American Option

An American option is a call option or put option that can be exercised at any time up to and including the expiration date, not just on that final day. This flexibility makes American options more valuable than otherwise identical european-option options, particularly when early exercise can be advantageous. American options are the standard contract on individual stock options in the United States.

The early exercise advantage

The defining feature of an American option is the right to exercise at any moment, not just at expiration. This flexibility has real value. Suppose you own a call option on a stock and a takeover bid is announced at a 40% premium. You can exercise immediately, pocket the shares, and enjoy the windfall. A European call holder must hold the option and wait for expiration, facing risk that the deal falls through in the interim.

Similarly, a put option holder benefits from early exercise when the underlying crashes. You can exercise the put, lock in profit by selling shares at the above-market strike price, and redeploy the cash into other investments. A European put holder cannot capture that advantage until expiration day arrives.

For dividend-paying stocks, American call option holders sometimes exercise just before the ex-dividend date to capture the upcoming dividend, even if the option is not yet in-the-money by much. This is often rational if the dividend is large and the call has little time value left.

Pricing American options

Valuing an American option is more complex than a european-option because the holder has a continuous decision to make: exercise now or wait? This cannot be solved with a closed-form equation like the Black-Scholes model; instead, traders use numerical methods.

The binomial-option-pricing model is the workhorse. It builds a tree of all possible future stock prices at each time step from now to expiration, then works backward from expiration to today, calculating at each node whether it is optimal to exercise immediately or hold on. The result is a probability-weighted value reflecting the optimal exercise strategy.

Monte-carlo-options-pricing is another approach, simulating thousands of possible price paths from today to expiration and calculating the payoff under the optimal early-exercise rule.

When early exercise makes sense

For American call option on non-dividend-paying stocks, the theoretical answer is: never exercise early. It is always worth more to sell the option (capturing both intrinsic value and remaining time value) than to exercise and throw away the time value. But for dividend-paying stocks, early exercise can be optimal just before the stock goes ex-dividend.

For American put option, early exercise is much more common. A put that is deep in-the-money—say, a $100 strike and the stock at $60—can be exercised immediately to lock in the $40 profit and redeploy capital. Waiting for expiration means accepting the risk that the stock bounces and sitting with capital tied up. This is why American puts trade at noticeably higher premiums than European puts.

Assignment risk

Because American options can be exercised at any time, the seller faces assignment risk any trading day. If you sell a call that goes in-the-money and the dividend is approaching, the call buyer may exercise and force you to deliver shares. If you sell a put that plummets in-the-money, the buyer may exercise and force you to buy shares.

This unpredictability is one reason selling American options (writing naked calls or puts) requires close risk management and broker approval. The assignment can force you into an unexpected position at the worst moment.

The option Greeks for American options

The options-greeks measure the same sensitivities as for european-option options—delta, gamma, theta, vega, rho—but the numbers reflect the early-exercise possibility. An American put option deep in-the-money may have lower theta than a European put because there is less time value left to decay; the holder will likely exercise soon anyway.

Gamma (the convexity of delta movement) tends to be higher for American options because the early-exercise boundary creates a kink in the value curve.

Typical stock option contracts

A standard American option on a US stock option contract represents the right to buy or sell 100 shares. The strike price typically comes in increments of $1 or $2.50, depending on the stock price. The expiration date is usually the third Friday of the month, though many stocks now also trade weekly and monthly expirations.

Implied volatility on American options is high in periods of market stress and lower in calm markets. The options Greeks are continuously updated and quoted by brokers and market data vendors.

See also