本文以日內資料研究台灣證券交易所於2005年3月1日實施股價升降單位新制後，市場交易因子與股價報酬波動率的變化；延伸討論市場參與者對新訊息之反應，進而評估實施股價升降單位新制之成效。本文首先比較四種常用來衡量報酬波動率的方法，並從中挑選出最穩健的測度方式；接著藉此分析股價日報酬波動率與市場交易因子之間的關係；最後，由於日內股價報酬波動的軌跡呈現U型曲線，為突顯波動較劇烈之時段股價報酬波動率是否亦隨股價升降單位縮小而趨緩，故著眼交易日開盤後一小時及收盤前一小時，再次檢驗上述關係。實證結果支持股價升降單位縮小使實現波動率大幅降低且交易筆數密切影響股價報酬波動率，且不論在日資料與日內資料都呈現相似結論；並發現愈接近開、收盤的時間點，股價報酬波動率降低比例亦愈大，顯示升降單位新制達成政策目的。 / In this study, we address the impact of the tick size reduction on the Taiwan Stock Exchange on March 1, 2005. We propose to investigate the variations of trading activities and return volatility, discuss investors' behaviors to the new information and evaluate the tick size reduction by analyzing intraday data. First, we select the most robust volatility measure for our study from four commonly used ones. Second, we examine the relationship between daily return volatility and trading activities. Eventually, due to the commonly observed U-shaped pattern of intraday return volatility, we re-examine the intraday relation between return volatility and trading activities. Our empirical results based on the robust realized volatility confirm that both daily and intraday return volatility decline significantly after the tick size reduction, and number of trades is a prominent trading factor in explaining realized volatility. More interestingly, we observe that the percentage decrease in realized volatility is most pronounced for trading sessions near the beginning or the ending of each trading day. Overall, our empirical findings support the arguments for tick size reduction intended by policymakers.

本研究主要針對 Breidt et al.(1991) 等多位學者所建構的 Mixed causal-noncausal model,探討其假設與可拆解特性,並仔細討論相關資料模擬估計及預測的方法,最後將其實際應用於隱含波動率指數 (Volatility Index)的估計及預測上。根據本研究的實證結果,我們發現隱含波動率指數確實包含非因果的特性,並可進一步對其拆解及預測。另外 , 我們也以移動窗格的方式觀察係數估計結果的變化,發現 Mixed Causal-Noncausal Model 的確能夠捕捉到泡沫或危機正在生成的過程。 / This paper first focuses on Mixed causal-noncausal model constructed by Breidt et al.(1991) and then conducts empirical research on the CBOE Volatility Index. The assumptions, simulation, estimation and prediction methods of Mixed causal-noncausal model are introduced in great detail. Our empirical results show that the CBOE Volatility Index really contains non-causal parts, such that we can filter this part from the index and then further predict it. Moreover, by employing the rolling window estimation scheme the resulting coefficients of Mixed causal-noncausal model really could detect a bubble or a crisis which is going to happen.

利用系統性風險之系列商品來擴大投資組合之投資集合與避險為近來非常熱門的議題，本文除了將波動率指數納入投資組合之外，並額外加入信用風險指數，藉由各種績效指標來衡量系統性風險指數能為投資組合所帶來的綜合效益。根據效率前緣與績效指標的結果顯示，投資級信用風險指數可以有效提升投資組合的夏普值，但卻不會使投資組合之風險值提升太多。 本文利用向量自我迴歸模型分析信用風險指數與大盤之間的動態關係，同時還利用分量迴歸進一步分析在不同報酬率之下，信用風險指數與大盤之間的關聯性。發現當市場狀況越差時，波動率指數與投資級信用風險指數間的相互影響幅度會越大，且分量迴歸其估計係數在中高分量時，明顯高於最小平方回歸模型。 　　綜合來說，根據本文的實證結果與過去眾多學者所做之研究，系統性風險指數確實可增進投資組合的投資效率，擴大投資組合的夏普值。更重要的是，研究信用風險指數的論文相當稀少，本文可增加此系列商品的文獻。同時也可當作台灣推出信用風險指數來促進市場效率以及作為風險管理之工具時的參考。

本篇論文使用SWARCH模型探討布蘭特原油期貨市場的波動性。SWARCH模型將條件變異設定為可隨時間變動而改變，甚至移轉到不同的區間上。實證結果顯示SWARCH (3,3)模型具有最佳配適度與最準確的預測能力。樣本在不同區間下的平滑機率的估計值有助於補捉資料特性，而且當樣本落在高波動率區間上時會對應著重大事件的發生，如1990年波斯灣戰爭、1997年亞洲金融風暴與2001年的911恐怖攻擊。 / This paper investigates the volatility of the Brent crude oil futures markets using Markov-switching ARCH (SWARCH) model. The SWARCH model allows the conditional disturbances to change as time passes and even to switch in different regimes. The empirical evidence shows that the SWARCH (3,3) model performs the best goodness of fit and the best forecast performance between different fitting models. The estimation of smoothing probabilities of data under different regimes facilitates to capture the characteristics of data, and the high-volatility regime is associated with the extraordinary events, such as the 1990’s Persian Gulf War, the 1997’s Asia Financial Crisis, and the 2001’s 911 terrorist attack.

利用風險值作為投資組合的風險管理工具，必須考慮金融資產報酬率通常具有厚尾、高峰、波動叢聚以及資產間訊息與波動性的變化也會交互影響等現象；因此實證上通常以多變量GARCH模型作為估計投資組合變異數矩陣的方法。然而多變量GARCH模型卻存在有維度上的詛咒，當投資組合包含資產數增加時會加重參數估計上的困難度。另一種估計波動率的方法，稱為實現波動率，能比多變量GARCH模型更簡易地處理投資組合高維度的問題。本文即以實現波動率、BEKK多變量GARCH模型與CCC模型，並以中鋼、台積電、國泰金為研究對象，比較三種方法估計風險值的表現。而實證結果得到利用實現波動率確實適合應用在風險值的估計上，且在表現上有略勝一籌的現象。

台灣期貨交易所於92年1月20日推出到期採實物交割的股票選擇權契約，希望能提供市場更豐富、更多元的避險以及套利機能。然自股票選擇權推出以來，市場成交量並未如預期般蓬勃發展，便失去台灣期貨交易所推出股票選擇權之用意，不能使其充分發揮其多元之避險套利機能。多數人主觀認為，採用現金交割方式的衍生性金融商品容易受到人為操縱。一般而言，研究市場的人為操縱因子多以報酬波動率及到期日效應作為觀察指標，因此商品之交割方式與報酬波動率及到期日效應有一定之關聯。然而近來國外許多相關研究發現，採實物交割與現金交割，對股票選擇權的到期日效應並未產生差異，反而是透過結算制度的設計，可以有效降低人為操縱的機率。本研究旨在研究股票選擇權改採現金交割之可行性分析，研究到期日採現金交割是否就是增加人為操縱機率的主要因素，且到期日效應與到期交割方式是否又有絕對的關係？而根據文獻了解，到期日報酬波動率與受人為操縱之跡象是呈現正向關係。 / 因此本研究對指數期貨在到期日與非到期日時對指數現貨價格以及個股股價報酬波動率的影響程度進行實證分析，以報酬波動率之異常現象判斷是否有所謂到期日效應。 本研究實證結果指出，在台指期貨到期日報酬波動率和摩根台指期貨到期日的報酬波動率實證結果發現所有樣本在台指期貨到期日的報酬波動率都顯著高於摩根台指期貨到期日的報酬波動率。顯示台指期貨結算制度雖為到期日下一交易日開盤前十五分鐘個股成交量加權平均價結算，但並未有效降低異常報酬波動率的發生。根據國外研究結果發現，個股期貨能降低到期日效應之影響。此外，採實物交割與現金交割，對股票選擇權的到期日效應並未產生差異。為了降低到期日效應且提升市場的效率性，建議股票選擇權改為現金交割之外，尚可考慮開放個股期貨的交易。 / Taiwan Futures Exchange launched stock options on January 20, 2003, hoping to provide the market with more hedging and arbitraging opportunities. However, the trading volume does not grow as was expected. The low trading volume does not meet Taiwan Futures Exchange’s goal to provide the market with hedging and arbitraging mechanism. Most people think that derivatives applying cash settlement lead to manipulation. Researchers studying manipulations take the volatility of returns and expiration effects as the factors of their studies. However, some recent studies suggest applying cash settlement or physical settlement does not have much impact on expiration effects, while applying proper settlement system can reduce manipulation. / This research investigated the possibility of stock options applying cash settlement and examined the volatility of returns of stock indexes and stock prices during settlement and non-settlement days to determine if expiration effects exist. In this study, we found the volatilities of returns of all samples during TAIFEX settlement days are significantly higher than the volatilities of returns during SIMEX settlement days. All of our samples have significant higher volatilities of returns during TAIFEX settlement days and SIMEX settlement days except CMO, which does not have significant higher volatility of returns during SIMEX settlement days. Other researches point out the adopting of stock futures reduces the expiration effects. Furthermore, adopting cash settlement or physical settlement does have much impact on expiration effects. To decrease the expiration effect and to increase the effectiveness of the market, this study proposes the adoption of cash settlement and the launching of stock futures.

本篇論文使用馬可夫移轉變異數模型探討台指選擇權之買權的波動性。馬可夫移轉變異數模型將條件變異設定為可隨時間變動而改變，甚至移轉到不同區間上。樣本在不同區間下的平滑機率估計值有助於捕捉資料特性，實證結果顯示當樣本落在高波動率區間上時，會對應著重大事件的發生，例如2004年台灣319槍擊案、2006年全球股災、2008年金融海嘯等。當樣本落在低波動率區間上時，會對應著投資人傾向將台股指數的上漲或下跌視為超漲或超跌，而賦予台指選擇權之買權負的時間價值。 / This paper investigates the volatility of TAIEX Call Options using Markov-switching variance model. The Markov-switching variance model allows the conditional disturbances to change as time passes and even switch between different regimes. The estimation of smoothed probabilities under different regimes facilitates to capture the characteristics of data. The empirical result shows that the high volatility regime is related to extraordinary events, such as 319 shooting incident in 2004, the global stock market crash in 2006, and the Financial Crisis in 2008. When in low volatility regime, investors tend to treat rise or fall in TAIEX as overreactions and give TAIEX Call Options turning points of time values.

本研究旨在探討信用違約交換市場與個股選擇權市場兩者的連動關係。研究發現，對於CDS價差，隱含波動率較歷史波動率有較佳的解釋能力。過去有文獻指出，CDS價差存在很明顯的狀態變換(Regime Switching)行為，故將前述使用的迴歸模型加入馬可夫轉換模型(Markov Switching Models)。結果發現，CDS價差與兩種波動率衡量方法間，無論是在經濟涵義上或統計上皆存在顯著的關係。然而，由於本研究使用的樣本期間裡，CDS價差面臨前所未有的劇烈波動，相較以往的研究結果有所出入，顯示當市場處在波動度過度放大的情形下，隱含波動率與CDS價差的關係將有所改變。接著，採用混合迴歸探討股票市場、選擇權市場與CDS市場的領先落後關係。得到的結果顯示，無論是CDS價差變動、隱含波動率變動或股票報酬率，各自的落後項、其他兩者變動及落後項均對之有顯著的解釋能力。此外，觀察各市場的殘差項如何影響其他市場後續的變化再次證實，CDS和選擇權市場彼此具有解釋能力。最後，從未來實現波動率和波動風險溢酬作為CDS價差解釋變數的迴歸結果可知，未來實現波動率較歷史波動率作為解釋變數來得顯著，可見良好的波動率估計值和CDS價差具有密切的關係。

本文旨在探討具有捕捉交易密集度特性的波動率測度模型是否能幫助投資者改 善其資產配置的決策。因此，本文分別考量了利用兩種不同價格抽樣方式所計算 出來的實現波動率 (realized volatility) 模型： (1) 日曆時間抽樣法 (calendar time sampling scheme) 與 (2) 交易次數時間抽樣法 (transaction time sampling scheme)。相較於另一廣為應用的一般化自我迴歸條件異質變異 (Generalized Autoregressive Conditional Heteroskedasticity) 模型而言，這兩種實現波動率模型的優點除了在於它們可以捕捉日內資產報酬率的動態變化之外，交易次數時間抽樣法更可以另外捕捉市場的交易密集度。因此利用交易次數間抽樣法所計算出的實現波動率相對提供給投資者較多的訊息。本文利用了West, Edison and Cho (1993) 所提出的資產組合期望效用模型衡量三種波動率測度的預測績效：(1) 實現波動率 - 日曆時間抽樣法 (2) 實現波動率 - 交易次數時間抽樣法 (3) 指數型一般化自我迴歸條件異質變異 (Exponential Generalized Autoregressive Conditional Heteroskedasticity)。我們的實證結果發現，只有在投資者風險趨避係數越小的條件下，此三種波動率測度模型兩兩之間才有較大的期望效用差距；另外，有趣的是，當市場存在異常的交易波動現象時，交易次數時間抽樣法下的實現波動率所產生的期望效用值總是不輸給另外兩種波動率測度模型的結果。 / This paper examines whether volatility measures that account for trading intensity would help investors make better decisions in their asset allocation. Specifically, we consider two versions of realized volatility (RV), namely, one (RV-C) constructed by regular calendar time sampling, and the other one (RV-T) constructed by transaction time sampling. Comparing to models in the GARCH family, both of these two RVs can capture intraday variations of asset return dynamics. In particular, the RV-T incorporates intraday trading intensity, and hence provides even more valuable information for investors. With the utility-based approach developed by West, Edison, and Cho (1993), we compare the predictive performance of RV-C, RV-T, and the EGARCH model in terms of utility generated with each of these three volatility measures. Our empirical results show that the three measures differ from each other mostly when investors are less risk-averse. Most interestingly, the time-deformed RV-T weakly dominates the RV-C and the EGARCH model when the markets are extremely volatile.

台灣特殊的兩黨對立政治環境及幾乎每年都會有的固定選舉，使得政治的不確定性深深的影響著國內的投資環境及投資人心態。本研究便是要探討，2002/1/1~2006/1/16 研究期間台灣的投資人在選舉前後的投資行為，是否真如大家所預期的，會受到台灣選舉事件的影響。 本研究首先利用適當的機率密度函數模型及選擇權市場資訊來導出隱含的風險中立密度值。再利用這些風險中立密度值，求出各個選舉事件相對應的機率分配圖形，並透過其機率分配圖形及波動率指數等統計值於投票日前後的變化來觀察某一選舉事件前後投資者的反應。 研究結果發現：1. 選舉事件的發生確實會影響投資者的心理，且投資者會透過選擇權市場有效率的反應預期的未來股價指數分佈情況。2. 越大型、越具爭議且全國性的選舉結果，其選舉期間機率分配圖形及波動率指數具有較高的波動性。3. 一般而言，選舉過後市場不確定因素降低，將使投資者對於股市的預期較為一致和樂觀。而若這個選舉結果使投資者感到意外，因而增加了市場的不確定性，則選後機率分配圖形及波動率指數的改變反而會更為明顯。4. 在此研究下對數常態混合法比傳統的 Black-Scholes 方法產生較低的誤差值，因此就實證的分析上能提供更好的配適。 / This research examines the behavior of investors during election periods from January 1st 2002 to January 6th 2006 in Taiwan. The research includes a few steps. First, we adopted a proper probability density function composed of stock index options data to construct the implied distribution. Then, when changing the whole shape of the risk-neutral implied distribution, the volatility indexes, and the statistics of the implied distribution, we observed investors' response around a specific election event. According to the empirical results, we found that: 1. An election event would influence investors’ behavior, and investors tend to reflect their expectation of future stock index in the option market in an efficient way. 2. The result of a large-scale and more disputed nationwide election will cause a higher fluctuation in both the implied distribution and the volatility index. 3. In general, the factor resulting from investors’ uncertainty of the market is likely to reduce after the election, which makes investors’ relatively unanimous and optimistic expectation of the stock market. However, if this election result surprises investors, their uncertainty of the market will increase, and thus the changes of the implied distribution and the volatility index become quite obvious. 4. The in-sample performance of the lognormal mixtures method employed in the research is considerably better than that of the traditional Black-Scholes model by having a lower root mean squared error.