American Option

An American option is an option that the holder may exercise at any time from purchase up to and including its expiry date. This sets it apart from a European option, which can be exercised only at expiry. The names describe the exercise style and have nothing to do with where the contract trades: both styles are listed on exchanges around the world.

Because the holder has every right a European holder has, plus the right to act early, an American option is worth at least as much as the matching European contract. The extra right matters most for puts and for calls on shares that pay dividends. It also changes the position of the seller, who can be required to perform on any day and not only at the end.

A holder who exercises a call option buys the underlying asset at the strike price; a holder who exercises a put option sells it at the strike. On an exchange, the clearing house then assigns the exercise to a seller of the same contract, chosen by a set procedure. The seller receives an assignment notice and must deliver the asset or pay for it.

The value obtained by exercising immediately is the option's intrinsic value. For a call and a put it is:

• $S$ is the current price of the underlying asset.
• $K$ is the strike price.

Suppose a put has a strike of $50 and the share trades at $40. Exercising yields $10 per share. If the same put trades in the market at $10.20, the extra 20 cents is time value, and a holder who exercises gives it up. Selling the option is the better choice unless that time value has all but vanished.

For a call on a share that pays no dividend before expiry, early exercise is never the best choice. Exercising means paying the strike sooner and losing the protection the option gives if the price later falls. The holder does better by selling the call. An American call on such a share is therefore worth the same as a European one.

Two cases break this rule:

• Calls before a dividend. Option holders do not receive a dividend, and the share price drops by about the dividend amount on the ex-dividend date. If the dividend is larger than the call's remaining time value, exercising the day before captures it.
• Deep in-the-money puts. Exercising a put brings in the strike price in cash, which can then earn interest. When a put is far in the money and interest rates are positive, the interest gained can exceed the time value lost.

The Black-Scholes model assumes exercise only at expiry, so it prices European options and does not directly price American ones. No simple closed formula exists for an American put. Practitioners use numerical methods instead.

The most common is the binomial option pricing model, which builds a tree of possible prices and works backward from expiry. At each node it compares the value of holding the option with the value of exercising and keeps the larger. Finite-difference grids follow the same logic, and a least-squares form of Monte Carlo simulation is used when there are several underlying assets. The difference between the American and European price is called the early exercise premium.

Listed options on individual shares and exchange-traded funds in the United States are American in style and are settled by delivery of the shares. Most options on broad stock indices, such as those on the S&P 500 listed by Cboe, are European and settle in cash. Options on futures contracts are commonly American. In over-the-counter markets, the style is whatever the two parties agree, and a middle form, the Bermudan option, allows exercise on a list of set dates.

The writer of an American option faces early assignment risk. A seller of calls may be assigned just before an ex-dividend date and then owe the dividend on a short share position. A seller holding an option spread may be assigned on the short leg while the long leg remains open, which changes the position's risk and may create a margin requirement overnight. Brokers also exercise in-the-money options automatically at option expiry unless told otherwise, so holders and writers need to watch contracts that finish close to the strike.

• The Options Clearing Corporation
• Cboe Global Markets