In contrast to the implied volatility extracted from an option pricing model, the VIX (volatility index) uses a model-free formula to derive expected volatility directly from the prices of a weighted strip of S&P 500 index (SPX) options over a wide range of strike prices, which incorporates information from the volatility skew. This VIX calculation supplies a script for replicating the VIX squared with a static portfolio of SPX options. This critical fact lays the foundation for tradable products based on the VIX, facilitating hedging and arbitrage of VIX derivatives. The Chicago Board Options Exchange (CBOE) launched VIX futures on March 26, 2004 and VIX options on February 24, 2006. These were the first of an entire family of volatility products traded in exchanges. VIX futures (VIX options) are the futures (options) contracts on forward 30-day implied volatility. The current prices of both VIX futures and VIX options consequently reflect the market’s expectation of the VIX level at expiration. As a result of expectation VIX futures prices can swing from a premium to a discount to spot VIX, but converge to spot VIX at expiration. Hence, the current VIX futures price, rather than the spot VIX itself, is the underlying price of VIX options. Although the construction of VIX squared is model-free, the simple formula for the fair value of VIX futures given in the CBOE website is model-dependent. It involves the variance of the VIX futures price from current time to its expiry.
After a spike in the level of the VIX, VIX options often appears to be trading at a discount. The reasons for this behavior are because VIX options are european style options and also because the VIX is a mean-reverting index. Firstly, because VIX options are european style options, they can only be exercised on expiration date, and so their valuation is based on the expected, or forward, value of the VIX on expiration date, rather than the current, or "spot" VIX value. Secondly, the VIX is a mean-reverting index. Often, spikes in the VIX do not last and usually drop back to moderate levels soon after. So, unless the expiration date is very near, the market will take into account the mean-reverting nature of the VIX when estimating the forward VIX. Hence, VIX calls seem heavily discounted whenever the VIX spikes.