I have been looking at pricing a barrier option that has payoff of your usual European Call option, $\max(S_T - K, 0)$ if the stock price exceeds a horizon $A$ and then afterwards drop under some level $B$. We have the constraints $B < S_0 < A$ and $B < K$ and are also assuming zero interest rate. I am told it can be priced by the pricing formula for European call options alone. I just don't see how the indicator functions on the stopping times can be set up to reduce it to the regular European calls. Any nudge in the right direction would be highly appreciated.