本論文主要探討台灣加權指數選擇權的平賭限制是否成立，即隱含指數是否與真實指數相等？其次，比較修正後Black-Scholes model和放寬平賭限制的Black-Scholes model之定價績效，並探討選擇權價內外程度和距到期日期間解釋限制及非限制模型定價誤差的能力。最後，探討平賭限制不成立是否與市場流動性不足有關？
實證結果如次：一、台指買權及台指賣權的隱含指數大於真實指數機率頗高。二、由於Black-Scholes model的偏誤，非限制模型在台指買權、台指賣權和台指選擇權之定價績效皆明顯優於限制模型。三、選擇權價內外程度與距到期日期間對於限制模型定價績效的解釋能力較非限制模型為高。四、由最佳配適度迴歸模型顯示，台指買權和賣權的價差比率與未平倉量有顯著相關，台指選擇權的價差比率都與未平倉量和成交量有顯著相關，這些結果意味著市場流動性不足可能對選擇權定價有所影響。

This study investigates Longstaff’s martingale restriction on Taiwan stock index option, where the martingale restriction means that the value of the underlying asset implied by option prices must equal its actual market value. Additionally, the study compares the pricing performance of Black-Scholes model with relaxing martingale restriction’s Black-Scholes model. Moreover, the study examines whether the pricing performance from restricted and unrestricted model can be explained by moneyness and time to maturity. Finally, we attempt to explore if the violation of martingale restriction is due to the lack of liquidity.

The empirical results are as follows. First, the implied indexes separately extracted from call and put option prices are significantly larger than the actual index. Second, because of Black-Scholes bias, the pricing performance of the unrestricted model reveals significantly better than the restricted model. Third, moneyness and time to maturity have stronger explanatory power in restricted model than in unrestricted model. Finally, the best fitting regression model provided by this study shows that the percentage pricing differences of call option and put option are related to open interest; the percentage pricing differences of option is related to open interest and option volume. These results implied the lack of liquidity in option market maybe influence the option pricing performance.

摘要 I
ABSTRACT II
謝誌 III
目錄 IV
圖表索引 VI
第壹章 緒論 1
第一節 研究動機 1
第二節 研究目的 3
第三節 研究架構 3
第貳章 文獻探討 5
第一節 國外文獻 5
第二節 國內文獻 7
第三節 台指選擇權與S&P100指數選擇權之交易制度 9
第參章 研究方法 11
第一節 BLACK-SCHOLES MODEL 11
第二節 平賭限制(MARTINGALE RESTRICTION) 14
第三節 隱含波動度與隱含指數 15
第四節 違反平賭限制因素 18
第肆章 實證結果 21
第一節 資料描述 21
第二節 驗證平賭限制是否存在 26
第三節 放寬平賭限制之實證 30
第四節 探討違反平賭限制的原因 46
第伍章 結論 54
參考文獻 56
附錄1 58
附錄2 60
作者簡介 61

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