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Delta is the measure of price movement of an options contract when the value of the underlying stock moves ${\$}$1 in value. Many people would assume that the value of an option will also move ${\$}$1 when the value of the underlying stock moves ${\$}$1. However, this is not true. As the cost of an option is much lower than the collective value of the underlying, the value of an option will change less than ${\$}$1 when the price of the underlying changes ${\$}$1.

Usually, calls have a positive delta. For example, if the value of delta for a call option is 0.50, the value of the option will go up 0.50 with the movement of the underlying stock’s ${\$}$1 value upside. Note that in case of delta calculation, only price movements are considered, taking all other remaining factors constant. Therefore, the time decay and strike price must remain the same while the delta of an option is considered. Notably, calls have a positive delta that remains between 0 and 1.

Put option contracts have a negative delta between 0 and -1. Therefore, if the delta for a put option is -0.50, and if the price of the underlying stock moves ${\$}$1, the value of the option will move -0.50 overall. That is, when the value of the underlying stock goes up to ${\$}$1, the value of the option will go down 0.50. When the value of underlying goes down $1, the value of the option will go up by -0.50.

In general, in-the-money (ITM) options move more than out-of-the-money (OTM) and short-term options react more than long-term ones with respect to the same price change of the underlying stock.

The delta for ITM options will be near 1 in value when expiration approaches. This will lead to one-to-one price change in the options.

Delta for OTM calls approach 0 and will not react to price changes as expiry comes near. It happens because if the calls are held till expiration, they will either become stock or go worthless due to maturity.

Similarly, the delta for ITM puts will approach -1, and the delta for OTM puts will approach 0. That is because if the put options are held until expiration, they will either be exercised or the put will be expired worthless.

If the option moves further in-the-money, the probability that it will be inthemoney during expiration increases. So, the delta will go up in such cases. On the other hand, when the option goes further out-of-the-money, the probability of it being in-the-money during expiration decreases, so the value of the delta will go down.

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