# Barrier option with zero-strike

Good morning, everybody,

I would like to know whether an up-and-out call option with a zero strike has a special name in the list of exotic options or is still a special case of a barrier option..

The payoff for this option is given by $$S_T \mathbb{I}_{\{M_T where $$M_T=\max\{S_t\, ,\, 0\le t\le T\}$$ and $$B>0$$ is barrier.

For the pricing formula I know it's easy with Girsavov's theorem and reflection principle but i don't have space in my paper for more proofs. I need a good reference. Could you help me?