VIX

隐含波动率 (Implied Volatility,IV)

VIX Volatility Products

In math lingo, the VIX index is expressed in percentage terms as an annualized one standard deviation move of returns on the S&P 500 index.

The VIX index calculation use SPX option prices. The prices investors are willing to pay for options typically reflect how much the underlying asset, in this case, the S&P 500, is expected to move over a given time frame.

The key word here is expected, which means the VIX index is a forward-looking indicator of market volatility.

Between 1990 and 2020, the closing range on the VIX index has been between 9.14 and 82.69.

Typically, the VIX index has an inverse relationship to the S&P 500 Index.

Cboe lists tradable VIX futures and options.

VIX Index

The VIX Index is a calculation designed to produce a measure of constant, 30-day expected volatility of the U.S. stock market, derived from real-time, mid-quote prices of S&P 500® Index (SPX℠) call and put options.

On a global basis, it is one of the most recognized measures of volatility -- widely reported by financial media and closely followed by a variety of market participants as a daily market indicator.

Volatility Index® Methodology:Cboe Volatility Index®

芝加哥期权交易所(Cboe) 波动率指数（简称VIX），用于预测美国股市在不久的将来可能高于和低于其当前水平的波动范围。具体而言，VIX 衡量标普 500®指数 (SPX)未来 30 天的隐含波动率。当隐含波动率处于高水平时，VIX数值会相应地提高，可能值范围亦较为宽阔。当隐含波动率处于低水平时，则 VIX数值会相应降低，可能值范围亦较为狭窄。

由于股市最不稳定时VIX会升至最高水平，所以媒体倾向将 VIX称为恐慌指标。这名称正好反映VIX如何衡量市场情绪，尤其是市场的担忧虑情绪。

Cboe波动率指数通常称为“VIX指数”——是对预期波动率的最新市场估计，通过使用实时标准普尔500指数（SPX）期权买入/卖出报价进行计算。只有周五到期的SPX期权用于计算VIX指数。（VIX指数的计算时间为美国东部时间凌晨2:15至8:15，以及美国东部时间上午8:30至下午3:15。将截至周五到期时间大于23天且少于37天的SPX期权进行加权计算VIX指数，然后产生标准普尔500指数预期波动性的30天不变指标）

VIX通过对众多看跌和看涨期权的价格求平均加权来衡量隐含波动率。当投资者买卖期权时，不论是看跌期权还是看涨期权，他们建立的仓位、愿意支付的价格以及选择的行使价格，都反映了他们认为相关指数水平未来的波动幅度与速度。事实上，波动率就是：波动的速度与幅度。在计算 VIX 时使用期权价格而非股价的原因是，期权价格反映买卖双方对波动率的预期。这就是隐含波动率中隐含的含义。

根据年化波动率推导某段时间的波动率：

$${\sigma }_t={\sigma }_{\text{annual}}\times \sqrt{\frac{t}{T}}$$

示例：年化波动率 15%，求 30 天波动率

$${\sigma }_{30}=15\mathrm{\%}\times \sqrt{\frac{30}{365}}\approx 15\mathrm{\%}\times 0.2867\approx 4.3\mathrm{\%}$$

以当前 S&P 500 指数为 5000 为例：

$$\text{上下波动范围}=5000\times {\sigma }_{30}=5000\times 4.3\mathrm{\%}=\pm 215$$

即：指数波动区间为

$$[5000-215,5000+215]=[4785,5215]$$

VIX 背后的隐含波动率平方公式：

$${\sigma }^2=\frac{2}{T}\sum _i\frac{\mathrm{\Delta }{K}_i}{K_i^2}{e}^{rT}Q(K_i)-\frac{1}{T}{(\frac{F}{K_0}-1)}^2$$

最终取平方根并乘以 100 得到 VIX：

$$\text{VIX}=100\times \sqrt{{\sigma }^2}$$

VIX与市场情绪

波动率指数(VIX)是什么? 它衡量的是什么？

时间与波动率

VIX报告按年化率予以记录。由于波动率在统计学上被界定为变化幅度的平方根，VIX 的按月隐含波动率可以一年分为 12 个月作为准则，将其水平除以 12 的平方根计算。

VIX Futures

Introduced in 2004 on Cboe Futures Exchange (CFE), VIX futures provide market participants with the ability to trade a liquid volatility product based on the VIX Index methodology.

VIX futures reflect the market's estimate of the value of the VIX Index on various expiration dates in the future. Monthly and weekly expirations are available and trade nearly 24 hours a day, five days a week.

VIX futures provide market participants with a variety of opportunities to implement their view using volatility trading strategies, including risk management, alpha generation and portfolio diversification.

VIX Options

Following the successful launch of VIX futures, Cboe Options Exchange introduced VIX options in 2006, providing market participants with another tool to manage volatility.

VIX options have monthly and weekly expirations and trade during U.S. regular trading hours and a limited global trading hours session (2:00 a.m. to 8:25 a.m. CT).

VIX options enable market participants to hedge portfolio volatility risk distinct from market price risk and trade based on their view of the future direction or movement of volatility.

Options on VIX Futures

Options on Cboe Volatility Index® (VIX® Index) Futures offer more choices to express directional views and manage equity market volatility exposure. These new, innovative contracts provide optionality into front month VIX futures, are physically settled, and trade on Cboe Futures Exchange, LLC.

Mini VIX Futures

At 1/10th the size of the standard VIX futures contract, Mini VIX futures allow market participants to trade or hedge equity market volatility or execute volatility strategies with a smaller notional size contract.

• VIX 的 29 年发展历程
• 波动率指数的由来与编制方法
• 「恐慌指数」VIX是什么？如何在大跌时交易？