Think of it like predicting the outcome of a football game. If your team is tied 14-14 at half time, you'd probably be 50% sure about whose going to win. That's like an at-the-money option and exactly why its delta is 0.50. The market is 50% sure it will be in-the-money since the stock price is exactly equal to the strike.

 

However, if your team is in the lead 14-7 at half time, you may have some confidence that they will win. There is, however, a lot of time remaining on the clock so you can't be 100% sure. You may raise your confidence level to 60%. That's what the market does when an option is "in the lead" or is in-the-money. Because it's in-the-money, it is a much safer bet to assume it will stay that way rather than betting it will fall out-of-the-money. Just like the football game, if the score is 14-7 at half time, you're slightly more confident that the leading team will, in fact, win.

 

What happens to your confidence if the score is still 14-7 but there are only 10 seconds on the clock? If your team is in possession, you're 100% certain. If the other team has the ball, you'd probably be 99% certain. The point is that once your team is in the lead, your confidence grows as time is reduced. That's exactly why an option's delta behaves the way that it does. It's a measure of confidence about the option expiring in-the-money.

 

Now think about this: if the option's market is, for example, 90% certain (0.90 delta) that an option will expire in-the-money, what is a $1 move worth in the stock? According to fair value, it's worth 90-cents and that's why the option will move 90 cents for the next dollar move in the stock.

Hope this helps!

Bill