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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?

  • This might be more at home n the Quants discussion than here. When people start using Greek letters to describe their investment idea, it's all Greek to me. – keshlam Dec 22 '16 at 14:40
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Options Greeks:

[Graph of Delta and Gamma vs Moneyness]

Delta

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.

Gamma

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.

Mathematics

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.

Definition of Delta

Definition of Gamma

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