Options: The binomial model for American Options

Question 1

What is the difference between using binomial trees for pricing European vs American options?

Answer 1

The only difference between the two lies in the fact that in all intermediate nodes we must check whether it is more convenient to keep the option alive or to exercise it immediately.

The value of early exercise is easily determined comparing with the strike price the spot price of the stock in a given node

Question 2

What is the option value for a theoretical node f_u within an american option binomial tree with two periods (t0, t1, t2)?

Answer 2

f_u = Max[e^-rt * [p * f_uu + (1-p) * f_ud]; K - Su]