The CBOE will soon begin trading options on its Volatility Index ($VIX). We consider this a major new derivatives product. It provides the first opportunity to trade options on volatility in a listed marketplace. (They have traded over-the-counter, institutionally, for some time.)

This product will be useful for a wide range of applications for stock and option traders. Wherever $VIX futures have been applicable, these options will be as well. Furthermore, option strategies on $VIX can now be constructed -- with their own unique sets of risk and reward parameters. As we will discuss in this article, however, $VIX does not behave like a stock, so some adjustments will have to be made to account for that fact in the modeling of $VIX option prices.

The Basics

These are cash-based index options, similar to $SPX or $OEX or $DJX options or any other index option. The underlying contract is the $VIX cash index itself, not the $VIX futures contract that trades on the CBOE Futures Exchange (CFE).

Some of the nomenclature and specifications of the futures contract are going to be used for these new, listed $VIX options. $VXB is an index that is $VIX times 10. This is to be the underlying index for these new $VIX options. And, in fact, the options will have a base ticker symbol of VXB. Striking prices will be at least 2-1/2 points apart, so this might be a typical array of strikes at a given time:

• $VIX: 14.24
• $VXB: 142.40
• Strikes available for VXB options:
  • 135
  • 137.5
  • 140
  • 142.5
  • 145, etc.

The options will be traded and quoted as $100 per point, as are all listed options, so, if a VXB December 150 call is selling for 9, it will cost $900 for one contract.

Also, similar to the futures, these options will have their last trading day on Tuesday prior to the third Friday of the expiration month. The settlement day for these options is an “a.m.” (morning) settlement on the Wednesday prior to the third Friday of the expiration month. These are exactly the same days that the futures expire and settle.

Continuing this similarity, the actual settlement value of the cash-based options will be based on a “special opening quotation (SOQ)” derived from the opening trades (or, if no trade, the average opening bid and offer) of the options used to calculate the $VIX Index itself.

• These options will trade until 4:15 p.m. Eastern Time each day, as do $SPX and $OEX options.
  
• At any one time, four series will be listed -- the same four expirations as the $VIX futures, in fact: The two near-term months, plus the next two months in the February cycle (i.e., February, May, August, November).
  

Pricing Considerations

To price $VIX options, we first need an estimate of the volatility of $VIX (i.e., the volatility of volatility). While that may sound a bit strange, it’s exactly what needs to be measured to estimate the price of an option on volatility. We looked at the historical volatility of $VIX in a time frame from 1993 to the present -- which encompasses the end of the previous bull market, plus the ensuing bear market, and, now, the rally since March 2003.

In other words, various market conditions are present. Moreover, the actual price of $VIX varied greatly over that time. It rose to 40 or so in the bear market and then collapsed to nearly 10 in the last year. Once again, a great variance in the price of $VIX is encompassed in the data just presented here. However, the one thing that stands out is that -- bull market or bear, high-priced $VIX or low-priced -- the historical volatility of $VIX remains amazingly constant -- averaging approximately 80%.

For a moment, let’s assume that the Black-Scholes model can be used to value these options (it sometimes can’t as will be shown shortly). Using an 80% volatility estimate, VXB options would be theoretically priced as follows:

Example: Assume $VIX is at 14 and, thus, VXB is at 140. The following option prices on VXB might theoretically exist. Furthermore assume that these are being priced one month before May expiration.

The problem with using the Black-Scholes model for valuing $VIX options is that $VIX does not conform to a log-normal distribution. For example, we know that there is a “floor” and a “ceiling” on $VIX. These limits are not fixed. ($VIX could theoretically trade down to 5, say, although it has never happened; or, $VIX could trade up to 100, although that has never happened either.)

Restated: When $VIX is near 10, there is a much greater chance that it will rise than that it will fall. Or, if it’s near its all-time highs in the 40s, there is a much greater chance that it will fall than that it will rise. (Note: If you recall $VIX shooting up to 60 in 2002, your memory isn't faulty -- $VIX is not computed the same way now as it was then; what we now call $VXO had those higher readings.) Neither of those descriptions fits a log-normal distribution. Moreover, it appears that $VIX conforms to different distributions, depending on where it’s trading at the time.

By inference, if we throw out the “extreme” points, $VIX does, more or less, conform to a log-normal distribution. Hence, despite the problems near the extremes, we can say that, most of the time, $VIX movements seem to be log-normally distributed. This is helpful, for it means that, if $VIX is not near the extremes, perhaps the Black-Scholes model can indeed be used to value $VIX (actually, VXB) options.

However, when $VIX is near the extremes, if one is using a Black-Scholes model to value the options, he or she will see a steep skew. When $VIX is low (say, below 15), out-of-the-money calls will seem expensive with respect to out-of-the-money puts. Conversely, when $VIX is very high, out-of-the-money puts will be trading with a higher implied volatility than out-of-the-money calls.

If one understands these limitations, I believe the Black-Scholes model can be used for valuing these new $VIX options. In actual practice, we will see how these valuations play out.