本篇論文透過結合美式選擇權定價理論和交易策略，探討芝加哥交易所的歐元兌美元選擇權(EC)其合約結構以及資料特性，並利用最小平方蒙地卡羅法(LSM)算出美式選擇權價值，過程中透過EGARCH模型估計LSM內的波動率參數，最後將LSM與Bernardo and Ledoit (2000)的gain-loss ratio做結合設計出交易策略，進而找出半套利價格空間。套利方式是透過主觀的風險意識下設定gain-loss ratio，我們能找出選擇權的合理價格區間，當市場價格脫離此價格區間時，價格高於上界做該選擇權賣方；價格低於下界則坐該選擇權的買方。
實證結果發現，當gain-loss ratio設定越高，選擇權價格區間越寬，交易頻率下降，發生極端損失的期望值也會有效下降，此外，提高波動率更新的頻率也能有效降低歐元選擇權交易策略的風險及提升報酬率；將交易策略套用於歐元選擇權遠月合約其報酬績效與風險比近月合約表現更佳。

The purpose of this paper is to evaluate the value of Euro FX options (EC) which is available at CME Group exchanges by combining the option pricing theory with practical trading strategy. By using Least-Squares Method (LSM) of Longstaff and Schwartz (2001) to estimate its early exercising value and using EGARCH model to estimate its volatility, we then combines LSM algorithm with the gain-loss ratio of Bernardo and Ledoit (2000) to create the trading strategies. Then we compare the pricing bounds with real trading prices to find existence of semi-arbitrage opportunities.
The empirical results show that the higher the gain-loss ratio we set, the wider the option bounds we get. The wider pricing bounds lower trading frequency, but decrease the numbers of extreme loss. Meanwhile, using higher frequency data to estimate volatilities would reduce the risk and increase the trading performance; the trading strategies perform better on the back month Euro FX options than the front month Euro FX options.

摘要 i
ABSTRACT ii
CONTENTS iii
LIST OF TABLES iv
LIST OF FIGURES v
Chapter 1 Introduction.............................1
Chapter 2 Methodology..............................2
2.1 Volatility Models.......................3
2.2 LSM algorithm...........................4
2.3 The Gain-Loss Ratio.....................6
2.4 Gain-Loss Pricing Bound................7
Chapter 3 Data.....................................8
3.1 Euro FX Options Contract Specifications.8
3.2 Descriptive Statistics of Data.........10
3.3 The Volatility of Data.................13
Chapter 4 Empirical Analysis......................15
4.1 Portfolio Strategies...................15
4.2 Performance on different sample period of volatility estimation........................................17
4.3 Performance on front month and back month data..............................................20
Chapter 5 Conclusion.............................23
5.1 Conclusion........................23
5.2 Research limitations..........................24
Appendix..........................................25
References........................................27

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