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.
EXHIBIT 2.3 Estimated delta of 50-strike call—impact of time.