A Tale of Two Indices
A Tale of Two Indices
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DOI：
10.3905/jod.2006.616865
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发表时间：
2004-03
期刊：
影响因子：
--
通讯作者：
P. Carr;Liuren Wu
中科院分区：
文献类型：
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作者：
P. Carr;Liuren Wu
定价期权涉及波动性输入。由于波动率不能直接观察到，而且随时间随机变化，因此波动率风险是大多数期权交易者非常关注的问题。因此，人们对芝加哥期权交易所（CBOE）的波动率指数（VIX）一直有相当大的兴趣就不足为奇了，尽管基于该指数的衍生品交易相对较少。最初的波动率指数是布莱克-斯科尔斯隐含波动率的加权平均值，这使得它（原则上）很好地估计了未来的波动率，但很难用交易证券来复制。原来的波动率指数最近被一个不依赖于模型的新公式所取代。在这篇文章中，Carr和Wu回顾了旧的VIX（现在被称为VXO）和新的VIX，并提出了关于它们行为的各种结果。一个有趣的区别是，新的波动率指数的平方，是对已实现方差很好的对冲。这使得新的波动率指数成为波动性衍生品合约的更好的基准，这些合约目前正由芝加哥期权交易所（CBOE）推出。本文考察了这两个指数作为已实现波动率预测的表现，并展示了波动率指数如何对不确定性减少的信息事件（联邦公开市场委员会会议）做出反应。Carr和Wu还通过直接测量VIX中的风险中性波动率，得出了关于市场波动风险溢价的有趣结果。
Pricing options involves a volatility input. Since volatility is not directly observable and it also varies stochastically over time, volatility risk is a significant concern for most option traders. Not surprisingly, then, there has always been considerable interest in the CBOE's VIX volatility index, although relatively little trading of derivatives based on it. The original VIX was a weighted average of Black-Scholes implied volatilities, which made it (in principle) a good estimator of future volatility, but hard to replicate with traded securities. The original VIX has been recently replaced by a new formula that is not model dependent. In this article, Carr and Wu review the old VIX (now called the VXO) and the new VIX and present a wide variety of results on their behavior. An interesting difference is that the new VIX, squared, is a good hedge for realized variance. This makes the new VIX a better underlier for volatility derivative contracts, which are now being launched into the marketplace by the CBOE. The article examines the performance of the two indices as forecasts of realized volatility, and shows how the VIX responds around an uncertainty diminishing information event, meetings of the Federal Open Market Committee. Carr and Wu also obtain interesting results on the market's volatility risk premium from direct measurement of risk neutral volatility in the VIX.