This dissertation consists of two parts. In the first chapter, we examine the relative performance of four options-based investment strategies versus a buy-and-hold strategy in the underlying stock. Specifically, using ten stocks widely held in 401(k) plans, we examine monthly returns from strategies that include a long stock position as one component. These strategies are long stock, covered call, protective put, collar, and covered combination. Ignoring early exercise for simplicity, we find that the covered combination and covered call strategies generally outperform the long stock strategy, which in turn generally outperforms the collar and protective put strategies regardless of the performance measure considered. Clearly, from the first chapter, strategies that involve writing options, in general, outperform the ones buying options. The second chapter provides a detailed study of the conditions where option writers can maximize returns while minimizing risk. The nonlinear nature of time value decay in options suggests that, theoretically, holding short positions only when the speed of time decay is high might improve the performance of option writing strategies. We examine monthly returns from five option strategies without a position in the underlying asset. These strategies are: short straddle, short strangle, short guts, “crash-neutral” short straddle, and long iron butterfly. The results from two portfolios are compared: a “benchmark” portfolio using standard SPX options that expire the following month and a weekly portfolio using SPXW options that expire at the end of the weekly holding period. The short strangle strategy with weekly options consistently outperforms the other strategies with both standard and weekly options, even after accounting for transaction costs. This finding suggests that short-dated out-of-the-money options can be useful in improving the risk-return characteristics of an option writing strategy. In an effort to improve the performance of the short straddle strategy, this chapter introduces an extremely short holding period portfolio, by stitching together three weekly option expirations into one week. Although the straddle still underperforms relative to the short strangle, the performance of the short straddle is improved by entering the market 15 minutes before the close and by using the extremely short holding period portfolios.

The aim of this diploma thesis is to analyze and implement selected option pricing models using statistical software. The first chapter introduces theoretical basics of options as financial instruments ideal for hedging and speculation. The second chapter constitutes the core part of this thesis since it unveils theoretical concepts of risk-neutral pricing and at the same time analyze some basic, as well as highly sophisticated option pricing models. In addition, each model is accompanied by a practical example of their effective implementation. The final chapter characterize the most widely used option trading strategies and defines the ideal expected market development linked to each strategy.

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.