Question

In which situation should you exercise an American call or an American put early, assuming no dividends? Provide your reasoning.

Answer 1

For an American call assuming no dividends, the early call is never optimal. The reason is that exercise requires payment of the strike price X. By holding onto X until the expiration time, the option holder saves the interest on X.

For an American put assuming no dividends, early exercise can be sometimes optimal. Suppose for example, that the stock price S falls to nearly 0. Then the option holder stands to gain more by exercise than by waiting. The reason is that the payout X −S (in case the option holder exercises the option) cannot increase much, but by early exercise, the option holder will get the interest on the payout as well.