Such problems can become intractable analytically. [fact]
The "tree" can be elaborated to take into account dividends, and `American" as well as "European" options can be treated (the former can be exercised at any time up to their expiration, raising the need to examine when early exercise may be rational). Such problems can become intractable analytically, but the Cox-Ross-Rubinstein model allows them to be solved numerically and recursively by working "backwards" through the tree.
Donald MacKenzie, An Engine, Not a Camera, loc. 1287