Persistent option volatilities

Options Laboratory requires a volatility estimate to predict the future value of an option. Ordinarily, the program uses the volatility of the underlying stock or index specified in the Environment panel. Let's think about this.

Suppose you buy a call today that is priced below its mathematical fair value; maybe you pay $1.75 when the calculated fair value is $1.85. Having entered this transaction, you look at the payoff graph (profit/loss). You move the projection date slider all the way to the left, so the program is predicting the P/L tomorrow. What will you see?

If the stock price doesn't change between today and tomorrow, the option price might also be virtually unchanged unless it is very near expiration. Yet the options model will forecast an immediate profit tomorrow of ten cents a share or $10.00 per contract, all other things being equal, because it assigns fair value to the option. These mathematical option models do not generate or explain the wide range of implied volatilities you see in the real-world data of a scatter diagram.

Yet there are good reasons why option chains exhibit complex volatility structure. For example, investors might consider the long-term prospects for a company to be poor, so long-term options would trade at a discount. At the same time, short-term uncertainties such as an upcoming earnings report or news affecting the company's industry sector might cause short-term options to be relatively expensive. Such situations are not unusual, and sometimes you can exploit them for an excellent rate of return.

As a position trader you will hold options for days, weeks, or occasionally months. You must therefore consider how volatility relationships might shift while you hold a position, including the possibility that they will not shift. This is something to remember whenever you evaluate a position based on pricing disparities within the option chain. In the simplest case, an option that was advantageously cheap when you bought it, might seem disadvantageously cheap when you want to sell it later to close the position. Because you have to get in, then get out again, persistent mispricing (deviations in the volatility structure) could leave you disappointed when it's time to unwind your strategy. The worst case is, of course, when the stock moves against you. But other things equal, the second-worst eventuality might be that the stock does what you hoped, but your options are worth less than you anticipated at unwind-time.

Options Laboratory includes a specific way to evaluate this eventuality. The program can run all its projections in the usual way, except that each option is valued at its current implied volatility instead of the volatility of the underlying stock. To invoke this method, choose the Miscellaneous | Persistent option volatilities menu item. An indicator appears next to the volatility slider (Environment panel) when persistent volatilities are being used. All subsequent graphical projections and generated strategies are affected while this selection is in effect.

It's important to appreciate that this setting will neutralize most strategies that are based on pricing disparities (structural volatility deviations) within an option chain. By definition, persistent volatility washes out the price disparity advantage your position might have at the outset, because to unwind the strategy you must buy back options you sold or sell options you bought, unless they have expired. The program isn't predicting that will happen; instead, it's showing you what would happen if you assume the current price relationships within your option combination remain in place.

If you force this assumption onto the model, Options Laboratory will reveal the consequences. But you must consider that such relationships to tend to normalize in the normal course of events; a long-term option becomes short-term before it expires; short-term concerns pass or get resolved, because they are short term.

Options Laboratory evaluates the possibility of persistent mispricing in a mathematically consistent way, but remember that as options approach expiration they necessarily converge upon their fair value. Persistent option volatilities are not the best mode for modeling the expected outcome of option strategies, unless you actually expect the disparities to persist! In its standard behavior, the program shows the most advantageous strategies under the assumption that prices converge toward fair value as options approach expiration.

Related topic: Volatility scatter plot