Given a Current Stock Price $S$ ,Strike Price $K$ ,And Barrier $H$ ,Which of the Following Statements Is Most Valid?
A)Given

Given a current stock price $S$ ,strike price $K$ ,and barrier $H$ ,which of the following statements is most valid?

A) Given $H < K < S$
,if the barrier
$H$
Is moved lower,then a down-and-in put increases in value and a down-and-out put falls in value.
B) Given $H < S < K$
,if the barrier
$H$
Is moved lower,then a down-and-in put and a down-and-out put both increase in value.
C) Given $H < K < S$
,if the barrier
$H$
Is moved lower,then a down-and-out call increases in value and a down-and-in call decreases in value.
D) Given $H < K < S$
,if the barrier
$H$
Is moved lower,then a down-and-out call and a down-and-in call both increase in value.