SFoyil

Thanks guys for the responses.

@jmh530 : Yeah, I could build a binomial tree (all good stuff for level 2), and use the parity principle. But it seems it only applies to European options... For American Call Down-and-In and American Put Up-and-In we can use the reflection principle, which gives us a nice formula, but it doesn't apply to american Call Up-and-In.

@ohai: Exactly, the stock price is currently at 1$, the option is currently not activated, but as soon as it touch 3$, it becomes a normal american call option with a 1$ strike price.

I guess I would have to simulate the stock price evolution, and when it touches 3$, evaluate a normal american call option with the remaining maturity, or something like that.