Explosive Missile says: "When the infused ammunition hits its target, it deals damage normally and detonates as if the alchemist had thrown the bomb at the target."
So the arrow would deal arrow damage normally (adjusted by merciful and all that), and then detonate as if a bomb had been thrown. Which, it seems to me, precludes the detonation being effected by merciful (but will include things like your int bonus to damage from throw anything ability).
That being said, I could see either way being equally fun to play, and not unbalanced so if this is a homegame, talk to your GM. Any consistent ruling would work fine.