It’s important to have realistic expectations about the price behavior of the options you trade. So the real question is, how much will the price of an option move if the stock moves $1? That’s where “delta” comes in.
Delta is the amount an option price is expected to move based on a $1 change in the underlying stock.
Calls have positive delta, between 0 and 1. That means if the stock price goes up and no other pricing variables change, the price for the call will go up. Here’s an example. If a call has a delta of .50 and the stock goes up $1, in theory, the price of the call will go up about $.50. If the stock goes down $1, in theory, the price of the call will go down about $.50.
Puts have a negative delta, between 0 and -1. That means if the stock goes up and no other pricing variables change, the price of the option will go down. For example, if a put has a delta of -.50 and the stock goes up $1, in theory, the price of the put will go down $.50. If the stock goes down $1, in theory, the price of the put will go up $.50.
As a general rule, in-the-money will move more than out-of-the-money, and short-term options will react more than longer-term options to the same price change in the stock.
As expiration nears, the delta for in-the-money calls will approach 1, reflecting a one-to-one reaction to price changes in the stock. Delta for out-of the-money calls will approach 0 and won’t react at all to price changes in the stock. That’s because if they are held until expiration, calls will either be exercised and “become stock” or they will expire worthless and become nothing at all.
As expiration approaches, the delta for in-the-money puts will approach -1 and delta for out-of-the-money puts will approach 0. That’s because if puts are held until expiration, the owner will either exercise the options and sell stock or the put will expire worthless.
So far we’ve given you the textbook definition of delta. But here’s another useful way to think about delta: the probability an option will wind up at least $.01 in-the-money at expiration.
Technically, this is not a valid definition because the actual math behind delta is not an advanced probability calculation. However, delta is frequently used synonymously with probability in the options world.
In casual conversation, it is customary to drop the decimal point in the delta figure, as in, “My option has a 60 delta.” Or, “There is a 99 delta I am going to have a beer when I finish writing this page.”
Usually, an at-the-money call option will have a delta of about .50, or “50 delta.” That’s because there should be a 50/50 chance the option winds up in- or out-of-the-money at expiration. Now let’s look at how delta begins to change as an option gets further in- or out-of-the-money.
As an option gets further in-the-money, the probability it will be in-the-money at expiration increases as well. So the option’s delta will increase. As an option gets further out-of-the-money, the probability it will be in-the-money at expiration decreases. So the option’s delta will decrease.
Imagine you own a call option on stock XYZ with a strike price of $50, and 60 days prior to expiration the stock price is exactly $50. Since it’s an at-the-money option, the delta should be about .50. For sake of example, let’s say the option is worth $2. So in theory, if the stock goes up to $51, the option price should go up from $2 to $2.50.
What, then, if the stock continues to go up from $51 to $52? There is now a higher probability that the option will end up in-the-money at expiration. So what will happen to delta? If you said, “Delta will increase,” you’re absolutely correct.
If the stock price goes up from $51 to $52, the option price might go up from $2.50 to $3.10. That’s a $.60 move for a $1 movement in the stock. So delta has increased from .50 to .60 ($3.10 - $2.50 = $.60) as the stock got further in-the-money.
On the other hand, what if the stock drops from $50 to $49? The option price might go down from $2 to $1.50, again reflecting the .50 delta of at-the-money options ($2 - $1.50 = $.50). But if the stock keeps going down to $48, the option might go down from $1.50 to $1.10. So delta in this case would have gone down to .40 ($1.50 - $1.10 = $.40). This decrease in delta reflects the lower probability the option will end up in-the-money at expiration.
Like stock price, time until expiration will affect the probability that options will finish in- or out-of-the-money. That’s because as expiration approaches, the stock will have less time to move above or below the strike price for your option.
Because probabilities are changing as expiration approaches, delta will react differently to changes in the stock price. If calls are in-the-money just prior to expiration, the delta will approach 1 and the option will move penny-for-penny with the stock. In-the-money puts will approach -1 as expiration nears.
If options are out-of-the-money, they will approach 0 more rapidly than they would further out in time and stop reacting altogether to movement in the stock.
Imagine stock XYZ is at $50, with your $50 strike call option only one day from expiration. Again, the delta should be about .50, since there’s theoretically a 50/50 chance of the stock moving in either direction. But what will happen if the stock goes up to $51?
Think about it. If there’s only one day until expiration and the option is one point in-the-money, what’s the probability the option will still be at least $.01 in-the-money by tomorrow? It’s pretty high, right?
Of course it is. So delta will increase accordingly, making a dramatic move from .50 to about .90. Conversely, if stock XYZ drops from $50 to $49 just one day before the option expires, the delta might change from .50 to .10, reflecting the much lower probability that the option will finish in-the-money.
So as expiration approaches, changes in the stock value will cause more dramatic changes in delta, due to increased or decreased probability of finishing in-the-money.
Don’t forget: the “textbook definition” of delta has nothing to do with the probability of options finishing in- or out-of-the-money. Again, delta is simply the amount an option price will move based on a $1 change in the underlying stock.
But looking at delta as the probability an option will finish in-the-money is a pretty nifty way to think about it.
Source: "Options Playbook.com"