# What does the VIX formula measure and how does it work?

I have read the CBOE's white paper on the VIX and a lot of other things, but I need to honestly say, I don't really get it, or I am missing something important.

In semi-layman's terms, is the VIX simply the a measurement of the volume of protective options bought?

That is, individual contract volatility increases when the option has been bid up by buyers due to desirability. One contract alone only marginally increases the overall market volatility, but if all contracts were bid up, then the entire VIX would be recalculated (on the fly) to reflect the higher value of protective options as a speculative/hedge solution.

Do I understand this correctly, or do I really need to put more time into understanding that formula which comprises the VIX?

VIX is a measure of implied volatility, specifically, model-free implied volatility, a concept originally developed by Demeterfi et. al. at Goldman Sachs in the 1990s. One of my recent questions, How to extrapolate implied volatility for out of the money options?, addressed some aspects of MFIV, and the papers mentioned in the question and answers will give you some more background on the concept. Also check out this JPMorgan research piece.

The VIX is the square root of the market-implied variance swap rate, calculated based on the exchange-traded options portfolio typically used to hedge an OTC variance swap. It has nothing to do with options volume.

As to the effect of individual contracts (strikes) on the VIX, that depends on how far out of the money they are. The CBOE's calculation uses exclusively OTM options. If the implied volatility of an option near the money changes, it will have a much greater effect than a far OTM option. All prices of all options are changing constantly in line with changes in the index, but the VIX calculation takes that into account in a very clever way (i.e., without resorting to the Black-Scholes model or its assumptions).

Also, (implied) volatility does not necessarily increase if an option's price increases, if the underlying has also been moving. Further, since VIX is based on the mid quoted price, no actual trading needs to take place for the VIX to change.

• I guess I need to learn more about variance swap to understand this. I also just read the VIX's wikipedia page which has things broken down better than the white paper, but there is more understanding necessary. Where did you learn this, I feel that someone somewhere is explaining this better than these articles? – CQM Nov 2 '11 at 14:49
• @CQM Just read a lot of papers and eventually you will get it. Some of the more recent papers also have plenty of references to the older foundational work. Also check out this JPMorgan piece. – Tal Fishman Nov 2 '11 at 14:59
• @TalFishman I would add that the VIX measure the fear (uncertainty) of the market. – Ricky Bobby Nov 2 '11 at 17:15
• Implied volatility? actually Vix is a measure of the so called integrated volatility that is a different thing. – Hard Core Jan 28 '18 at 23:36

Simple explanation of VIX formula is that it is a square root of weighted sum of out of the money SPX options. If options are more expensive (implying that market is paying more for insurance from a major move) VIX will be higher, if options are cheap (implying that the market does not think that there will be a lot of movement in the SPX) VIX will be lower.

The weighting formula has a particular meaning - roughly corresponding to the area under the put and call curves.

I tried to provide intuitive explanation of VIX formula in http://onlyvix.blogspot.com/2011/09/intuitive-understanding-of-vix-formula.html