I agree with Haf that nihilism is technically not the belief that nothing exists, but that nothing has value. But solipsism is not the belief that nothing exists, but that nothing outside me exists.
As I see it, solipsism is all about subjectivity, so if I were a solipsist, the question if I exist or not (from an objective perspective) would probably not even make sense.
As for nihilism, from my perspective, for something to exist it must have value. Therefore, if I were a nihilist, then saying that nothing has value would simply imply that nothing exists.
However, I'm not a nihilist, and I'm not a solipsist either. I believe in value, as well as in an objective (mathematical) universe. And I think there's enough evidence that we are endowed to handle both. Shall we fail or not - that's another story. It's the game we're playing. As someone said, the meaning of life is finding a door in a wall that has none.