American options can be exercised early. Their prices must always be no less than those of otherwise equivalent European options.

American call options:

C₀ = Max[0, S₀-X/(1+r)T]

American call options, however, are never exercised early unless there is a cash flow on the underlying. The extra value of an American option, if any, comes from the fact that it can be exercised immediately.

American put options:

P₀ = max[0, X - S₀]

American put options nearly always have a possibility of early exercise, so they ordinarily sell for more than their European counterparts.