American options, due to the early exercise feature, may trade at a premium to
European style options. To compute the price of an American
put option on an equity underlyer with dividends requires special techniques. Note that
Put-Call Parity does not apply for American options.
It is rare to actually exercise an exchange traded American style option, such as an option on
Eurodollar Futures.
One can consider the American option as a particular kind of
Bermudan Option. A
Bermudan option is exercisable on a particular set of dates, for example, the first of the month.