# Why is it that Gamma is always positive

Does anyone know why gamma is always positive for call and puts?

Gamma is positive for â€ślongâ€ť calls and puts (when you buy options). Perhaps someone can explain it better than me, but here goes:

1. Gamma = measure of how Delta changes when the price of the underlying stock moves up or down. It is a change measurement for Delta. (Remember that Delta = change in the option value due to a change in the underlying stock price).

2. When you buy options, youâ€™re adding positive Gamma. When you sell options, youâ€™re adding negative Gamma. You can be Gamma neutral if you combine buying and selling options into one strategy.

3. Long story short - positive Gamma for long calls and puts means: (a) the Delta of â€ślongâ€ť calls will become MORE positive (approaching +1) when the stock price rises, and LESS positive (approaching 0) when the stock price falls; and (b) the Delta of â€ślongâ€ť puts will become MORE negative (approaching -1) if the stock price falls, and LESS negative (approaching 0) when the stock price rises.

Thatâ€™s as I understand it anyway, someone might have a better explanation.

Cheers - good luck - you got this

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Makes sense. Thanks.

The price curves for call options and put options are convex (mathematicians would say, "concave upward). The second derivative of a convex (concave upward) function is positive; the slope of the tangent line (delta) is increasing from left to right.

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Thanks.

Donâ€™t ignore the â€śsquaredâ€ť in the second order derivative.

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