有鑒於目前市場大都以Black-Scholes隱含波動度作為探討波動度的主要工具，而根據Jiang and Tian(2005)在服從跳躍擴散過程(jump-diffusion process)下所提出的無模型設定隱含波動度(model-free implied volatility)的觀念，進一步探討無模型設定隱含波動度與Black-Scholes隱含波動度在台灣指數選擇權上的波動度的差異，並且了解樣本內，兩種隱含波動度以Black-Scholes反推出的估計選擇權價格與真實選擇權價格的差異。另外比較樣本外與樣本內兩種模型有無變化。
    實證結果可發現兩種隱含波動度相關性相當高，但是在誤差分析時可發現明顯差別。另外可發現不論樣本內或樣本外，Black-Scholes模型有較小的價格誤差，無模型設定隱含波動度有較大且不好的價格誤差，但在無模型設定隱含波動度在樣本外的估計選擇權價格誤差不完全比樣本內差，而Black-Scholes模型則有是有完全樣本外比樣本內差。

In recent years, Black-Scholes Implied Volatility has become the most famous tool in volatility researching. According to the idea of model-free implied volatility with jump-diffusion process that proposed by Jiang and Tian(2005), I prefer to know the difference between model-free and Black-Scholes Implied Volatility in TXO. More further, I compare in sample performance of two implied volatilities using Black-Scholes option pricing formula. Otherwise, I would like to know how pricing error going between in sample and out–of–sample. 
  Although empirical result shows these two implied volatilities has high correlation, there are distinct discrepancy in error test. No mater in or out-of-sample, Black-Scholes model has better performance in error test. In error test, in sample of model-free model is not exactly better than out-of-sample. But, in sample of Black-Sholes model is exactly better than out of sample.

目錄
第一章	緒論	- 1 -
1.1 研究背景	- 1 -
1.2 研究動機與重要性	- 2 -
1.3 研究目的	- 2 -
第二章	文獻回顧	- 4 -
2.1 各種波動率模型相關文獻	- 6 -
2.1.1 Black - Scholes Model	- 6 -
2.1.2 跳躍-擴散模型(Jump Diffusion Model)	- 7 -
2.1.3 定態波動率模型(Deterministic Volatility Model)	- 7 -
2.1.4 隨機波動率模型(Stochastic Volatility Model)	- 8 -
2.1.5 時間序列模型(Time Series Model)	- 9 -
2.1.6 模型比較	- 10 -
2.2 未來波動率的預測及資訊分析文獻	- 10 -
2.2.1 隱含波動率VS.歷史波動率	- 10 -
2.2.2 隱含波動率VS.交易量	- 13 -
2.2.3 隱含波動率VS.ARCH、GARCH系列模型	- 13 -
2.2.4 隱含波動率VS.跳躍-擴散模型	- 15 -
第三章	研究方法	- 16 -
3.1 實證研究資料	- 16 -
3.1.1 台灣指數選擇權(TXO)	- 16 -
3.1.2 資料篩選	- 18 -
3.2 無模型設定隱含波動度(Model-free Implied Volatility)	- 21 -
3.2.1 無模型設定的隱含波動度推導	- 22 -
3.2.2 實務上的限制	- 24 -
3.2.3 擷取誤差(Truncation Errors)	- 25 -
3.2.3 離散化誤差(Discretization error)	- 26 -
3.2.4 曲面擬合法(Curve-fitting Method)	- 27 -
3.2.5 無模型設定隱含波動度計算方式	- 28 -
3.3 誤差分析指標	- 30 -
第四章	隱含波動度與誤差分析	- 32 -
4.1 隱含波動度模型的圖形分析	- 32 -
4.2 誤差分析	- 34 -
4.3.1	樣本內誤差分析	- 35 -
4.3.2	樣本外誤差分析	- 39 -
第五章	結論與建議	- 44 -
第六章	參考文獻	- 46 -

表目錄
表3-1	台灣指數選擇權契約規格 22
表3-2	台指選擇權成交量 25
表3-3   選擇權契約分類方式 27
表4-1   MF模型與BS模型隱含波動度基本統計量 40
表4-2   樣本內近月份契約BS模型與MF模型誤差分析 43
表4-3   樣本內遠月份契約BS模型與MF模型誤差分析 44
表4-4   樣本內30天到期BS模型與MF模型誤差分析 45
表4-5   樣本外近月份契約在BS模型與MF模型誤差分析 46
表4-6   樣本外遠月份契約在BS模型與MF模型誤差分析 47
表4-7   樣本外30天到期BS模型與MF模型誤差分析 48
表4-8   30天到期BS模型樣本內、外誤差分析比較 49
表4-9   30天到期MF模型樣本內、外誤差分析比較 49

圖目錄
圖3-1	台指選擇權成交量 25
圖4-1   30天期無模型設定隱含波動度與B-S隱含波動度 39

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