本研究利用台灣股價指數選擇權資料來檢驗BS模型基礎下隱含波動度與無模型建構下隱含波動度的預測能力及其所包含的資訊，試圖找出一個可做為未來真實波動率最佳的預測指標，希望能提供台灣股市交易者一個較佳的參考資訊。本文除了比較了歷史波動度、BS隱含波動度和Britten-Jones and Neuberger (2000)所提出的無模型隱含波動度外，亦考慮了台灣期貨交易所近年所引用CBOE分別在1993與2003年所推出的新舊兩種波動度指數(VXO、VIX)與其修正的台灣選擇權波動度指數(TVXO)。
    本文的實證研究結果發現，所有的隱含波動度預測值皆包含了未來實現波動度一定程度的資訊在內，資訊內涵也較歷史波動度來的多。在BS模型基礎下所計算出的隱含波動度中，使用多種履約價格算出的隱含波動度，對於未來實現波動度將會比使用單一履約價格的隱含波動度保留更多的資訊。無模型建構下的隱含波動度使用了不同履約價格的選擇權資訊而計算的，相較於BS模型的隱含波動度而言，無模型設定的隱含波動度對於未來波動度保留了較多的資訊。預測能力也較只使用單一履約價格的BS隱含波動度來的高。

This article use the data of TAIEX Options to test the information contain and forecast ability of the Black-Scholes implied volatility and the model-free implied volatility, try to find a more efficient indices of real volatility. This article not only compare the Black-Scholes implied volatility and the model-free implied volatility which were derived by Britten-Jones and Neuberger (2000), but also consider the market volatility indices which were introduced by CBOE in 1993 and 2003(VIX and VXO) and the TAIEX Options volatility indices by Taiwan(TVXO).
  The empirical study in this article finds that all the implied volatility subsumes some information contained of the realized volatility, and the information contain of implied volatility is more than historical volatility. And our results from TAIEX Options support that the model-free implied volatility subsumes more information contained than the Black-Scholes implied volatility and historical volatility and is a more efficient forecast for future realized volatility.

第一章 序論……………………………………………………………1
  第一節 研究動機……………………………………………………1
  第二節 研究目的……………………………………………………2
  第三節 研究架構……………………………………………………3
第二章 文獻探討………………………………………………………4
  第一節 隱含波動度相關文獻………………………………………4
  第二節 無模型隱含波動度…………………………………………6
  第三節 波動度指數相關文獻………………………………………7 
第三章 研究方法………………………………………………………9
  第一節 資料來源與選取……………………………………………9
  第二節 VXO指數編製方式…………………………………………10
  第三節 VIX指數編製方式…………………………………………11
  第四節 台灣選擇權TVXO指數編製方式 …………………………14
  第五節 無模型隱含波動度之建構 ………………………………16
  第六節 歷史波動度與實現波動度之估計 ………………………19
  第七節 迴歸分析模型 ……………………………………………21
第四章 實證結果分析 ………………………………………………24
  第一節 樣本基本分析 ……………………………………………24
  第二節 簡單迴歸分析 ……………………………………………28
  第三節 BS模型基礎下之隱含波動度比較 ………………………32
  第四節 無模型建構下之隱含波動度比較 ………………………36
  第五節 隱含波動度之總合比較 …………………………………39
第五章 結論與建議 …………………………………………………48
參考文獻………………………………………………………………50

表目次
表一：波動度預測能力比較 ……………………………………………5
表二：各隱含波動度的基本統計量……………………………………25
表三：各種波動度之間的相關性矩陣…………………………………26
表四：隱含波動度之簡單迴歸結果(OLS) ……………………………30
表五：隱含變異數之簡單迴歸結果(OLS) ……………………………31
表六：BS模型基礎下之隱含波動度包含迴歸結果(OLS) ……………34
表七：無模型建構下隱含波動度之簡單迴歸與包含迴歸結果(OLS) 37
表八：歷史波動度與各種隱含波動度之包含迴歸結果(OLS) ………40
表九：隱含波動度之簡單迴歸與包含迴歸結果(OLS) ………………42
表十：波動度指數之簡單迴歸與包含迴歸結果(OLS) ………………45

圖目次
圖一：不同隱含波動度與實現波動度的走勢圖 ……………………27
圖二：不同隱含波動度與實現波動度的走勢圖(續) ………………27

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