Would be great if someone can provide a graphical explanation to show changes in gamma and delta as price goes toward in the money and away as further out the money. Are there differences that I should note between call and put option's delta and gamma movements?
As you can see from the graphs above, as absolute distance from ATM (At The Money) increases, the ratio represented by Delta begins to approach 0:1 or 1:1. Meaning, as Delta approaches 1 the option price moves up 1 dollar for every 1 dollar the stock price moves up. As Delta approaches 0 the option price does not move as the stock price moves.
As the absolute distance from ATM increases Gamma approaches zero (0). Meaning, as the price of the option increases or decrease the change in delta is at its highest as the option price is nearest the money. As the price of the option moves away from the money, in either direction, it changes less drastically.
Interestingly, Delta is the first derivative of the value of the option price with respect to the underlying asset price. And Gamma is the first derivative of Delta.