What is the VIX index and how is it calculated?
Level 1 - Zero to Options Hero - History, a bit on methodology, and why we care.
If you read financial press such as the Wall Street Journal or watch CNBC, you may have heard of something called the VIX index, commonly referred to as a ‘Fear Index.’ These commentators may have mentioned that the VIX has something to do with options prices on US equities. To get a clearer picture of what the VIX index is exactly, read on!
In 1993, the Chicago Board Options Exchange (CBOE) decided to launch a broad index of US option volatilities. They commissioned Professor Robert E. Whaley to develop the formula, which consists of the weighted average of the implied volatilities of eight options that had strikes close to ‘at-the-money’ (ATM) and had maturities close to 30 calendar days from the calculation date. These were options on the CBOE S&P 100 Index (ticker OEX). For the mathematically inclined, more details on the weighted average calculation method can be found in this paper from the Fall 1993 issue of the Journal of Derivatives.
In 2003, the CBOE decided to revamp the methodology and also changed the underlying asset for the VIX Index from the S&P 100 to the S&P 500 Index (ticker SPX). Instead of focusing on options with strikes close to ‘at-the-money’ (ATM), the new methodology takes a weighted average of a wider range of out-of-the-money puts and out-of-the-money calls. It continues to limit the maturities included as being close to 30 calendar days (the data set is options with 23 < days to expiry < 37 to be precise). In fact, the average includes all strikes in this range where the out-of-the-money puts have a non-zero bid price and the out-of-the-money calls have a non-zero bid price.
Again, for the math whizzes in the audience, the CBOE has a good whitepaper on the VIX which goes into detail on the weighting formulas and a numerical example of how the VIX is calculated given a set of option price data. To simplify though, the two most important points to know about the weighting methodology are:
The weighting used gives a higher weight to options that are closer to ‘at-the-money’, and are weighted by the square of their ‘moneyness.’ In this case, moneyness can be thought of as 1 - (call strike - forward price) for out-of-the-money calls, or 1 - (forward price - put strike) for out-of-the-money puts.
Options that are deemed more liquid (by measuring traded volumes as well as the tightness of bid-offer spreads) are given a higher weighting by a proprietary methodology.
The old methodology on the S&P 100 was renamed the VXO. Due to the fact that options that are further out-of-the-money tend to trade at higher implied volatilities than at-the-money options, one would expect the VIX to be higher than VXO given the fact that the weighted average includes a wider range of options in terms of strikes/moneyness1.
Since the new VIX was introduced in 2003, futures and futures options referencing the index have been introduced, and these ‘volatility derivatives’ have become a deep and thriving market, with dedicated trading teams at Wall Street banks that trade and provide liquidity specifically in the ‘VIX complex.’ Because the US has the deepest capital markets in the world and the S&P 500 is the most important equity index in the US, traders around the world across different asset classes pay attention to trading in the US equity options market, with the VIX being a favorite benchmark2.
I hope this post was helpful, wanted to keep it fairly short and sweet after the previous lengthier posts. Happy to answer any questions in the comments, and until next time!
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Note, this does not take into account the fact that the realized volatility of the S&P 100 may be higher than the S&P 500.
Equity volatility is usually viewed as a good gauge of fear or risk aversion, as investors who can allocate between equities and bonds will tend to sell equities and buy bonds during times of market stress. Also, equity in a company’s capital structure is the riskiest liability and hence has higher levels of volatility and volatility of volatility.