At work, I am sometimes asked this simple but challenging question: “Where does VIX come from?” There is a reason I am asked this – I am our company’s product manager for volatility indices. But I admit that I have struggled to come up with an approachable way to explain the methodology of the CBOE Volatility Index (VIX). I am going to give it shot, though, in this post. Wish me luck.

**An Overview of VIX**

Any good answer should start with a summary. Here is an overview of how VIX is calculated.

The CBOE Volatility Index, which communicates the range of possible outcomes investors expect from the US equity market 30 days from now, is derived from the prices of options based on the S&P 500. Because it always looks 30 days forward, VIX cannot be based on options attached to a single expiration date, as these are hard set. The VIX methodology instead asks that we determine the implied volatility of options of two expiration dates, specifically those of the next two months. We then essentially draw a line between those two volatility figures to estimate the expected volatility for 30 days.

But how do you figure out the volatility implied by the options of the next two expiration dates in the first place? This involves a messy formula, but this can be distilled down into two key steps: selecting the options and then weighting them properly. For the VIX calculation to be robust, the options contracts that have no bidders and sellers need to be weeded out. To do this, we look at the options tied to various strike prices and check whether buyers and sellers are quoting prices for them. If they are, then they are included. But if there are no quotes, then the options contract for that particular strike price are excluded from the calculation. This tends to happen more and more as you look at options based on strike prices further from the S&P 500 index level. When you get to the point that there are no price quotes for two consecutive strike prices, you stop looking. Those options that already qualified will be used to calculate VIX.

After you select your options, you have to weight them in a way that makes sense. The VIX methodology assigns more weight to options associated with low strike prices than to those with high prices. This is done for a specific reason – to counteract the fact that options with high strike prices tend to be more sensitive to changes in expected volatility. By assigning more weight to options with less sensitivity to changes in implied volatility, you can create a set of options that is more uniform in its capacity to contribute to the final VIX level. The sensitivity of far out of the money call options will not have an outsized impact on VIX, as they would have had without this adjustment.

Now you have the summary. In future posts, I will fill in the details and go through the key methodology points again, but also provide some graphs and illustrations to make them clearer.

Coming posts:

- How VIX is able to constantly look 30 days ahead.
- How options are screened to be included in the VIX calculation.
- How options are weighted.

## Where VIX Comes From

At work, I am sometimes asked this simple but challenging question: “Where does VIX come from?” There is a reason I am asked this – I am our company’s product manager for volatility indices. But I admit that I have struggled to come up with an approachable way to explain the methodology of the CBOE Volatility Index (VIX). I am going to give it shot, though, in this post. Wish me luck.

An Overview of VIXAny good answer should start with a summary. Here is an overview of how VIX is calculated.

The CBOE Volatility Index, which communicates the range of possible outcomes investors expect from the US equity market 30 days from now, is derived from the prices of options based on the S&P 500. Because it always looks 30 days forward, VIX cannot be based on options attached to a single expiration date, as these are hard set. The VIX methodology instead asks that we determine the implied volatility of options of two expiration dates, specifically those of the next two months. We then essentially draw a line between those two volatility figures to estimate the expected volatility for 30 days.

But how do you figure out the volatility implied by the options of the next two expiration dates in the first place? This involves a messy formula, but this can be distilled down into two key steps: selecting the options and then weighting them properly. For the VIX calculation to be robust, the options contracts that have no bidders and sellers need to be weeded out. To do this, we look at the options tied to various strike prices and check whether buyers and sellers are quoting prices for them. If they are, then they are included. But if there are no quotes, then the options contract for that particular strike price are excluded from the calculation. This tends to happen more and more as you look at options based on strike prices further from the S&P 500 index level. When you get to the point that there are no price quotes for two consecutive strike prices, you stop looking. Those options that already qualified will be used to calculate VIX.

After you select your options, you have to weight them in a way that makes sense. The VIX methodology assigns more weight to options associated with low strike prices than to those with high prices. This is done for a specific reason – to counteract the fact that options with high strike prices tend to be more sensitive to changes in expected volatility. By assigning more weight to options with less sensitivity to changes in implied volatility, you can create a set of options that is more uniform in its capacity to contribute to the final VIX level. The sensitivity of far out of the money call options will not have an outsized impact on VIX, as they would have had without this adjustment.

Now you have the summary. In future posts, I will fill in the details and go through the key methodology points again, but also provide some graphs and illustrations to make them clearer.

Coming posts:

Education, VIX, Volatility

education, VIX, Volatility