American Exercise Currency Options
American currency options allow exercise at any time before expiration. Some interbank currency options and most listed currency options feature American exercise privilege.
American exercise privilege results in arbitrage conditions that differ from those implied by European exercise. Denote American currency calls and puts as C′ and P′, respectively.
Immediate Exercise Value
The minimum value of an in-the-money American option is equal to the value of immediate exercise:
for all times in the life of the option, 0 ≤ t ≤ T.
The value of an American option is a positive function of its remaining time to expiration, all other things being equal:
where (T – t0) and (T – t1) are times to expiration and t1 > t0. Since exercise is permitted at all times before expiration, incremental time to expiration has a non-negative effect on the value of American calls and puts. This result is not always true for European options.
American and European Exercise
The minimum value of an American option is the value of an otherwise identical European option. That is
A complete lower bound for American options is obtained by ...