國內選擇權市場波動率指數(VIX)之建構與分析

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張富達(Fu-Ta Chang) 查詢紙本館藏

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財務金融學系在職專班

論文名稱

國內選擇權市場波動率指數(VIX)之建構與分析
(The Construction and Analysis of the Volatility Index of Taiwan’s Option Market)

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摘要(中)

基於國內選擇權市場的蓬勃發展、情緒指標的研究日益受到重視以及國內選擇權市場分析工具的缺乏，本文介紹國外選擇權波動率指數的編製方法，諸如美國的VIX、法國的VX1, VX6 以及德國的VDAX。其主要的目的在建構國內選擇權的波動率指數 (VIX)以及VIX對國內加權指數的分析。
研究方法為在Black-Scholes 模型下，運用CBOE的方法以編製國內的VIX，並以各種不同參數的選用下共編製12種VIX。同時運用統計分析及檢定那一個VIX最能解釋台灣加權指數的狀況，以找出最適的VIX。並研究此VIX與加權指數在各月及各季的相關性和顯著性，和加權指數在上升及下降趨勢時VIX的反應，以及分析影響VIX的因子及建構迴歸模型。
研究結果顯示，VIX與加權指數呈中度負相關，是一個有用的反向指標；且發現對10月、11月及12月呈相關係數為-0.9以上的高度負相關，並可解釋加權指數的變異高達90%左右。另從本文的研究可以發現，當月VIX的中位數與第一四分位數同時向下逼近5%分位數時，為加權指數高點所在；而當月VIX的中位數與第三四分位數向上逼近95%分位數時為加權指數低點所在。
至於有那些因素影響VIX，在假設因子的迴歸分析與經過最佳自變數選擇後，研究結果顯示影響VIX的因素有，來自加權指數的有日成交量、指數位置、與前一日的報酬、波段漲跌；來自台指期貨的有與加權指數的正逆價差、日高低振幅；來自期間的有四季；以及來自VIX本身與前一日的報酬；此迴歸模型可以解釋VIX 40.04%的變異。

摘要(英)

In light of the booming volume of the option trade, the growing study on the sentiment indicator and the lack of analysis method for the domestic option market, this thesis aims to introduce the construction of volatility index (VIX) applied to the major markets worldwide. The reference index, such as the VIX for US, the VX1 and VX6 for the French and the VDAX for the German market will be discusses in depth in order to build up the domestic VIX and its further analysis.
By adopting the Black-Scholes model together with the method by CBOE (Chicago Board Option Exchange), 12 sets of VIX are constituted with its respective parameters. The employment of statistic test helps to identify which VIX would apply to Taiwan’s weighted index. Furthermore, the emphasis will be placed upon the correlation and significance level between the VIX and the weighted index with different time interval. By doing so, the VIX could be clearly depicted responding to the weighed index, upward or downward together with factors contributing to it. And the regression model would thus be conducted.
The result shows that VIX and the weighted index are in moderate correlated negatively，which constitutes an efficient contrary indicator. Moreover, the study proves that in Oct, Nov and Dec, the correlation coefficient is above –0.9, a figure that would apply to approximately 90% of the variance of the weighted index. When the median and the first quartile of the month reach the 5% significance level, the critical value is what’s at the high for the weighted index. Whereas when the median and the third quartile of the month reach the 95% significance level, the critical value is where the averaged low weighted index hit.
With regard to what may contribute the VIX, the indication from the regression analysis for hypothesis factors and the best independent variance choice by SAS. The following factors are related to the weighted index, that is the daily trading volume, the independent index figure, the reward from the previous day and the advance or decline of wave band. What concerns the Taiwan Index Future are the spread and daily amplitude. And what concerns the period is season, whereas the reward from the day and the day previous are VIX-linked. The regression model perfectly demonstrate the VIX’s variance of 40.04%.

關鍵字(中)

★ 波動率
★ 選擇權
★ 波動率指數
★ 情緒指標

關鍵字(英)

★ volatility
★ VIX
★ sentiment indicator

論文目次

圖次目錄.....................................III
表次目錄......................................IV
第一章緒論....................................1
第一節研究動機與目的.......................1
第二節研究架構.............................5
第三節研究內容.............................7
第二章文獻回顧................................8
第一節隱含波動率...........................8
第二節行為財務學及情緒指標................10
第三章編製波動率指數.........................15
第一節美國CBOE VIX 編製方法介紹...........15
第二節法國 VX1, VX6及德國 VDAX編製方法介紹.22
第三節國內選擇權VIX的編製..................24
第四章國內選擇權VIX 統計分析..................28
第一節各種VIX的統計資料描述及分析..........28
第二節最適VIX的統計資料描述及分析..........36
第三節 VIX在加權指數多種狀況下的相關........47
第四節影響VIX的因子........................55
第五章結論....................................63
參考文獻.......................................66
附錄A：不同參數選用下的12種VIX.................69
附錄B：CBOE VIX 期貨合約......................80

參考文獻

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指導教授

張傳章(Chuang-Chang Chang)

審核日期

2004-7-13

推文