This question can be answered using the online Option Sensitivities Java applet or the Option Sensitivities subject of Option Tutor. Online click on option sensitivities or you can select it either from the main Screen in Option Tutor:

Here is what you can do using the default data or data that you enter directly. You can plot the variable listed under Y-Axis as a function of what is listed under X-Axis. When the subject first starts, it shows you the put option value as a function of the price of the underlying asset. The various parameters corresponding to the Black-Scholes model are listed as follows:

You can view a put or a call. The default parameters are set to provide a plot of the predicted option value against changes in the underlying asset value. For the current put example this appears as follows:

That is, as the underlying falls the put option increases in value. However in this exercise we are interested in the behavior of an option's "Delta." That is, the predicted sensitivity of the option's price with respect to a small change in the underlying asset price. For example, if one option has a delta of 0.50 then this predicts that given a $1 change in the underlying asset price the change in the option's price is $0.50. If you have one contract that controls 100 shares of the underlying then you would multiply the option number by 100 ($1 change in the underlying stock price would result in a predicted $50 change in the value of 1 contract). Clearly, if you are trading options delta is an important number for managing your exposure to underlying asset price risk.

To start solving the exercise, select Delta for the Y-Axis, leave the X-Axis on Value, select Call and click on Plot, as shown below:

You will get the following display:

This is how the delta of the call option depends on the underlying asset price. Note that the underlying asset ranges in price from 25 to 100 in the display, while the strike price is 50. The X-axis is the price of the underlying asset and the Y-axis the delta of 1 option. One thing you may notice from the from the graph is that as the stock price declines from 50 (so the call moves out of the money), the delta falls quite quickly until it levels off. On the other hand, as the call moves into the money, the delta rises less quickly.

To examine the effect of "moneyness" of the option, click "Strike Price" as shown here and then plot for the default strike price equal to $50. Now the Y-axis is call delta and the X-axis is the strike price. The plot is for the case where the underlying asset price is $50. You can see that when the underlying asset price is $50 (i.e., at-the-money) that the call delta increases as strike price reduces (i.e., the call option goes into the money because we are holding the underlying asset price fixed at $50). Similarly, call delta decreases as the strike price increases (i.e., the call option goes out of the money relative to holding the underlying asset price fixed at $50).

To interpret this from a trading perspective you can see that as the option gets more in the money, the delta becomes a steeper function of the underlying asset price. This means that if you held an option that is currently out of the money call, then the call delta would react more sharply to increases in the price of the underlying asset than if you held an in the money call.

If you are trading options based upon a view of price increases or decreases in the underlying then understanding how delta behaves is important if you want to get the most price action for your trade.