After reading the Wikipedia article on the Black-Scholes model, it looks to me like it only applies to European options based on this quote:
The Black–Scholes model (pronounced /ˌblæk ˈʃoʊlz/1) is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives the price of European-style options.
American options and options on stocks paying a known cash dividend (in the short term, more realistic than a proportional dividend) are more difficult to value, and a choice of solution techniques is available (for example lattices and grids).
Is this correct? If so, is there a similar model for American Style options? My previous understanding was that the options price was based on it's intrinsic value + the time value. I'm really not sure how these values are arrived at though.
I found this related question/answer, but it doesn't address this directly: Why are American-style options worth more than European-style options?