The delta of a up-and-out call option with barrier $H$ lying above the strike $K$ is most likely to be negative when
A) The underlying stock price $S$ is at or near $K$ .
B) The underlying stock price $S$ is close to and less than $H$ .
C) The underlying stock price $S$ is well below $K$ .
D) The delta of a call cannot be negative.

Question

Quizplus · Accepted Answer

The delta of an up-and-out call option can be negative when the stock price is close to and less than the barrier $H$. This is because as the stock price approaches the barrier from below, the probability of the option knocking out increases, which can lead to a decrease in the option's value with a small increase in the stock price, hence a negative delta.

The Delta of a Up-And-Out Call Option with Barrier HHH Lying Above the Strike

The Delta of a Up-And-Out Call Option with Barrier $H$ Lying Above the Strike