We don't know where the VIX will go at any one time, but where is it possible that it can go? What are the possible mathematical highs and lows for the VIX?

Back in October, 2008, some intraday quoting services were quoting numbers above 100 for the VIX. Those values no longer show up on charts, so they must have been an aberration. That doesn't erase the question this article proposes about possible values for the VIX.

Was it even mathematically possible to have the VIX over 100? another commentator asked when I mentioned it in the Market Monitor that day in October, 2008. A recent "Ask the Institute" question to the CBOE's educational arm posed another question about the possible values for the VIX. The writer had noticed that, on the quoting service the writer used, no VIX values below 10 were visible. Were such values mathematically possible? this questioner asked.

Values below 10 certainly are, the CBOE's "Ask the Institute" expert answered. That expert referred the questioner to historical data for the VIX. VIX data going back to 1990 has been recalculated using the new methodology that was incorporated in 2003. The responder mentioned several recalculated (new methodology) values below 10 found in 1993. Quickly scanning the historical data found at this CBOE-sponsored page, I found some in 2005 and 2006, too. I did not find any over 100, although my charting service was certainly giving me intraday values that high in late October, 2008.

So, how is VIX calculated and what are possible values for the VIX? The VIX was first introduced in 1993, employing a carefully constructed mix of at-the-money OEX options to determine an estimation of the "market's expectation of 30-day volatility." We all know that volatility is one of the inputs into an option's price. With all other inputs such as strike price, price of the underlying, time to expiration and others being static, volatility is rather changeable and can plump up or deflate an option's price. Looking at those prices in a specified way gives an estimate of how volatile the market is predicting prices will be. Starting with OEX options, the number crunchers could determine an estimate for the market's volatility.

The OEX's options had comprised a highly liquid and frequently traded market, but some argued that the SPX options would provide a better estimate for the entire market. The methodology for computing the VIX's value was revised in 2003, with the old methodology then used to compute the VXO.

A 19-page CBOE white paper explains how the specific SPX strikes are chosen, but those 19 pages are rife with calculations that involve such mathematical constructs such as exponential functions and the more pedestrian square root. They're not fun to follow unless one is particularly interested in the mathematics. Comparisons are made of near- and next-term puts and calls, including only those at least a week from expiration that don't have non-zero bids. [For the English majors among you, I understand the awkwardness of that double-negative sentence construction. However, the "non-zero" term is one that the CBOE uses, requiring that awkward sentence structure.] Those are manipulated in various ways to determine a base strike price. Then all the puts below that strike that don't have non-zero bids are chosen until there have been two consecutive ones with zero bids, at which point no further are chosen. All the calls above that base strike price are chosen until two consecutive calls with zero bids are found.

And then the real number crunching begins. You don't want to know about all that, do you? If you do, you can follow all the blissful details found in that 19-page white paper. What all that number crunching turns out is an implied volatility measure "that is lognormal in nature," Michael McCartney, options strategist at Meridian Equity Partners Inc. said in an October, 2008 article for Bloomberg (Kearns, "VIX Exceeds 75 for the First Time in 'Panic' of Global Stocks"). McCartney was quoted as saying, not only that a VIX move over 100 was possible, but also that it wasn't "unfathomable" at the time the article was written.

In fact, CBOE's historical data showed the old VIX, now the VXO, hitting values above 100 every day from October 19, 1987 through October 28, 1987. The highest intraday high during that period was 172.79 on October 20.

What would a VIX of 172.79 tell us if it had occurred the day this article was being roughed out, on October 2? The SPX closed October 2 at 1025.21, so that will be one of the inputs. Let's use the VIX to then figure out an anticipated one-standard deviation move, with one standard deviation measuring where the SPX is predicted to range 68.2 percent of the time over the next month if it had that volatility. A simple formula for calculating a one-standard deviation move would be as follows:

1025.21 x 1.7279 x Square root of (30 days/365.25 days) = +/-507.69.

Although the VIX is usually written in percentage form, it's used in decimal form (1.72) here for the purposes of that calculation. In this instance, the VIX would be expressing the possibility that in 68.2 percent of the cases when it was measuring that hypothetical 172.79 at the time the SPX was at 1025.21, the SPX would range from 517.52 to 1,532.90 over the next 30 days.

That move would certainly throw a hitch in any iron condor trader's month, wouldn't it, although it would be a day trader's dream if only the right direction was chosen. We hope such VIX values never occur, but perhaps the standard-deviation calculation shows that, although we hope the VIX never measures that high, it can indeed do so.