Call_option: Meaning, Criticisms & Real-World Uses

What Is a Call Option?

A call option is a financial contract that grants the buyer the right, but not the obligation, to purchase an underlying asset at a predetermined strike price on or before a specified expiration date. This type of option contract is a core component of derivatives, a broader financial category whose value is derived from an underlying asset, such as a stock, commodity, or index. When an investor buys a call option, they typically anticipate that the price of the underlying asset will increase above the strike price before the expiration, allowing them to profit from the difference. In exchange for this right, the buyer pays a non-refundable fee, known as the premium, to the seller (or writer) of the call option.

History and Origin

The modern options market, and thus the widespread trading of call options, has its roots in the establishment of the Chicago Board Options Exchange (CBOE). Prior to the CBOE's founding, options were traded over-the-counter with varying and often complex terms, making them less accessible and liquid. The CBOE, launched on April 26, 1973, by the Chicago Board of Trade (CBOT), revolutionized the market by introducing standardized options contracts²⁰, ²¹. This standardization paved the way for a transparent and liquid exchange, which initially listed only call options before expanding to include put options in 1977¹⁹.

A pivotal moment in the pricing and understanding of options, including call options, occurred with the publication of the Black-Scholes model. In 1973, Fischer Black and Myron Scholes published their groundbreaking paper, "The Pricing of Options and Corporate Liabilities," in the Journal of Political Economy¹⁶, ¹⁷, ¹⁸. This mathematical model provided a formula for theoretically calculating the fair price of European-style options, integrating variables such as the underlying asset's price, strike price, time to expiration, volatility, and the risk-free interest rate. The Black-Scholes model significantly contributed to the growth and sophistication of the derivatives market by offering a quantitative framework for valuation.

Key Takeaways

A call option grants the buyer the right, but not the obligation, to buy an underlying asset at a set strike price by a specific expiration date.
Buyers of call options anticipate an increase in the price of the underlying asset.
The maximum loss for a call option buyer is limited to the premium paid for the contract.
Call options are widely used for speculation on upward price movements and for hedging purposes.
One standard stock options contract typically represents 100 shares of the underlying stock.

Formula and Calculation

The theoretical price of a European-style call option can be calculated using the Black-Scholes formula. While the full derivation is complex, the formula for a call option price ((C)) is:

$C = S_0 N(d_1) - K e^{-rT} N(d_2)$

Where:

(S_0) = Current price of the underlying asset
(K) = Strike price of the option
(T) = Time to expiration date (in years)
(r) = Annualized risk-free rate
(N(x)) = The cumulative standard normal distribution function
(e) = The base of the natural logarithm (approximately 2.71828)
(d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}})
(d_2 = d_1 - \sigma\sqrt{T})
(\ln) = Natural logarithm
(\sigma) = Volatility of the underlying asset

This formula helps assess the fair value of a call option based on several market variables, assisting traders in making informed decisions.

Interpreting the Call Option

Interpreting a call option involves understanding its potential profitability and risk profile based on the underlying asset's price relative to the strike price.

In-the-Money (ITM): A call option is in-the-money when the underlying asset's current market price is above the strike price. For example, if a call option has a strike price of $50 and the stock is trading at $55, the option is $5 in-the-money. This means it has intrinsic value and would yield a profit if exercised immediately (before accounting for the premium paid).
At-the-Money (ATM): A call option is at-the-money when the underlying asset's price is equal to or very close to the strike price.
Out-of-the-Money (OTM): A call option is out-of-the-money when the underlying asset's price is below the strike price. These options only have time value and no intrinsic value, and they will expire worthless if the underlying price does not rise above the strike price by expiration.

The decision to exercise or sell a call option depends on whether it is in-the-money and profitable, considering the initial premium paid.

Hypothetical Example

Consider an investor, Sarah, who believes that shares of Company XYZ, currently trading at $95 per share, will increase significantly in the next two months. She decides to buy a call option on XYZ.

Contract Details: Sarah buys one XYZ call option contract with a strike price of $100 and an expiration date two months from now.
Premium Paid: The call option has a premium of $3.00 per share. Since one option contract typically represents 100 shares, Sarah pays $3.00 x 100 = $300 for the contract. This $300 is her maximum potential loss.
Scenario 1: Price Rises: One month later, Company XYZ announces positive earnings, and its stock price jumps to $110 per share. Sarah's call option is now in-the-money. She can:
- Exercise the option: Buy 100 shares of XYZ at the strike price of $100 per share ($10,000 total) and then immediately sell them in the market at $110 per share ($11,000 total). Her profit would be $11,000 - $10,000 (purchase price) - $300 (premium) = $700.
- Sell the option: The value of her call option has likely increased due to the rise in the underlying stock price. She could sell her option contract in the open market for a profit. If the option's value increases to, say, $12 per share, she could sell it for $1,200, resulting in a profit of $1,200 - $300 = $900. Many option traders prefer to sell the option rather than exercise it and deal with the underlying shares.
Scenario 2: Price Falls or Stays Flat: By the expiration date, if XYZ's stock price is below the $100 strike price (e.g., $98 or $90), Sarah's call option will expire worthless. She would not exercise the right to buy at $100 when she can buy it cheaper in the market. In this case, she loses the entire $300 premium she paid.

This example illustrates how a call option can offer significant leverage compared to buying the shares directly, but also highlights the risk of losing the entire premium.

Practical Applications

Call options are versatile financial instruments used by investors for various strategic purposes in the financial markets:

Speculation: One of the most common uses of call options is for speculation on an upward movement in the price of an underlying asset. By paying a relatively small premium, an investor can gain exposure to a larger block of shares, potentially magnifying returns if the asset price rises significantly.
Income Generation (Selling Covered Calls): Investors who own the underlying stock can sell call options against their holdings, a strategy known as a "covered call." This generates immediate income from the premium received. If the stock price stays below the strike price, the option expires worthless, and the investor keeps the premium and their shares. If the price rises above the strike price, the shares may be "called away" (sold) at the strike price, but the investor still profits from the premium and any appreciation up to the strike price.
Portfolio Diversification and Risk Management: While complex, options can be part of a broader portfolio strategy to add income or protect against certain market movements. However, investors should be aware that "options trading can come with significant risks," and broker-dealers are required to perform due diligence before approving accounts for options trading to ensure it is appropriate for the customer¹⁴, ¹⁵. Firms like FINRA provide guidelines for broker-dealers regarding risk disclosures and supervision of options trading accounts¹³.

Limitations and Criticisms

While call options offer flexibility and potential leverage, they come with inherent limitations and risks:

Time Decay (Theta): Options have a finite lifespan, expiring on a specific date. As the expiration date approaches, the extrinsic (or time) value of an option erodes, a phenomenon known as time decay. Even if the underlying asset's price moves favorably, if it does not do so quickly enough, the option can lose value and expire worthless¹².
Volatility Risk: The value of a call option is highly sensitive to changes in the volatility of the underlying asset. Unexpected changes in implied volatility can significantly impact an option's premium, potentially leading to losses even if the underlying asset's price moves in the anticipated direction¹¹.
Complexity: Options trading strategies can be highly complex, ranging from simple outright buys to intricate multi-leg spreads. Understanding the nuances of these strategies, including their risk-reward profiles and the Greek letters (e.g., Delta, Gamma, Theta, Vega) that measure various sensitivities, requires substantial knowledge and experience¹⁰.
Potential for Total Loss: For the buyer of a call option, the entire premium paid can be lost if the option expires out-of-the-money. For call option sellers (writers), especially those selling "naked" (uncovered) calls without owning the underlying asset, the potential for losses can be theoretically unlimited if the underlying asset's price rises significantly⁸, ⁹. Regulators like the U.S. Securities and Exchange Commission (SEC) and the Financial Industry Regulatory Authority (FINRA) emphasize the substantial risks associated with options trading, including the possibility of losing more than the initial investment for sellers⁶, ⁷.

Call Option vs. Put Option

A call option and a put option are the two primary types of options contracts, representing opposite rights and expectations.

A call option gives the holder the right to buy the underlying asset at a specified strike price by the expiration date. Buyers of call options typically anticipate that the price of the underlying asset will increase. Their potential profit is theoretically unlimited as the underlying price rises, while their maximum loss is limited to the premium paid.

Conversely, a put option gives the holder the right to sell the underlying asset at a specified strike price by the expiration date. Buyers of put options generally expect the price of the underlying asset to decrease⁵. Their potential profit increases as the underlying price falls (down to zero), and their maximum loss is also limited to the premium paid.

The confusion often arises because both are derivatives that offer the right, not the obligation, to perform a transaction. However, the directional view and the action (buy vs. sell) are diametrically opposed for the buyer of each type of option.

FAQs

What does "exercise" a call option mean?

To exercise a call option means the buyer of the option contract formally invokes their right to purchase the underlying asset at the agreed-upon strike price. This typically occurs when the underlying asset's market price is above the strike price, making the purchase at the lower strike price profitable⁴.

What is the maximum loss when buying a call option?

When you buy a call option, your maximum potential loss is limited to the premium you paid for the contract. If the underlying asset's price does not rise above the strike price by the expiration date, the option expires worthless, and you lose the premium³.

Can a call option be sold before its expiration date?

Yes, most exchange-traded call options can be sold in the open market at any time before their expiration date. This allows buyers to realize profits or cut losses without needing to exercise the option and take possession of the underlying asset².

Is options trading suitable for beginners?

Generally, options trading is considered complex and carries significant risks, making it less suitable for most beginner investors. It requires a deep understanding of market dynamics, various strategies, and risk management. Financial regulators often advise that investors should be aware of the potential to lose all of their initial investment, and sometimes more, depending on the strategy¹.