Delta is one of the five Greek letters which is used for measuring option risk, i.e., it measures the effect of the change in the price of the underlying asset on the option’s premium. It explains the relationship between the spot price and the option price. Delta expresses the percentage of change in the price of the underlying asset that is reflected in the price of the option.
It has positive value for the call option and a negative value for a put option its value ranges from 0 to 1 for the call option and 0 to -1 for a put option. The reason put option have a negative value is due to the inverse correlation with the underlying assets. Put option premium fall when the price of the underlying assets rises and put option premium increases with the decrease in the price of the underlying assets. On the other hand, for a call option, the option premium price increases with the increase in the underlying assets and option price decreases with the decrease in the underlying asset. This is the reason Delta has a positive slope for the call option and a negative slope for the put option.
If the Delta of a particular call option is 0.50 this specifies that the price of the option will rise by Rs 0.5 for every Rs 1 increase in the spot price of the underlying security. The opposite effect is also seen that is for every Rs 1 decline in the price of the underlying security the price of the option will fall by Rs 0.5.
For a put option if the Delta is -0.5 this specifies that the price of the option will fall by Rs 0.5 for every Rs 1 increase in the spot price of the underlying security and the option price will rise by Rs 0.5 for every Rs 1 decrease in the price of the security.
Gamma is used to determine the rate of change of Delta with respect to the price of the underlying asset. Mathematically Gamma is the first derivative of Delta and is used to measure the price movement of an option relative to the amount it is in or out of the money.
Let us consider an example, where the strike price of an asset is Rs 100 and the spot price is Rs 10 and the option price is equal to 0.2 now this situation can be considered as deep out of the money for a call option. Delta, in this case, will be zero because even if the spot price increases from Rs 10 to Rs 11 the price of the option will remain same as it is deep out of the money. Gamma which is the measure of the rate of change of Delta will also be equal to zero as Delta is equal to zero.
Similarly, when the situation is deep in the money, i.e., the spot price is Rs 500 and the premium price is Rs 400, there is a proportional increase in the value of premium price with respect to the spot price. In this case, Delta is 1 but Gamma is equal to zero because Gamma is the rate of change of Delta and since Delta is not changing Gamma is equal to zero.
For at the money Delta value is 0.5 because the strike price is almost equal to the spot price and in this Gamma has the highest value because Delta varies much under this situation.