# Why is the VIX computed that way?

The VIX as a clear definition as defined in this paper I am interested to know why they came up with this formula.

I smell some reasonably complicated explanation here so any pointer to a paper would be fine with me. Thanks

• You should look at this question on Quora: quora.com/… Demeterfi et al. (1999) showed that the variance can be replicated by taking positions sensitive to the price, S, and the log price, ln(S), of the underlying asset. In this sense, recalling that a log contract can be replicated by taking long positions on call and put options, the CBOE computes VIX using out-of-the-money and at-the-money SP500 call and put options. – Julian Lopez Baasch Oct 18 '13 at 20:42
• Thqnks for the link I'll go for it. Not sure why I got this downvote though – statquant Oct 19 '13 at 7:38
• Oh... looks like some dude downvoted all my questions... nice ! – statquant Oct 19 '13 at 7:53

In that white paper itself they quote where it came from: “More than you ever wanted to know about volatility swaps” by Kresimir Demeterfi, Emanuel Derman, Michael Kamal and Joseph Zou, Goldman Sachs Quantitative Strategies Research Notes, March 1999. This is a classic article which you should definitely read if you are trading volatility. While there might be a clearer explanation somewhere, this is the original and quite comprehensive work.

For some intuitive ideas behind this, also see this post in OnlyVIX blog.

The calculation of VIX itself is taking this Volatility Swaps idea and approximating it with discrete set of options (sum instead of integral), throwing away some ridiculously OTM options (prices of which are not representative at all). Since there is not always an expiration 30 days ahead, they approximate this point by interpolating (or extrapolating). These are merely some technical things they have to do to apply the formula.

• Ok... I did not think is was usefull as VIX came in 2006 and the paper is dated 1999. Thanks for the pointers – statquant Oct 19 '13 at 7:51