台指選擇權隱含波動率指標之資訊內涵—新編VIX指標之實證

The Information Content of TAIEX Options Implied Volatility Index—Empirical Study of New VIX

江木偉(Mu-Wei Chiang)

指導教授 ： 李存修

國立臺灣大學/管理學院/財務金融學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00499

摘要

摘要
芝加哥選擇權交易所CBOE於1993年公佈VXO波動率指標(Volatility Index)，用來衡量選擇權交易人對於未來股票市場波動率之預期。尤其在指數出現恐慌性下跌時更能夠清楚表達投資人的恐慌程度，故波動率指標亦被稱為「投資人恐懼指標」。波動率指標具有即時化、標準化及簡單化等特性，故在推出後，很快為投資人所接受並參考。經過多年廣泛的討論與研究，各國亦開始建立屬於自己的波動率指標，並發展其衍生性金融商品。本文介紹了CBOE於1993年以及2003年9月所推出新舊波動率指標(VIX與VXO)，詳細說明整個理論基礎與推導，並且對新舊指標的不同進行實證分析，探討新舊波動率指標與加權指數間的關係與比較，以及可能的應用。本文採用了2002/7/1~2004/3/31期間的日資料，所得之結論歸納如下：
1. 在同時性分析下，兩波動率指標變化量與指數報酬存在負相關與不對稱關係。當指數下跌(上升)時，波動率指標上漲(下跌)，當指數下跌時波動率指標上漲的幅度，大於指數上漲時指標下跌的幅度。
2. VXO指標敏感性以 及對市場未來波動率之預測能力優於VIX 指標，而且VXO具有均數回歸之現象，而VIX則無。
3. 在星期效應與到期日效應下，兩指標對於到期日效應無顯著關係，但星期效應方面，兩者出現不同的結論。
4. 在交易策略上，波動率指標於指數出現下跌可作為良好的反向交易訊號，當波動率指標高於相對高點時，買進指數可獲得正的報酬

因此，就目前選擇權市場發展狀況來看，反而以VXO指標較能夠對台灣股票市場提供較多之資訊以及預測能力。但未來仍可持續對兩指標進行研究與分析，並期待台灣能夠建構屬於自己的波動率指標，推出相關之衍生性商品，以促進國內衍生性商品之完整性。

關鍵字

波動率 ； 波動率指標

並列摘要

In 1993, the Chicago Board Options Exchange (CBOE) introduced the Market Volatility Index (VXO) which measures market expectations of near term volatility conveyed by stock index market. VXO is often referred to as the “investor fear gauge”. VXO provides a real-time, standard and simple estimate of short-term market volatility. It is quickly followed and has been cited in hundreds of investors. Other countries have developed the volatility index for their own markets based option implied volatility as well. This article makes a description of the market volatility indices which were introduced by CBOE in 1993 and 2003/9(VIX and VXO). Besides we compare the empirical study of the different indices and examine the relationship between VIX/VXO and TAIEX.
We focus on the July 1 2002-March 31 2004 time period. The conclusions are as follows：
1. There is a negative and asymmetry relationship between the contemporaneous changes in the stock index and implied volatility indices. The indices are more sensitive to the decrease of the stock index than the increase.
2. The sensitivity and the prediction of short-term market volatility on VXO are better than on VIX. VXO has mean-reverting effect but VIX don’t.
3. There isn’t an obvious expiration effect of VIX and VXO. But the paper shows the different results in intraweek effect.
4. Volatility index could be a useful trading signal when the market dropped. Positive forward looking returns are to be expected for long positions in the stock index triggered by relative high levels of the implied volatility indices.

並列關鍵字

volatility ； volatility index ； VIX ； VXO

參考文獻

1. 盧佳鈺(2003)，”台指選擇權隱含波動率之資訊內涵”

2. John C. Hull，Options, Futures, and Other Derivatives, 5thed, 2003

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4. Brenner M. and D. Galai, “New Financial Instruments for Hedging changes in Volatility”, Financial Analysis’s Journal, July-August 1989,pp.61-65

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