American style option

What Is American-style option?

An American-style option is a type of financial instrument that grants its holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before its expiration date. Unlike a European-style option, which can only be exercised at expiration, the key distinguishing feature of an American-style option is its flexibility for early exercise. This characteristic provides the holder with the ability to capture gains or limit losses if market conditions become favorable prior to the contract's expiry. American-style options are a core component of the derivatives market, offering investors avenues for both speculation and hedging.

History and Origin

The concept of options has roots in ancient times, with early forms believed to have existed in Greek philosophy and the Dutch tulip mania. However, the modern, standardized options trading market as we know it today began in the United States. A pivotal moment was the establishment of the Chicago Board Options Exchange (CBOE) in 1973. The CBOE, spun off from the Chicago Board of Trade (CBOT), was the first exchange to offer standardized, exchange-traded stock options. This standardization, along with the creation of the Options Clearing Corporation (OCC) for centralized clearing, transformed an unstandardized, over-the-counter market into a transparent and liquid one. The CBOE's efforts, including the vision of its founding president Joe Sullivan, revolutionized how options are traded and laid the groundwork for the modern options market⁹. The introduction of puts by the CBOE in 1977 further expanded the options market⁸.

Key Takeaways

• An American-style option allows the holder to exercise the option at any point up to and including the expiration date.
• This early exercise feature differentiates American options from European options, which can only be exercised at expiration.
• The flexibility of an American-style option adds complexity to its valuation compared to European options.
• American-style options are commonly traded on exchanges and used for diverse investment strategies, including income generation, speculation, and risk management.
• While a call option on a non-dividend-paying stock is typically not optimally exercised early, an American-style put option can often benefit from early exercise, especially if the underlying asset's stock price drops significantly.

Formula and Calculation

Unlike European options, there is no simple closed-form analytical solution like the Black-Scholes model for pricing American-style options due to the optimal stopping problem posed by the early exercise feature⁶, ⁷. Instead, numerical methods are primarily used to determine their theoretical value. These methods involve discrete time steps and consider the optimal decision to exercise at each step.

Common numerical methods include:

• Binomial Tree Model: This model discretizes time into a series of steps and, at each step, the underlying asset's price can move up or down. The option's value is calculated backward from expiration, evaluating the value of exercising early versus holding the option.
• Finite Difference Methods: These methods solve the partial differential equations associated with option pricing by approximating derivatives with finite differences.
• Monte Carlo Simulations: For more complex options, Monte Carlo simulations can be adapted to price American options, although they typically require techniques like the Least Squares Monte Carlo (LSM) method to identify the optimal exercise boundary⁵.

The complexity of valuing an American-style option stems from determining the optimal time to exercise, which depends on factors like the underlying asset's price, volatility, remaining time to expiration, and interest rates.

Interpreting the American-style option

Interpreting an American-style option involves understanding its inherent flexibility. For a holder, this means constantly evaluating whether exercising the option early is more beneficial than holding it until expiration. This decision hinges on the option's intrinsic value and time value. If the intrinsic value becomes significantly high, or if the underlying asset is expected to undergo a major corporate action (like a large dividend payment for a call, or a bankruptcy for a put), early exercise might be optimal.

Conversely, for writers of American-style options, the early exercise feature represents an additional risk. They must be prepared for the possibility that the option will be exercised against them at any time, requiring them to deliver or take delivery of the underlying asset. Market participants often use advanced analytical tools to interpret the potential for early exercise, considering factors like implied volatility and dividend schedules of the underlying security.

Hypothetical Example

Consider an investor, Sarah, who believes that Company XYZ's stock, currently trading at $50 per share, will increase in value. She decides to purchase an American-style call option on XYZ with a strike price of $55 and an expiration date three months from now, paying a premium of $2 per share.

• Initial Cost: Sarah pays $200 for one contract (100 shares x $2 premium).
• One month later: Company XYZ announces unexpectedly strong earnings, and its stock price jumps to $65 per share.
• Decision Point: Sarah now holds an American-style call option that is deeply in-the-money.
  • Option 1 (Early Exercise): Sarah could exercise her option immediately. She would pay $55 per share to acquire XYZ stock, which she could then sell in the market for $65 per share. Her profit would be ($65 - $55 - $2 premium) x 100 shares = $800.
  • Option 2 (Hold until Expiration): Sarah could hold the option, hoping the price goes even higher. However, holding a call option on a dividend-paying stock might involve missing out on a large dividend payment if it occurs before expiration, potentially making early exercise more attractive. In this case, since the stock price has already risen significantly, and assuming no immediate large dividends are expected, she might weigh the benefit of realizing profit now versus the potential for further gains, offset by the risk of a price decline.

The flexibility of the American-style option allowed Sarah to lock in a substantial profit by exercising early, rather than being forced to wait until the expiration date.

Practical Applications

American-style options are widely used in financial markets for a variety of purposes:

• Income Generation: Investors can write covered calls or cash-secured puts on American-style options to generate premium income, provided they are comfortable with the obligation to buy or sell the underlying asset.
• Risk Management: Portfolio managers often employ American-style options for hedging existing positions. For instance, buying an American-style put option can protect against a decline in the value of an owned stock by providing the right to sell it at a predetermined price.
• Speculative Trading: Traders can use American-style options to profit from anticipated price movements in the underlying asset with a relatively small capital outlay compared to buying or shorting the shares directly. The ability to exercise early provides an additional strategic dimension to speculative trades.
• Employee Stock Options (ESOs): Many companies issue American-style options to employees as part of their compensation, allowing them to purchase company stock at a set price after a vesting period.
• Regulatory Framework: The trading of American-style options, like other financial derivatives, is subject to extensive regulation to ensure market integrity and investor protection. In the U.S., bodies such as the Securities and Exchange Commission (SEC) set rules governing options contracts and trading practices⁴. Information on trading volumes and market activity for American-style options is readily available from exchanges like Cboe, the largest U.S. options market operator³.

Limitations and Criticisms

The primary limitation of an American-style option lies in its valuation complexity. While the early exercise feature provides flexibility, it also means that a simple, universal formula for pricing, like the Black-Scholes model for European options, does not exist. This absence necessitates the use of more sophisticated and computationally intensive numerical methods for accurate pricing, such as binomial trees, finite difference methods, or Monte Carlo simulations².

Another aspect is that for American-style call options on non-dividend-paying stocks, it is generally not optimal to exercise early because holding the option provides the time value, and the maximum gain is realized by selling the option or exercising at expiration. However, for dividend-paying stocks, a large dividend payment can make early exercise of an American-style call option rational just before the ex-dividend date. Conversely, American-style put options frequently benefit from early exercise if the underlying asset's price drops significantly.

Furthermore, the very flexibility that makes American-style options attractive can also lead to suboptimal decisions by inexperienced traders who might exercise early without fully understanding the loss of remaining time value. This can result in lower profits or higher losses compared to holding or selling the option itself. Academically, the challenge of efficiently pricing American options, especially in more complex models, continues to be an active area of research, with new approaches like machine learning algorithms being explored¹.

American-style option vs. European-style option

The fundamental distinction between an American-style option and a European-style option lies in their exercise rights. An American-style option can be exercised by the holder at any time between the purchase date and the option's expiration date. This provides maximum flexibility, allowing the holder to capitalize on favorable price movements or manage risk throughout the life of the contract.

In contrast, a European-style option can only be exercised on its specified expiration date. Regardless of how favorably the underlying asset's price moves before expiration, the holder cannot realize the option's intrinsic value by exercising early. This difference in exercise flexibility leads to European options generally being simpler to price mathematically than American options. Because the early exercise privilege adds value, an American-style option will typically trade at a premium to an otherwise identical European-style option, assuming all other factors like strike price, underlying asset, and expiration date are the same. Investors often confuse the two because of geographical names, but the naming convention refers to the exercise style, not where the options are traded.

FAQs

Q: Can all options be exercised early?
A: No. Only American-style options grant the holder the right to early exercise. European-style options can only be exercised on their expiration date.

Q: Are American-style options always more expensive than European-style options?
A: Generally, yes. The added flexibility of being able to exercise at any time before expiration provides extra value to an American-style option, making it typically more expensive than an otherwise identical European-style option.

Q: Why would someone choose an American-style option over a European-style option?
A: Investors might choose an American-style option for its flexibility in risk management or to capitalize on specific events like large dividend payments (for calls) or sharp declines in stock price (for puts), allowing them to lock in profits or mitigate losses at any point before expiration.

Q: Is it always optimal to exercise an American-style option early if it's in-the-money?
A: Not necessarily. While an American-style put option might often be optimally exercised early when deeply in-the-money, an American-style call option on a non-dividend-paying stock is generally not optimally exercised early because doing so would mean forfeiting any remaining time value. The decision to exercise early depends on various factors, including dividends, interest rates, and the time value remaining.