Show that for a dividend-paying stock, the values of (otherwise identical: S,T,K) American and European call options need not be the same. Hint: Suppose that a large dividend is to be paid. What is the value of the stock before and after the divdend payment?

What assumptions are required to show that the value of an American call option on a stock is the same as the value of an otherwise identical European option? Construct a model where the values are not the same.

Why doesn't the argument that American and European calls have the same value work for puts?