麻烦老师详细讲下这道题

问题如下：

Of the following options, which one does not benefit from an increase in the stock price when the current stock price is $100 and the barrier has not yet been crossed?

选项：

A.

A down-and-out call with barrier at $90 and strike at $110

B.

A down-and-in call with barrier at $90 and strike at $110

C.

An up-and-in put with barrier at $110 and strike at $100

D.

An up-and-in call with barrier at $110 and strike at $100

解释：

ANSWER: B

A down-and-in call comes alive only when the barrier is touched; so an increase in S brings it away from the barrier. This is not favorable, so B is the correct answer. A down-and-out call (answer A) where the barrier has not been touched is still alive and hence benefits from an increase in S. An up-and-in put (C) would benefit from an increase in S as this would bring it closer to the barrier of $110. Finally, an up-and-in call (D) would also benefit if S gets closer to the barrier.