American and European Options

This is an introductory page in Options. If you are unfamiliar with any of the terms, you can refer to the Options Glossary.

The style of an option helps us to identify properties that are common to many different types of options. European options may only be exercised on expiration, while American options may be exercises on any trading day up to expiry. Other options which have different payoffs / exercise rules are known as exotic options.

A European option can only be exercised on the expiration date of the option. As such, an existing position can only be closed by trading out of it in the market.
Most over-the-counter options are European. Options on the indexes are generally European.

Note that European index options stop trading one-day earlier (IE at the close of business on the Thursday preceding the third Friday). Based on the opening price for each stock in the index, the exact value of the future is determined, and all of the options settle into the cash value of the option's intrinsic value. Note that this calculated price need not be in line with the price of the future, due to uncertainty / imbalances in the opening price of individual stocks

European options are typically valued using the Black-Scholes model which offers a simple equation with a closed-form solution. This has become the standard in the financial community.

An American option can be exercised on any trading day up to the expiration date of the option.

All (most) stock and equity options traded on the exchanges are American options. Most future options are American, though commodity options could also be European.

The most common choice of models for an Americal option are Binomial tree and Monte Carlo. There is no general formula to value an American option.

Early exercise refers to exercising an (American) option prior to its expiration date. Early exercise of call options allows the investor to purchase the underlying security at the strike price today, while early exercise of put options allow the investor to sell the underlying security at the strike price today.

American options are rarely early exercised for the following reasons:

1. American options have a non-negative time value, which is lost when exercised.
2. It is often less costly to trade out of the position (pay bid-ask spread + trading fees) then to exercise the option (commissions charged by the broker).
3. For call options, it costs more to exercise the option today and buy the stock for the strike price of K, then it would to exercise it in the future.

Thus, based on the above, there are several guidelines that should influence your decision of early exercise:

1. The time value should be compensated for.
   For calls: The (extrinsic) value of the put + cost of financing the strike < dividend that would be received.
   For puts: The (extrinsic) value of the call < dividend that would be received + cost of financing the strike.
   The tax implications of a trade (e.g. capital gains tax from closing a position, income tax from dividend payments) should also be considered.

2. The delta of the call should be 1, the delta of the put should be -1.

3. There is no need for the protection / insurance which the option provides. If not, this cost needs to be accounted for.

4. The option is trading (close to) intrinsic value, IE it has little/no extrinsic value.

For option sellers / those trading multi-leg strategies, the possibility of early exercise could affect the overall position that you have. The above guidelines will offer you a warning of when your short positions may be early exercised, and you can trade accordingly. In other cases, it is most likely the the option buyer made a mistake and you would likely have profited from it (assuming that the future does not move significantly).