Moneyness and Delta

The next observation is the effect of moneyness on the option’s delta.Moneyness describes the degree to which the option is in- or out-of-themoney.As a general rule, options that are in-the-money (ITM) have deltas greater than 0.50. Options that are out-of-the-money (OTM) have deltas less than 0.50. Finally, options that are at-the-money (ATM) have deltas that are about 0.50. The more in-the-money the option is, the closer to 1.00 the delta is.

The more out-of-the-money, the closer the delta is to 0.But ATM options are usually not exactly 0.50. For ATMs, both the call and the put deltas are generally systematically a value other than 0.50.Typically, the call has a higher delta than 0.50 and the put has a lower absolute value than 0.50. Incidentally, the call’s theoretical value is generally greater than the put’s when the options are right at-the-money as well. One reason for this disparity between exactly at-the-money calls and puts is the interest rate.

The more time until expiration, the more effect the interest rate will have, and, therefore, the higher the call’s theoretical and delta will be relative to the put.Effect of Time on Delta:In a close contest, the last few minutes of a football game are often the most exciting—not because the players run faster or knock heads harder but because one strategic element of the game becomes more and more important: time. The team that’s in the lead wants the game clock to run down with no interruption to solidify its position.

The team that’s losing uses its precious time-outs strategically. The more playing time left, the less certain defeat is for the losing team.Although mathematically imprecise, the trader’s definition can help us gain insight into how time affects option deltas. The more time left until an option’s expiration, the less certain it is whether the option will be ITM or OTM at expiration. The deltas of both the ITM and the OTM options reflect that uncertainty.

The more time left in the life of the option, the closer the deltas tend to gravitate to 0.50. A 0.50 delta represents the greatest level of uncertainty—a coin toss. Exhibit 2.3 shows the deltas of a hypothetical equity call with a strike price of 50 at various stock prices with different times until expiration. All other parameters are held constant.As shown in Exhibit 2.3, the more time until expiration, the closer ITMs and OTMs move to 0.50. At expiration, of course, the option is either a 100 delta or a 0 delta; it’s either stock or not.

Effect of Volatility on Delta:The level of volatility affects option deltas as well. We’ll discuss volatility in more detail in future chapters, but it’s important to address it here as it relates to the concept of delta. Exhibit 2.4 shows how changing the volatility percentage (explained further in Chapter 3), as opposed to the time to expiration, affects option deltas. In this table, the delta of a call with 91 days until expiration is studied.

Notice the effect that volatility has on the deltas of this option with the underlying stock at various prices. In this table, at a low volatility with the call deep in- or out-of-the-money, the delta is very large or very small,respectively. At 10 percent volatility with the stock at $58 a share, the delta is 1.00. At that same volatility level with the stock at $42 a share, the delta is 0.But at higher volatility levels, the deltas change.

With the stock at $58, a 45 percent volatility gives the 50-strike call a 0.79 delta—much smaller than it was at the low volatility level. With the stock at $42, a 45-percent volatility returns a 0.30 delta for the call. Generally speaking, ITM option deltas are smaller given a higher volatility assumption, and OTM option deltas are bigger with a higher volatility.

Effect of Stock Price on Delta:An option that is $5 in-the-money on a $20 stock will have a higher delta than an option that is $5 in-the-money on a $200 stock. Proportionately,the former is more in-the-money. Comparing two options that are in-themoney by the same percentage yields similar results.As the stock price changes because the strike price remains stable,the option’s delta will change. This phenomenon is measured by the option’s gamma.