nitoha

i don't think this is right -- you don't get compensated for time value when you exercise an option. (time value helps determine the cost of the option, but you don't get reimbursed for it when you exercise).

you might exercise an American call option early if the underlying stock is about to pay a dividend that would take your option out of the money (when the stock price drops after going ex-dividend).

you would exercise an American put early if the company was almost bankrupt and its shares were at close to zero -- because you have already made the maximum payoff on your position, there's no point in waiting until expiry to get your profit.