The delta of a cash-or-nothing binary call option and the gamma of such an option
A)is always positive;is always positive.
B)is always positive;can be positive or negative.
C)can be positive or negative;is always positive.
D)can be positive or negative;can be positive or negative.

Question

Quizplus · Accepted Answer

The delta of a cash-or-nothing binary call option is a step function with a zero slope everywhere but at the strike price, where it becomes infinitely large (for European options) or where it is usually very large (for American options). Therefore, the delta is always positive for prices above the strike and always zero for prices below the strike. 
The gamma of such an option can be positive or negative depending on whether the option is in-the-money or out-of-the-money. When the option is at-the-money, the gamma is at its highest point, and changes in the underlying asset price will have the largest impact on the option price. Hence, gamma can be positive or negative, depending on whether the underlying asset price is above or below the strike price.

The Delta of a Cash-Or-Nothing Binary Call Option and the Gamma