What Is an American Call Option?
An American call option is a financial derivative that grants the holder the right, but not the obligation, to buy an underlying asset at a specified strike price on or before a particular expiration date. This flexibility to exercise at any point up to and including the expiration date distinguishes it from a European call option, which can only be exercised on the expiration date itself. Investors typically pay a premium to acquire an option contract, betting on the future price movement of the underlying asset.
History and Origin
While the concept of options trading has roots stretching back to ancient times, the modern, standardized exchange-traded options market originated in the United States with the founding of the Chicago Board Options Exchange (CBOE) in 1973. Prior to this, options were primarily traded over-the-counter (OTC) with non-standardized terms. The CBOE revolutionized the market by introducing standardized option contract sizes, strike price increments, and expiration dates, bringing transparency and liquidity to a previously opaque market. Cboe Global Markets was the first marketplace for trading listed options, beginning trading on April 26, 1973, with 16 stocks.5 This standardization, coupled with the development of sophisticated pricing models, significantly propelled the growth and widespread adoption of derivatives.
Key Takeaways
- An American call option grants the holder the right to buy an underlying asset at a fixed strike price at any time until its expiration date.
- The flexibility of early exercise is a key characteristic that differentiates it from a European call option.
- Buyers of American call options anticipate an increase in the price of the underlying asset.
- The value of an American call option is influenced by factors such as the underlying asset's price, strike price, volatility, time decay, and interest rates.
Formula and Calculation
Unlike European call options, which can often be valued using closed-form analytical solutions like the Black-Scholes model, there is no simple, widely accepted closed-form formula for pricing an American call option. This is due to the embedded early exercise feature, which introduces a complex optimal stopping problem. The Black-Scholes model, for instance, assumes options can only be exercised at expiration and thus undervalues American options, especially those on dividend-paying stocks.
Instead, the valuation of an American call option typically relies on numerical methods. These methods include:
- Binomial Option Pricing Model: This model discretizes time into a series of steps, allowing for the evaluation of the option at each step to determine if early exercise is optimal.
- Finite Difference Methods: These methods solve the partial differential equations that govern option prices by approximating them on a grid.
- Monte Carlo Simulation (with adjustments for early exercise): While standard Monte Carlo methods are more suited for path-dependent options, adaptations exist to handle early exercise.
These numerical techniques account for the possibility of exercising the option at any point before the expiration date, evaluating the potential payoff of immediate exercise versus holding the option.
Interpreting the American Call Option
When interpreting an American call option, the holder focuses on the relationship between the underlying asset's current market price and the strike price. If the underlying asset's price rises significantly above the exercise price, the call option becomes in-the-money, gaining intrinsic value.
The decision to exercise an American call option early is crucial. Generally, it is not optimal to early exercise a non-dividend-paying American call option before its expiration, as holding the option provides the benefit of time decay and the possibility of further price appreciation without having to commit capital. However, if the underlying asset pays a dividend, exercising an American call option early just before a dividend payment might be rational to capture the dividend, provided the dividend is substantial enough to outweigh the remaining time value of the option.
Hypothetical Example
Consider an investor, Sarah, who believes that Company XYZ's stock, currently trading at $100 per share, will increase in value. Sarah decides to purchase an American call option on XYZ with a strike price of $105 and an expiration date three months from now. The premium for this option contract is $3.00 per share, meaning a standard contract representing 100 shares would cost her $300.
One month later, Company XYZ announces surprisingly strong earnings, and its stock price jumps to $115. At this point, Sarah's American call option is significantly in-the-money. She has two main choices:
- Sell the option: If the option's market price has risen, say to $12.00, she could sell her contract for $1,200 (100 shares * $12.00). Her profit would be $1,200 (revenue) - $300 (initial premium) = $900.
- Exercise the option: Sarah could exercise the option, buying 100 shares of XYZ stock at the exercise price of $105 per share, totaling $10,500. She could then immediately sell these shares in the open market at $115 per share, generating $11,500. Her net profit, after accounting for the initial premium, would be $11,500 - $10,500 - $300 = $700.
In this scenario, selling the option yields a higher profit for Sarah, demonstrating that exercising an American call option early is not always the most profitable strategy, especially when there is significant time value remaining.
Practical Applications
American call options are widely used in financial markets for various purposes, primarily speculation and hedging. Traders may purchase American call options to speculate on an anticipated rise in the price of an underlying asset. This provides leveraged exposure, as a small premium can control a larger value of the underlying asset.
For hedging, an investor holding a short position in a stock might buy an American call option to cap their potential losses if the stock price rises unexpectedly. Additionally, American call options are components in various complex options strategies, such as spreads and combinations, allowing sophisticated investors to tailor their risk-reward profiles.
The introduction of standardized options trading by the CBOE significantly simplified and democratized access to these powerful derivatives. The evolution of trading processes, from manual execution to electronic platforms, has also transformed how these options are bought and sold, increasing efficiency and accessibility for market participants.4 The Securities and Exchange Commission (SEC) plays a crucial role in regulating options trading in the U.S. to ensure fair and orderly markets and protect investors.3 The SEC's oversight includes rules pertaining to exchanges like the CBOE, which list and trade these contracts.2
Limitations and Criticisms
While American call options offer significant flexibility, they come with their own set of limitations and criticisms. The primary complexity lies in their valuation. As previously noted, the early exercise feature means there is no straightforward closed-form solution like the Black-Scholes model for European options, necessitating more complex numerical methods. This complexity can make it challenging for less experienced investors to accurately price and understand the fair value of an American call option.
Another limitation stems from the concept of time decay. As an option approaches its expiration date, its extrinsic value erodes. This means that even if the underlying asset price remains stable or moves slightly against the investor's position, the option can lose value simply due to the passage of time. The volatility of the underlying asset also plays a significant role; unexpected drops in volatility can negatively impact the option's value, even if the price of the underlying does not move drastically.
Furthermore, the leveraged nature of options trading, while offering potential for high returns, also exposes investors to the risk of substantial losses, potentially up to the entire premium paid if the option expires out-of-the-money.
American Call Option vs. European Call Option
The fundamental distinction between an American call option and a European call option lies in their exercise rights. An American call option grants the holder the flexibility to exercise the option and buy the underlying asset at the specified strike price at any time between the purchase date and the expiration date. In contrast, a European call option can only be exercised on its expiration date.
This difference in exercise flexibility impacts their valuation. Due to the added right of early exercise, an American call option will theoretically always be worth at least as much as, and typically more than, an identical European call option on the same underlying asset, assuming all other factors are equal. However, for non-dividend-paying stocks, it is generally not optimal to exercise an American call option before expiration, making its theoretical value often equal to that of a European call option in such cases. The Black-Scholes model, a widely used pricing model, was originally developed for European options because of their simpler exercise constraint.1
FAQs
What does "American" mean in an American call option?
The "American" in an American call option refers to the ability to exercise the option contract at any point before or on its specified expiration date. This contrasts with European options, which can only be exercised on the expiration date itself.
Can an American call option expire worthless?
Yes, an American call option can expire worthless if the price of the underlying asset is below the strike price at the time of expiration. In such a scenario, the option is "out-of-the-money," and exercising it would result in buying the asset at a higher price than its market value, making it economically irrational.
Why would someone buy an American call option?
Investors buy an American call option primarily for speculation on the rise of an underlying asset's price or for hedging against potential upward movements in price. It offers leveraged exposure, meaning a relatively small investment (the premium) can control a larger amount of the underlying asset.
Is it always better to have an American call option due to early exercise flexibility?
While the flexibility of early exercise is an advantage, it is not always optimal to use it. For non-dividend-paying stocks, exercising an American call option early typically means forfeiting the remaining time value of the option. However, for dividend-paying stocks, early exercise might be considered just before a dividend payment to capture the dividend.