The volatility index is a set of implied volatilities of a whole series of call and put options for a particular stock index. As a rule, a volatility index includes implied volatility of a stock index, but more complex volatility indices are calculated based on the implied volatility of individual shares included in the index.

The most popular volatility index is VIX, which is traded on the Chicago Options Exchange (CBOE).

**VIX volatility index**

VIX is a derivative instrument that is traded on the CBOE through futures. It is the most popular volatility index in the world, as its value reflects the market view on the expected 30-day volatility of the S&P 500 index.

VIX based on S&P 500 options, which we are seeing today, has been trading since 2004. Prior to that, the VIX was based on the S&P 100 index. The VIX based on the S&P 100 is still available, called VXO, and is also traded on CBOE.

**Why is VIX popular?**

VIX is regarded by many investors and economists as an indicator of fear, as the VIX index can be used to determine the level of market anxiety among market participants regarding the current market situation. As we know, options are a form of insurance, so when option prices are high due to increased volatility, there is great uncertainty in the market.

Let us consider the chart below.

As can be seen from the chart, VIX usually has a negative correlation with the S&P 500 stock market index. When there is panic in the market, investors sell risk assets (i.e. stocks) and the volatility increases. The increase in volatility is mainly due to the fact that prices fall faster than rise.

This does not mean that VIX is an accurate indicator of market direction. However, as can be seen from the chart, with a significant drop in the S&P 500 index, the volatility rises sharply. As investors are more uncertain about their future prospects when prices fall, compared to the period of rising stock prices, the cost of insurance (i.e. options) increases when stocks fall.

When the market collapses, investors become nervous and this panic immediately affects the prices of risky assets, which fall sharply, resulting in increased volatility.

**VIX calculation**

If the reader is interested in the exact calculation of the formula used for VIX, you can download the file from the CBOE website.

The VIX volatility index is calculated based out of the money call and put options that expire in the next month and month after this. The values are weighted according to a specific algorithm to obtain the final volatility number.

**What does the volatility index VIX mean?**

The VIX value represents the expected volatility (market-defined) of the S&P 500 index in annual terms. It is the price volatility of the S&P 500 Index that can be expected over the next 30 days with a probability of approximately 68% (one standard deviation).

**Example **

Let's assume that VIX is 24. This means that the market expects the S&P 500 index to fluctuate with a volatility of 24% (or 1.5% per day) over the next 30 days. This does not mean that the S&P index will in fact change 24% over the next 30 days, but the S&P 500 price is likely to fluctuate on average 1.5% per day (in either direction).

1.5% is the daily equivalent of 24% annual volatility. Given that VIX represents the expected annual volatility over the next 30 days, it is necessary to divide 24% by the square root of 252.

Note that this VIX value is based on normal distribution and represents one standard deviation (68% of observations):

68% of observations - 1 standard deviation

95% of observations - 2 standard deviations

99.7% of observations - 3 standard deviations

Given the above, with a VIX value of 24%, we can expect that with 99.7% confidence the S&P 500 will trade in the range of plus minus 20.64% for the next 30 days (24% * 3 * root(30/365)).

**VIX and VXO Indices**

When the CBOE first introduced the VIX volatility index, it was based on the S&P 100 stock index (OEX). The indicator averaged 8 out of the money call and put options for the S&P 100 and used the Black Scholes pricing model to calculate VIX values.

However, in 2003, CBOE changed the underlying asset for VIX to S&P 500 and also changed the calculation method used.

The volatility index for S&P 100 is now called VXO and the volatility index for S&P 500 is now called VIX.

VXO is still widely used, primarily because it has a longer history and in-depth dynamics analysis.

**Options and Futures on VIX**

Futures on VIX were first traded on the CBOE in 2004 and are one of the (if not the most) actively traded contracts on the exchange. Options for the VIX index began trading 2 years later in 2006. The code for VIX options is VRO.

**Option Expiration and futures on VIX**

The last trading day for VIX options is Tuesday after the third Friday of the month.