If you've been reading these pages long, you have a rough idea of what delta might be. It measures how much an option's price is expected to change with each point change in the underlying. The experienced option trader familiar with the Greeks of option pricing will know that delta tells you something else, something rather neat. It provides you with an estimate of how likely it will be that this option will be in the money at expiration.
Theoretically, then, a call option with a delta of 0.12 or 12, if your quote provider automatically multiplies the 100 multiplier, has a 12 percent likelihood of being at or in the money at expiration. This makes sense intuitively if you think about options that are currently at the money. Those options have deltas of about 0.50 in the case of calls and -0.50 in the case of puts. That means that there's about a 50 percent chance that they'll be at or in the money at expiration.
Is there another way to test whether this theoretical probability is correct? Sure there is or I wouldn't be writing this article. We can go straight to standard deviations. As I type this on January 30, 2010, the RUT MAR 660 call had a delta of 0.12. The RUT had closed the previous day at 602.04. The implied volatility of a near-the-money 600 MAR call was 23.34 percent.
To calculate a standard deviation for the RUT until expiration, we need the implied volatility of the ATM call in the month of that expiration. The ATM call's IV in the month being examined is the one typically used in standard deviation calculations, not the implied volatility of the option that's purchased. That's because the ATM call's implied volatility usually provides the best estimate of expected price volatility in the underlying. It was, at the time, 47 days to MAR expiration. For the RUT to move from 602.04 to 660 would require a rally of 57.96 points. These are all inputs that would be included in a computation of the probability of the RUT's price being at 660 at expiration.
An online search turns up sites that will calculate the probability that an underlying will be at a certain price on a certain date if the implied volatility is at a certain level, using standard deviation calculations. One such calculator, the Hoadley calculator, returned the probability as 12.41 percent, slightly higher than the 12 percent that the option price indicated. That particular calculator was calculating the probability that price would be above 660, not at 660, which might account for some of the difference, too, as could some rounding differences in the quote service providing the implied volatility. An implied volatility of 0.1241 would have been rounded down to 0.12, for example. Still, we can see that the delta value also provides us with a quick-and-dirty estimate of how likely it is that the underlying's price will be at that strike at expiration.
This information can be used in many ways. For example, if an option trader is looking at an option trade, thinking that they'll buy a speculative put or call to hang onto into expiration, a low delta can alert that trader that the market's best forward estimate is that the option will not be at or in the money at expiration.
A trader who has purchased an OEX debit spread for $5.00 (buying a long call or put and selling a further-out call or put) needs an underlying to be $5.00 beyond the strike of the long call or put at expiration. That OEX trader can look at the delta of the call or put at the level needed to estimate the likelihood of price being at that point at expiration. Or, alternately, an online calculator can be used. If the calculation returns only a 23 percent likelihood of the price being $5.00 beyond the strike of the long call or put, perhaps a different option strategy might be best.
Iron condor traders, however, want to sell options with low deltas, as this represents a lower likelihood that the sold options will be in the money at expiration. Iron condor traders and others selling options need to be aware of one reality, however: the probability that price will be at or above a certain level at expiration is lower than the probability that the price will be at that level any time between the time the trade is entered and expiration. In fact, our RUT MAR 660 option had a 25.34 percent theoretical possibility of being above 660 some time between January 30 and MAR expiration. That's still low, but it's far higher than its theoretical 12 percent probability of being at or above that level at expiration.
Whether you're all that interested in the Greeks or not, you're likely interested in a rough-and-ready calculation of how likely your option is to be in the money at expiration. Delta can provide that rough-and-ready estimation. Online calculators can help you figure out the probabilities for other dates.