芝加哥選擇權交易所(CBOE)在1993年推出以S&P100指數選擇權為基礎的波動率指數(CBOE OEX Volatility Index, VXO)，提供了投資人預期波動率的參考指標。2003年，CBOE改變波動率指數的編製方法與其標的資產，推出以S&P500指數選擇權為基礎的波動率指數。台灣期貨交易所亦於2006年12月18日推出臺指選擇權波動率指數，其編製法採用2003年CBOE的編製法，而本研究則參考Arnold and Earl (2007)之方法，自行編製一新的波動率指數，來描述臺灣股市的波動性，並利用不同的模型檢視其對股市波動性之預測能力，此外，模型中亦加入選擇權市場中買權及賣權之交易量，以反映出選擇權市場資訊對股市波動性的不對稱性影響。
本文的結論是自行編製的波動率指數在波動性的解釋和預測上優於臺灣期貨交易所發佈之波動率指數，而選擇權市場的交易量對未來股市波動性的影響則較為不明顯。在以各種模型配適後發現，股市波動性的預測上是以包含選擇權交易量在報酬率均數方程式的二階段GJR-GARCH模型為最佳，而波動率指數之最適落遲期數則為10期。

In 1993, the Chicago Board Options Exchange (CBOE) introduced the CBOE S&P100 Volatility Index (VXO), which provided a measure of market expectations of near-term volatility conveyed by the S&P100 index options. In 2003, CBOE changed the method of constructing the index (CBOE Volatility Index, VIX) and its underlying asset to measure the expected volatility derived from the S&P500 index options. On December 18, 2006, the Taiwan Futures Exchange (TAIFEX) established the Volatility Index of Taiwan Stock Index Options, which is constructed by using the method suggested by CBOE in 2003. Based on Arnold and Earl (2007), this study constructs a new Volatility Index of Taiwan Stock Index Options. The new index is then used in different models to test its ability of forecasting stock market volatility. Besides, the trading volumes of call options and put options are also included in the models to reflect the asymmetric influences on stock market volatility from the information of option markets.
The empirical results of this study reveal that our new Volatility Index has a better performance on forecasting stock market volatility. However, the impact of the option trading volume on stock market volatility is insignificant. Among the different models tested, the two-stage GJR-GARCH model, including the option volume in the mean equation, has the better performance, and the volatility index with an optimal lag-length of 10 days is a better predictor for future stock market volatility.

第一章 緒論 1
第一節 研究背景 1
第二節 研究動機 3
第三節 研究目的 3
第二章 文獻探討 5
第三章 研究方法 10
第一節 資料來源 10
第二節 波動率衡量指標 10
第三節 編製波動率指數 13
第四節 資料檢定 20
第五節 研究模型 21
第六節 準確度分析 27
第四章 實證結果 29
第一節 編製波動率指數 29
第二節 模型中其他變數 30
第三節 GJR-GARCH 31
第四節 二階段GJR-GARCH 34
第五節 GJR-GARCH(volume in variance equation) 37
第六節 二階段GJR-GARCH(volume in variance equation) 40
第七節 雙變量GJR-GARCH 43
第八節 預測力綜合比較 47
第五章 結論與建議 49
第一節 結論 49
第二節 建議 50
參考文獻 51

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