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.

本文考量波動度不對稱效果(Volatility Asymmetric Effect)與均數回歸(Mean Reverting)兩個特性，並考量台股市場特性，嘗試建立一個適合台灣市場的波動度交易策略。利用GARCH(1,1)波動度與VIX指標建構第一個交易訊號，並建立當日沖銷部位。以賺取日內行情為出發點，利用時間序列模型捕捉波動度的高估或低估且搭配純跨式(Pure Straddle)策略或根據Delta調整後的跨式(Adjusted Straddle)策略。第二個交易訊號則是利用市場敏感指標，觀察外資與自營商在交易部位與未平倉部位的變化，找出對於波動度的影響。建立由選擇權與期貨組成的Delta-Hedged部位，藉由觀察市場上主力籌碼的變化，動態調整部位契約，尋找波段之間的獲利機會。 實証部分以期交所公布的每日交易資料與VIX日資料，利用2007至2008兩年的歷史資料，估計參數與測試交易訊號。樣本外期間為2009年1月開始至3月結束共55個交易日。考量交易成本後，兩個不同型態的交易訊號，仍然能夠藉由本研究的策略，獲得正的報酬。本文認為台灣為一個淺碟市場，過度反應資訊的特性，讓波動度策略出現獲利的機會。藉由這個波動度交易系統的研究，除了讓資金豐沛的機構投資人使用外，也能夠讓一般投資大眾建立自己的波動度交易策略 關鍵字:波動度交易，選擇權交易策略，GARCH(1,1)，VIX，市場情緒指標 / Trying to apply a preliminary study of volatility trading strategies in Taiwan derivative market is the topic of this dissertation. Capturing the market movement or even the dynamic of underlying asset is a Pandora’s Box for academic researchers and industry participants. Mean-reverting and asymmetrical effects are the two special characteristics of volatility for us to design our trading system according to the previous empirical studies. In our study, we use different type of volatility signal to capture the trading opportunities. Use the new released information form TAIFEX including VIX and Position Structure of Institutional Traders to design our signal. We apply the idea to use pure option position and delta-hedged position as our trading tools in this volatility trading system and look for the opportunities between realized volatility and implied volatility. An over-reaction may rises the uncertainty and also lead the market volatility change coherently. We use history data from 2007 to 2008 test our trading signal and parameters. The out sample period is from 2009 January to 2009 March which has 55 trading days to simulate our strategies. In the end, we see a positive result in both trading signals which earns positive return after considering the trading cost. Key words: Volatility Trading, Market Sentiment Indices, Option Strategies, VIX, GARCH(1,1)

本論文提出線性規劃的方法以還原隱藏於選擇權市場價格中的風險中立機率測度，並利用該機率測度計算選擇權的合理價格。模型中假設選擇權對應同一標的資產與到期日，資產價格於到期日的狀態為離散點且個數有限，當市場不具任何套利機會時，以極小化市場價格與合理價格之離差總和作為挑選風險中立機率測度的準則。最後，以臺指選擇權(TXO)的交易資料做為實證對象。實證中發現，加入平滑限制式與離差權重之線性規劃模型在評價歐式選擇權合理價格的效能最為優異。 / The thesis proposes a liner programming to recover the risk-neutral probability distribution of an underlying asset price from its associated market option prices, and we evaluate the fair prices of options via the resulting risk-neutral probability distribution. Assume that we face a series of European options with different exercise prices on the same maturity and underlying asset in this linear programming model. The criterion of choosing a risk-neutral probability distribution is minimizing the sum of total deviations subject to requiring that the fair prices of options are consistent with observed market option prices. Finally, we take the trading data of TXO as an empirical study. The empirical study indicates that the model with smooth constraints and weighted deviations has the best performance in pricing the rational price of European options.

世界上成功之交易所大多可以提供附廣度以及深度的商品，滿足各種投資人。若交易所提供證券、金融期貨、商品期貨、選擇權等商品以供投資人選擇，這就是附有廣度的交易所，具備完整性的市場，此外流動性也是交易所各類商品是否得以成功上市之關鍵因素之一，高度流動性可以降低交易成本，提高投資人繼續參與市場之意願，進而帶動商品後續的成長動力，這就是附有深度的市場。兼具廣度與深度性質之交易所，不僅僅能滿足各類投資人之需求，更能幫助經濟之發展。 臺灣期貨交易所（Taiwan Futures Exchange；TAIFEX）現行交易商品包括臺股期貨、電子期貨、金融期貨、小型臺指期貨、臺灣50指數期貨等等，這些商品是以金融期貨（Financial futures）為主，為了建構市場的完整性，增加市場的廣度，是有必要推出商品期貨（Commodity futures），不僅可滿足更多投資大眾之需求、促進商品現貨之避險套利活動，並且有助於市場效率。在眾多商品期貨中挑選貴重金屬期貨當成先發在目前此一環境是相當重要的，因為天然資源最大的先天限制在於蘊藏量在短期下是有限量的，再加上近幾年總體經濟面臨通膨壓力下，與通膨高度相關的黃金投資將再度成為市場上的寵兒。在這樣背景之下臺灣期貨交易所擬在2006年3月27日推出第一檔商品期貨－黃金期貨是很受肯定的，因此本論文將以黃金期貨（GDF）為例子，進一步闡釋如何為商品期貨市場建立相關的提供流動性之制度與計畫，使得市場的深度得以透過此等制度而成功建造。 在國外交易所剛推出商品期貨或者金融期貨都會面臨到流動性不足之現象，但是前者標的商品並不若後者來的具備齊一性，使商品期貨流動性的問題較金融期貨來更受重視。因此國外交易所在推出商品期貨常會順勢引入造市者制度，透過造市者在市場建立之初創造流動性，使買賣價差縮小，將有助於交易者的交易成本降低，另外遠期現貨價格也將透過高流動性逐漸反映在期貨的價格上，避險者也會有信心進場避險，如此一個成功的期貨商品才算是真正成功推出。所以造市者制度對於新期貨商品之推出是很關鍵的，尤其是對商品期貨更是如此，因此臺灣期貨交易所在推出黃金期貨時，為了樹立成功的商品期貨典範並且吸引更多投資者進入商品期貨市場交易，實有建立屬於期貨市場造市者制度之必要。 / Successful exchanges could provide both breadth and depth of financial products to fulfill investors’needs. An exchange filled with breadth indicates that it could provide many different kinds of financial products to investors. As for depth, also called liquidity, it means the ease of entering or exiting a market. Generally speaking, liquidity plays an important part and is also one of the successful keys in financial markets. Because high liquidity could reduce the transaction cost and enhance investors’interests towards the markets, it could bring the growth engine of financial products. As a result, an exchange filled with breadth and depth could not only fulfill investors’needs, but also help the development of the economy. As for Taiwan Futures Exchange (TAIFEX), until 27th March, 2006, it has already provided TAIEX futures, Taiwan 50 futures, and so on. Among these products, it is easy to tell that TAIFEX only provides financial futures but no commodity futures. Therefore, to improve the completeness and efficiency of the market, TAIFEX considers providing commodity futures so that all kinds of investors, such as speculators, hedgers, and arbitrager, could be effectively satisfied. As for the underlying assets of this commodity futures, since the price of gold has been getting higher and higher, and financial products associated with gold have also become more important, TAIFEX decided to launch gold futures on 27th March, 2006. Based on the previous background, this thesis would concentrate on illustrating how liquidity of commodity futures could be improved by executing the market maker program of gold futures. Usually, when exchanges launched new futures, most of them had difficulties in the illiquidity. Moreover, the underlying assets of commodity futures are not as identical as that of financial futures. Therefore, exchanges need to make more efforts in creating the liquidity of commodity futures. Market maker program is a good solution to this problem. Through actively trading of the market makers, it could increase market’s liquidity, reduce bid-ask spread, and further decrease the transaction cost. As a result, in order to provide successful commodity futures and attract more investors entering the markets, it is necessary for TAIFEX to adopt and design their own market maker program. To sum up, if TAIEX set a good example through gold futures, it will pave the light way for the other kinds of commodity futures.

【第一篇論文中文摘要】 本文檢測公司負債合約中的利差是否可被最終的違約後償還率所解釋。透過1962年至2007年間在美國金融市場上發行但最後卻違約的負債合約資料來進行實證，發現違約後償還率的確有反映在發行時的利差上，且此關聯性會隨著美國開放商業銀行進行證券承銷業務後隨之更加顯著。我們並且進一步發現此償還率的資訊能更加有效反映原因與發行公司的資訊不對稱程度降低有關。此外，我們同時又發現此負債合約中的利差與違約後償還率的關聯性對於公司治理較差、以及非投資等級的發行公司會更為顯著。最後，我們的實證結果在考量內生問題、潛在可能遺漏解釋變數、以及其他模型設定後，仍同樣具有堅實性。 【第二篇論文中文摘要】 本文使用臺指選擇權的日內資料來探討選擇權提前交易期間是否具有資訊內涵與價格發現的功能。就作者所知，我們是第一篇透過選擇權資料探討提前交易期間資訊內涵的研究。首先，我們分別透過價、量、與高階動差三類資訊變數指標來衡量提前交易期間的資訊內涵。實證結果顯示：選擇權提前交易期間不只能有效反映隔夜資訊 (公開資訊)，且具有預測當日現貨指數開盤後5分鐘內股價指數移動的能力 (反應私有資訊)，說明提前交易期間的確具有資訊內涵與價格發現的功能。此外，我們進一步發現價平選擇權包含最強的資訊內涵，此應與投資人尋求交易流動性最高的價平選擇權來迅速實現其利潤以反映其資訊有關。最後，本研究亦發現前一日海外市場 (美國) 投資人情緒傳染效果的強度會影響提前交易期間選擇權的資訊內涵，而前一日是否交易 (週末效果與假日效果)則不會影響此資訊內涵。 / 【第一篇論文英文摘要】 We investigate whether the spread of corporate debt contacts can be explained by their ultimate recovery rates. Using the actual realized recovery rates of defaulted debt instruments issued in the U.S. from 1962 to 2007, we find that recovery rate is reflected in the spread at issuance, and that this relationship has become more significant since commercial banks were allowed to underwrite corporate securities. Our further investigation indicates that the enhanced informativeness of recovery rate can be attributed to the lowering of information asymmetry of individual firms. Besides, the relation between the spread at issuance and the recovery rate is stronger for weak corporate governance and non-investment grade issuers. Our conclusions are found to be robust to endogeneity issues, potentially omitted variables and alternative model specifications. 【第二篇論文英文摘要】 This study uses tick-by-tick data to examine the information content and price discovery of TAIEX option trading during the pre-opening period. To the best of our knowledge, this is the first study that focuses on the options market. We construct three groups of information variables to measure the information content of the pre-opening period, including the price, volume, and high moment information variables. We find that option trading during the pre-opening period not only can reflect the overnight information (public information) but also predict the 5-minute intraday returns after the opening of spot market (private information), showing the information content and price discovery of option trading during the pre-opening period. We also find that at-the-money options contain the strongest richness of information content, which may result from its highest liquidity. Finally, we also find that the empirical results would be stronger depending on the intensity of investor sentiment from overseas (U.S. market) of last day but not the length of hours without trading (weekend and holiday effect).