The Constant Elasticity of Volatility
Steve Lentz

Have you noticed that option prices sometimes do not move with the price of the underlying asset in the way you would expect? That is usually due to changes in implied volatility (IV). In equities IV typically increases when the price of the underlying stock or index falls and decreases when equity prices rise – an inverse relationship. This relationship does not necessarily hold for commodity futures options, where it is not unusual to see a positive relationship between IV and the price of the underlying.
 
What does that mean for traders for equity options? It means that if you are long the call options of a stock or index you may not profit as you would expect when the price moves up, since declining IV works as a drag on the option price. On the other hand, long put options might increase in value more than you expect when the underlying price falls, as the increase in IV adds more to your profits.
 
This phenomenon is called the Constant Elasticity of Volatility, or CEV, and OptionVue 6 includes this effect in all the “what-if” modeling throughout the program. For example, the Graphic Analysis screen factors in the effects of changes in time, the price of the underlying, dividends, interest rates, commissions, slippage, and the CEV factor on every position. The results received from TradeFinder include the CEV effect also. 
 
To get a better understanding of the inverse relationship between price and IV look at the Volatility Chart below for the S&P 100 index (Symbol: OEX) with the Price Chart superimposed on it. The important relationship to observe is how IV (the blue line) moves in relation to the price of the OEX.
 

OEX Volty Chart

 
Take a look the price versus volatility on 0/11/02 in particular (where the wand is located). Here IV spiked to a six year high as the price of the OEX neared a six year low, a dramatic illustration, but you can see this same inverse relationship throughout the chart. This strength of this relationship is recorded for every underlying asset in the Background Database (BDB) by OptionVue Systems through a proprietary analysis that assigns a “CEV factor” to every asset. 
 
The CEV factor is then used for modeling purposes throughout the program to ensure the most accurate projections possible. The illustration below shows the Settings screen under Model Volatility for the S&P 100 with its current CEV factor. 
 

Model Volatility Box

 
A CEV factor of .80 is one of the lowest numbers you will encounter for any asset. The fact that is less than 1.00 indicates an inverse relationship between IV and the price of the OEX. A CEV factor greater than 1.00 would indicate a positive relationship.
 
But what is the significance of CEV on this position, and does it really make that much of a difference? The answer is easily found by comparing a modeled option position with the CEV factored in with one that does not. 
 
The figure below shows the Graphic Analysis of a position that is long 5 of the April 590 call options in the OEX. These are the at-the-money call options, with 39 days to expiration. Notice that if the OEX increase 30 points to 620 in 20 days (halfway to expiration) the analysis shows you will have a profit of $11,650. 
 

OEX Position Analysis 1

 
Now take a look at the figure below, which shows a Graphic Analysis of the same position without CEV factored into the modeling. Notice that the profit level shown at a price of 620 is now $12,650, a much higher figure than that shown in the previous analysis. Without the effect of CEV included, a trader would be led to expect a much more optimistic outcome than what reality has in store for them.
 

OEX Position Analysis 2

 
Clearly the CEV factor can have a significant impact on the projected profitability of an option position. The larger the price move, and the shorter period it occurs in, the more pronounced the CEV effect will be. OptionVue 6 includes this effect by default, although advanced users can override this setting or even input their own estimate of CEV. But including it by default ensures that the program is already set up to make the most accurate projections and recommendations as possible throughout the program.