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It is defined as the first derivative of the binary call option delta with regard to a change in the underlying price. Therefore, the gamma indicates the slope of the delta profile. It reflects whether the corresponding futures position of a binary call option becomes longer or shorter when the underlying price rises or falls.
Therefore, the gamma of binary call options can be seen as a number that indicates whether the equivalent underlying position is higher or lower when the underlying price rises. If the equal position increases from 20 to 25, for example, it has a positive gamma. If the equivalent position falls to 15 (in case that the market rises), it has a negative gamma.
Thus, the gamma of conventional calls is always positive. When buying traditional calls, the equivalent position always rises when the underlying asset rises, regardless of whether the option is in the money or not.
Binary up and in call options behave differently in that binary call options that are out of the money, because always have a positive binary call option gamma. In contrast, binary call options in the money always have a negative gamma.
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