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Gamma decreases when a call option goes either deeper in, or deeper out of the money. That is due the demand for the call option. I can imagine the demand for the option would decrease as it goes deeper out of the money, but I would expect the demand for the option should increase as it goes deeper in the money because it would make more profit for the holder of the option. Why is this not true? In other words, why does the demand for the option decrease despite the fact that a deep in the money option is more profitable?

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Gamma is not linked to the supply/demand for an option. It is a purely analytic effect that reflects the convexity of the product.

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Gamma is the speed at which Delta changes. When options are deep in the money, they trade like the underlying. In other words the Delta doesn't change and therefore Gamma is zero. In mathematical terms, the second derivative which measures the rate of change of the first derivative, is zero if the first derivative is a constant.

With respect to demand for the option, if it trades like the underlying, I would expect that the traders of options that are using it for the optionality would not be in the market for those options. For those that are looking for constant Delta, the could just buy the underlying and adjust for any implied leverage in the option by just taking a leveraged position.

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