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    Title: 國際隱含波動度指數的緩長記憶、共動性與共同因子之研究
    Other Titles: Long Memory, Co-Movement, and Common Factors of International Implied Volatility Indices
    Authors: 郭維裕
    Contributors: 國際經營與貿易學系
    Keywords: 緩長記憶;共動性;共同因子
    long memory;co-movement;common factors
    Date: 2012
    Issue Date: 2014-09-02 09:07:08 (UTC+8)
    Abstract: 自從芝加哥選擇權交易所（Chicago Board Options Exchange, CBOE）於1993年推出CBOE波動度指數（VIX）以來，該指數便廣為市場與學術界所接受，成為短期市場波動度期望值的基準指標。之後，更成為許多波動度衍生性商品（volatility derivatives）的標的指數，使得投資人有機會投機未來市場波動度的漲跌與針對其投資風險進行更直接的避險。由此可見VIX的重要性。 VIX是由八個價平之S&P100指數（代碼為OEX）買權和賣權合約的隱含波動度加權平均而得的。當時之所以利用S&P100指數作為標的指數，乃因為OEX選擇權為交易最活絡，流動性最佳的選擇權合約。隨著市場的變化，以S&P500指數為標的指數之SPX選擇權合約的交易量不知為何竟然大幅超越OEX選擇權的交易量，導致CBOE決定於2003年9月22日推出以SPX選擇權隱含波動度為計算基礎的新版VIX。不僅如此，CBOE也將價外的選擇權合約納入VIX的計算過程，其主要的考量為價外選擇權合約含有關於市場內投資組合保險需求的資訊，而且納入更多的選擇權合約有助於降低VIX對於特定選擇權合約價格的敏感度，也因此免於被人為操縱的風險。 有鑑於CBOE VIX的成功，全球各個交易所無不積極跟進紛紛推出屬於自己的隱含波動度指數。例如，德國交易所（Deutsche Borse）於1994年推出VDAX指數；法國巴黎選擇權交易所（French Marche des Options Negociables de Paris, MONEP）於1997年推出VX1與VX6兩個指數；NYSE Euronext於2008年六月推出以FTSE100指數為標的指數的隱含波動度指數。 本計畫為三年期的研究計畫。在計畫的第一年中，我們將檢定全球的隱含波動度指數是否具有緩長記憶（long memory）的特性。這是個重要的研究課題。雖然相關文獻屢屢發現條件式波動度（conditional volatility）以及已實現波動度（realized volatility）呈現相當高程度的自我相關性，並經過檢定後確認其緩長記憶特性，關於隱含波動度指數之緩長記憶的研究卻仍付之闕如。一旦迴歸式中納入VIX指數為自變數且忽略其緩長記憶的特性，所估得的係數必定是偏誤的，因此檢驗隱含波動度指數是否具備緩長記憶是個重要的財務研究課題。在確定緩長記憶特性的存在後，我們打算進一步研究其來源，包括結構性變化（structure breaks）、總和效果（aggregation effect）和隨機平均數（time-varying mean）等。 在第二年的計畫中，我們擬對所蒐集到的八個全球隱含波動度指數進行共動性（co-movement）研究。自從雷曼兄弟於2008年9月倒閉而引發百年難得一見的次級房貸金融危機以來，實務界與學術界皆投入大量的資源研究並預測全球金融市場間的共動性。但金融市場間的共動性並非完全由經濟基本面所引起的，投資人的恐慌情緒對危機的規模與擴散程度應有一定的貢獻度。基於這樣的論點，我們決定研究全球隱含波動度指數間的共動性。未來可能採用的模型包括Bae, Karolyi, and Stulz (2003)的ordered multinomial logistic regression model以及Jiang and Tian (2010)的long-memory vector regression model。本研究的結果有助於大家更進一步瞭解全球金融市場的互動關係與來源。 在確認了全球隱含波動度指數的緩長記憶特性與其之間的共動性後，我們將於第三年的計畫中進行導致緊密共動性之共同因子（common factors）的確認與檢定。由於緩長記憶的關係，傳統的共同因子檢定法，如主成分分析法（principal component analysis）與因素分析法（factor analysis），皆不適用。我們因而決定採用Ray and Tsay (1995)所發展的模型來決定共同因子的個數並加以抽取。最後我們將所估計得的共同因子和一些相關總體經濟變數進行相關性分析，以其確認共同因子的經濟意涵。
    In 1993 Chicago Board Options Exchange (CBOE) introduced a market volatility index, termed VIX, that soon became a popular benchmark of expected short-term market volatility. It has also been dubbed the “investor fear gauge.” The higher the VIX, the greater the fear. The original VIX is calculated as a weighted average of implied volatilities estimated from the prices of eight at-the-money OEX options. The implied volatilities are estimated based on the Black-Scholes-Merton options pricing model. The main reason that the OEX options are used to compute the VIX is that these options contracts were most actively traded ones at that time. For unknown reasons, the trading volume of SPX options outpaced that of the OEX options significantly and became the most actively traded options contracts. In contrast, by 2008, the average daily trading volume in OEX options was less than half its volume of 16 years earlier. In addition, the index option market has come to be dominated by portfolio insurer, who routinely purchase out-of-the-money and at-the-money index puts for insurance purposes. These two fundamental changes in the option market structure drove the CBOE to move toward SPX implied volatility measures. On September 22, 2003, the CBOE introduced a new version of VIX calculated based on the prices of SPX options. These options include not only at-the-money options but also out-of-the-money options, especially out-of-the-money put options that are expected to contain important information regarding the demands for portfolio insurance. Including more option series also makes the VIX less sensitive to any single option price, and therefore less susceptible to manipulation. Moreover, the new VIX is computed as a model-free implied volatility for which a theoretical options pricing model is no longer necessary. In view of the tremendous success of the VIX, the exchanges around the world began to develop their own volatility indices. In particular, Deutsche Borse introduced the VDAX in 1994; French Marche des Options Negociables de Paris (MONEP) introduced two implied volatility indices in 1997, VX1 and VX6. More recently, the NYSE Euronext has launched the FTSE 100 Volatility Index based on the UK benchmark equity index. The main purpose of this three-year research project is to study the long memory property of these global implied volatility indices, their co-movement, and their common factors. These research topics are very important since volatility has long been a key variable in the portfolio construction and risk management decisions. Understanding the properties and dynamics of volatility indices will greatly facilitate such decision making. In the first year of this project, we attempt to establish the evidence that implied volatility indices follow a long-memory process. Although the evidence on the long-memory property of the conditional variance, realized volatility, and other forms of volatility measures has been well documented in the literature, there exist relatively few studies on the long-memory property of VIXs. Our study intends to fill this gap. We also look into the sources of long-memory, including the aggregation effect, the level shift or structural break effect, and the time-varying mean effect. The results from this first-year study will provide more valuable information about the underlying stochastic processes for the VIXs that are important to the pricing models of volatility derivatives. Since the collapse of Lehman Brother in the wake of the subprime crisis in 2008, the co-movement among global financial markets has attracted a lot of academic interest. The literature mostly focuses on the co-movement among stock market indices. Our study in the second year takes another perspective by examining the co-movement among global implied volatility indices. In other words, we would like to investigate the common fear of global investors beyond the explanation of economic fundamental variables. We plan to employ the multinomial logistic regression model or the long-memory vector regression model to identify the co-movement among the global VIXs and their potential causality. In the last year of the project, we try to identify the common factors underlying the co-movement and their origins. Due to the long-memory property, the traditional principal component analysis (PCA) and factor analysis (FA) cannot be used to extract common factors. Instead, we decide to utilize the method proposed by Ray and Tsay (1995) to identity common persistent components of global VIXs. We then perform further correlation analysis between the common factors and various macroeconomic variables to search for the origins of these common factors and therefore the underlying causes of the co-movement among the global implied volatility indices.
    Relation: 行政院國家科學委員會
    計畫編號NSC101-2410-H004-063
    Data Type: report
    Appears in Collections:[Department of International Business] NSC Projects

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