Over the last decade, researchers have attempted to show how efficient the markets are by using Fama’s Efficiency Market Hypothesis (EMH). The theory states that an investor cannot increase his returns without taking additional risk. The markets can be efficient in different forms depending on the information included in the traded asset. It is quoted that: "There ain't no such thing as a free lunch". However, the topic still remains disputable since researchers have introduced controversial findings after investigating different markets. Overall, emerging markets have been characterized with higher volatility which consequently declares for market imperfections. Commonly, these market inefficiencies are quickly captured by the eye of the investors who are lurking for potential benefits through exploiting them. These are the so called arbitrage opportunities which exist on different level of impact, depending on the attitude of the market. The existence of arbitrage is clear evidence against Fama’s theory and it has been documented in numerous studies. Unfortunately those events occur rarely and disappear in a matter of seconds, thus; is highly competitive to capitalize. Over the last decade high frequency trading (HFT) became popular on different markets and it allowed traders to make decisions and execute transactions in a matter of milliseconds using algorithms. The market we are interested in is the Forex market which is a decentralized market where currencies from all over the world are traded. Main participants include multinational banks which rely heavily on HFT. The method used to benefit from inefficiency is called triangular arbitrage and it involves selling and buying 3 sets of currency pairs in times when a parity is violated. The goal of this study is to answer the following research question, “Is there a difference in triangular arbitrage opportunities between emerging markets and developed ones?” The main objective of this research is to examine how the number of arbitrage occurrences varies considering different market characteristics. Furthermore, the originality of the research stems from the comparison between strategies using currencies from developed economies and emerging ones. Moreover, the additional academic value comes from the analysis of a new dataset that has not yet been examined. Lastly, our results make an empirical contribution into a country’s economy by reducing market inefficiencies and increasing economic stability. Our sample consists of quantitative data totaling to 2.4 million observations per quotation taken from 2011 and 2013 for currencies picked using a non-probability convenience method based on their property to be converted to EUR and USD currency and availability of information. The research revealed that differences between the two types of market exist, and indicates that the “early” markets possess higher arbitrage activity in contrast to the mature economies. These results should boost the potential for a better trading management and upgrade the profit growth.

投資者面對到期日相同的一序列不同履約價格的選擇權時，應如何建立最佳的組合交易策略，這個問題雖已有許多標準的交易公式可依循，但這些標準的交易策略無法全面涵蓋複雜多變的組合策略。本論文提出整數線性規劃模型用來建立選擇權的最佳交易策略。模型針對到期日相同的買權、賣權如何買賣的組合，建立最佳交易策略。若我們預期在到期日時，標的股價將會落在某一範圍內，則我們可修改原來的規劃模型配合此項預期，以尋求最佳的交易策略。最後，我們以Ericsson的選擇權為例，驗証本模型的效能。 / The problem of how to construct the optimal combination trading strategy for investors when they face a series of options of different exercise prices on the same maturity date can be solved by many standard trading rules. Yet these standard trading rules cannot completely cover the complex and highly changeable combination strategy. This thesis proposes an integer linear programming (ILP) model to construct the optimal trading strategy for option portfolio selection. This model focuses on constructing the optimal strategy for an option portfolio of call- and put-options on the same maturity date. Given the investor's belief of the stock price, we also provide an extended ILP model to include this belief. Finally, an empirical study will be presented by using the ILP model applied to the Ericsson's call and put options.

投資者面對到期日相同的ㄧ序列不同履約價格的選擇權，已有許多文獻提出如何建立選擇權最佳投資組合，但模型中均未考慮交易成本。選擇權在實際市場的交易過程中，投資者所支付的手續費與賦稅即為選擇權的交易成本。本論文針對買賣到期日相同但不同履約價格的買權與賣權如何組合，提出考慮交易成本的整數線性規劃模型，建立選擇權最佳交易策略。我們不考慮股價變動的機率分配型態，延伸楊靜宜 (2004)所建立之整數線性規劃模型和Liu與Liu (2006)的大中取小模型，建構考慮比例制、固定制與混合制交易成本之整數線性規劃模型。最後，我們以台指選擇權(TXO)為例，驗證模型的效能。 關鍵字：交易成本，選擇權交易策略，整數線性規劃，選擇權套利機會。 / There are many researchers focus on constructing the optimal strategies and propose integer linear programming (ILP) for a series of options which are on the same maturity date with different strike price, but they neglect transaction costs in their models. The transaction costs of options are the handling charge and taxes which investors should pay for trading in the market. The thesis proposes an ILP with transaction costs to construct the optimal strategy for an option portfolio of call- and put- options on the same maturity date with different strike price. We leave the distribution of the variety of stock price out of consideration and extend Yang’s (2004) model and Liu & Liu’s (2006) min-max regret model to construct ILP with proportional, fixed, and mixed transaction costs. Finally, we take the trading data of TXO as an empirical study to test and verify the efficiency of our models. Key words: transaction costs, option trading strategies, integer linear programming, option arbitrage opportunities.