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American options vs European options

American options differ from European options in that they can be exercised before the expiry date. This is additional flexibility which shows that the value of American options should be greater than or equal to equivalent European options. Whether the difference exists depends on the time to expiry and whether the underlying has any associated benefits or costs.

Minimum price of American options

The minimum price of an American call equals greater of zero and the excess of the current spot price minus the present value of the exercise price determined at the risk-free rate. But the minimum price of an American put equals greater of zero and any excess of the exercise price over the spot price.

Deciding when to exercise an American option

When the underlying does not pay any cash flows, it is not profitable to exercise an American call option early because an investor is better off is he instead can earn interest on the amount that would otherwise be expended in exercising the call. However, if the underlying pays dividends, it might make sense to exercise an option just before a dividend/coupon is paid. But if significant carrying costs are to be incurred, the advantage of early exercise may be weakened.

An American put option is more likely to be exercised early because it is better to sell the underlying today and accumulate interest on it. But if the underlying pay dividends/coupons, it is less likely that the put shall be exercised because it is better to receive the dividends/coupons as long as possible. However, if the underlying has carrying costs, it may increase the advantage of early exercise.

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