本文期望能將選擇權定價理論與實務操作連結，採用Bernardo and Ledoit (2000) 的做法，捨棄以往的Black-Scholes選擇權理論價格，改以gain-loss bound作為合理價格區間，認定超出此區間外之選擇權價格為市場過度反應之不理性價格，並藉由調整gain-loss ratio得到不同的gain-loss bound，再以此區間擬定台指選擇權之交易策略，研究此策略之實際的獲利與虧損比(realized gain-loss ratio)是否會趨近於設定的gain-loss ratio。
實證結果顯示，控制gain-loss ratio相當於控制交易策略的realized gain-loss ratio，當gain-loss ratio越大時，gain-loss bound越大；而樣本數越大時，realized gain-loss ratio會趨近我們所設定的gain-loss ratio。此外，根據此交易策略操作所得到的績效也相當穩定。

This article links the option pricing theory with the practical trading strategy, using the Bernardo and Ledoit (2000) approach instead of the classical Black-Scholes option price, which defines the option price as a reasonable gain-loss bound. The option price falling out of the bound is regarded as an irrational or a semi-arbitrage price.
The trading strategy is based on the gain-loss bounds, and various bounds can be obtained by adjusting the gin-loss ratio.
The empirical result shows that controlling the gain-loss ratio of trading strategy is equivalent to set the realized gain-loss ratio of the trading strategy. The greater the gain-loss ratio, the wider the gain-loss bound, and the realized gain-loss ratio converges to the target gain-loss ratio as the numbers of observation getting larger. Finally, the return of our trading strategy is stable during the years of 2008 and 2013.

壹、緒論 1
一、研究動機 1
二、研究目的 1
三、研究方法 2
四、研究架構 2
貳、文獻回顧 4
第一節、選擇權價格區間 4
第二節、選擇權價格區間後續文獻 5
第三節、選擇權波動率 6
第四節、交易策略 6
參、均衡定價與Gain-Loss Bound估計模型 7
第一節、均衡定價模型 7
第二節、Gain-Loss Bound估計模型 8
一、Gain-Loss Ratio 8
二、Gain-Loss Bound Model 9
三、考慮交易成本後的Gain-Loss Bound Model 11
第三節、Black-Scholes 選擇權理論價格 12
一、波動率估計 12
二、蒙地卡羅模擬Black-Scholes價格 14
第四節、交易策略 15
肆、實證分析 16
第一節、台指選擇權及資料簡介 16
一、台指選擇權簡介 16
二、資料來源 17
三、研究期間與限制 17
第二節、Gain-Loss Bound模擬結果 18
一、Gain-Loss Bound模擬結果 18
二、Gain-Loss Ratio變化的影響 19
三、不同執行價的Gain-Loss Bound 19
第三節、交易策略績效 20
一、Gain-Loss Ratio變化的年度交易結果 20
二、不同月份的Realized Gain-Loss Ratio變化 23
三、考慮交易成本後Gain-Loss Ratio變化的年度交易結果 23
伍、結論與建議 27
一、結論 27
二、建議 27
參考文獻 29

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