Level: Advanced

Overview

The VIX (Volatility Index) is a benchmark of implied volatility for thirty days in the future. It was created by the Chicago Board Options Exchange, or CBOE, in 1993. This article will focus on what the VIX is, how it is calculated, and how it can be applied. This is a concise version of CBOE’s white paper report for the VIX, which is quite a long and mathematical read.

What is the VIX?

The VIX is a measure of implied volatility in the market. Implied volatility is simply the expectation for how much an underlying asset will move within one standard deviation.

The VIX originally was calculated based on the S&P 100 index at-the-money calls. However, it was revised a decade after it was introduced so that it was based on a wide range of strike prices for options on the S&P 500. We will be focusing on the newer calculation method.

VIX Formula

This is the formula for calculating the VIX:

• σ is the VIX/100. That means that the VIX is σ * 100. Notice that the formula gives you the square of σ.
• T is how much time there is until options expiration. More on this below.
• ∑ means summation (addition many times, don’t be scared). The i underneath means that i is a variable within the summation.
• F is the forward index level. This is basically what people are predicting the S&P 500 index will be at in the future, based on options prices.
• Ko is the first strike below the forward index level.
• Ki is also a strike price, but of the ith out-of-the-money option. Remember the summation? For each value of i, Ki will change too. Ki is the strike of a call option if Ki is greater than Ko, a put option if Ki is less than Ko, and if they are equal it is the strike of both the put and call.
• ∆Ki is just the interval or difference between strike prices around Ki.
• R is the risk-free interest rate until expiration. This is not determined by options but rather by bonds. This is for the U.S. Treasury Bill maturing closest to the options contract.
• Q(Ki) is the quote or the price of the Ki option. It is the average of the bid and the ask.

That’s all! The raw equation is quite simple, but some of the values used in the calculation require more in-depth analysis.

Keep in mind that the VIX measure expectations for 30 days, or a month, in the future. The time to expiration is calculated as follows:

T = {M_(Current day) + M_(Settlement day) + M_(Other days)} / Minutes in a year

• M_(Current day) is how many minutes are left until midnight today.
• M_(Settlement day) is how many minutes are from midnight on the settlement day to 8:30 AM for standard options, and till 3 PM for weekly options.
• M_(Other days) is how many minutes are in the days between today and expiration

As we can see, T is just a fraction of the year representing how long it is until settlement of a contract.

VIX Calculation Process

This information is a simplified version of CBOE’s white paper on VIX calculation. The steps CBOE uses to calculate the VIX figure are outlined here:

1. Select the options to be used in the VIX calculation. For EACH month:
   1. Take the the strike price at which the difference between prices for calls and puts is the smallest (price is the average of bid and ask). Do this for both the near term (or current term) expiration and the next term expiration.
   2. F = Strike Price from above + e^(RT) x (Call Price – Put Price). Recall that this is the forward index level, or F. You will get F1 for the near term and F2 for the next term options.
   3. Take Ko as the strike price below F. You will get two of these for each value of F: one for the near term, one for the next.
   4. Start iterating through the put options with strike prices less than Ko, and go down from there. Skip ones with bid prices of zero. If two consecutive strikes have bids of zero, stop. Select all of the options iterated through here for use later.
   5. Start iterating through the call options with strike prices greater than Ko, and go up from there. Skip ones with bid prices of zero. If two consecutive strikes have bids of zero, stop. Select all of the options iterated through here for use later.
   6. Select both the call and put with strike Ko. This will be treated as a single contract in the formula, with the prices for the call and put averaged.
2. Calculate volatility or the σ values using the above formula for both near-term and next-term options (these are the contracts and values calculated in the outer step 1). The weighting of any contract to the VIX value is proportional to ΔK (the difference between strikes) and the price of the option. It is inversely proportional (negatively affected by) to the square of the option’s strike price.
3. Calculate the 30-day weighted average of σ1 squared and σ2 squared. Square root that value and multiply it by 100 to get the VIX (look back at the VIX Formula section).

How the VIX is Used

The VIX itself is just a number used to gauge the amount of “fear” in the market. The nature of the VIX’s usefulness arises from the formula above, and is essentially provided by looking at how much people are paying for options (protection) from a market move. In terms of raw values, values above 32 are times of fear, and options pricing is generally more conducive toward premium sellers. On the other hand, values below 16 reflect a calmer market in which premium buyers get a better deal.

Over the years, the VIX has evolved from being just a number. Futures on the VIX index itself trade also, and multiple ETFs are plays on where the VIX will move.

Summary

The VIX is a powerful tool that uses a simple formula to calculate the amount of “fear” in the market. Although the raw calculation process is a bit dreary, understanding it will allow you to realize from where the VIX derives its meaningfulness. Of course, computers now track the index and its value is widely accessible on the web. Hopefully, this article has provided you insight on the inner workings of the CBOE Volatility Index.