I come across an interesting question about barrier option as shown below.
Two barrier options are given with the same parameters including the barrier level. The first one is knocked out when it first hits the barrier. The second one is knocked out when it hits the same barrier the second time.
Question: Under the Black-Scholes framework, what is the relation of these two option prices?
(My thought: it probably can be said that the second option is more valuable because it is less likely to be knocked out. But what else?)