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The option's delta is the rate of change of the price of the option with respect to its underlying security's price. The delta of an option ranges in value from 0 to 1 for calls (0 to -1 for puts) and reflects the increase or decrease in the price of the option in response to a 1 point movement of the underlying asset price.

Far out-of-the-money options have delta values close to 0 while deep in-the-money options have deltas that are close to 1.

As the delta can change even with very tiny movements of the underlying stock price, it may be more practical to know the up delta and down delta values. For instance, the price of a call option with delta of 0.5 may increase by 0.6 point on a 1 point increase in the underlying stock price but decrease by only 0.4 point when the underlying stock price goes down by 1 point. In this case, the up delta is 0.6 and the down delta is 0.4.

As the time remaining to expiration grows shorter, the time value of the option evaporates and correspondingly, the delta of in-the-money options increases while the delta of out-of-the-money options decreases.

The chart above illustrates the behaviour of the delta of options at various strikes expiring in 3 months, 6 months and 9 months when the stock is currently trading at $50.

As volatility rises, the time value of the option goes up and this causes the delta of out-of-the-money options to increase and the delta of in-the-money options to decrease.

The chart above depicts the relationship between the option's delta and the volatility of the underlying security which is trading at $50 a share.

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