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Call an option

What Is a Call Option?

A call option is a financial instrument that gives the holder the right, but not the obligation, to buy an underlying asset at a specified price, known as the strike price, on or before a particular date, the expiration date. As a type of derivative, call options derive their value from the performance of the underlying asset, which can be stocks, commodities, or indexes. Investors typically purchase call options when they anticipate an increase in the underlying asset's price, aiming to profit from the upward movement. Conversely, a seller, or "writer," of a call option is obligated to sell the underlying asset at the strike price if the option is exercised by the holder.

History and Origin

While rudimentary forms of options contracts have existed for centuries, their modern, standardized exchange-traded form began with the establishment of the Chicago Board Options Exchange (CBOE). The CBOE opened its doors on April 26, 1973, marking a significant milestone in financial markets by introducing standardized options contracts for the first time15, 16. Before this, options were traded over-the-counter with varying terms, making them illiquid and complex14. The standardization provided by the CBOE, along with the subsequent development of a robust pricing model, propelled options trading into the mainstream12, 13. Just months after the CBOE's inception in 1973, Fischer Black and Myron Scholes published their groundbreaking paper, "The Pricing of Options and Corporate Liabilities," which introduced the Black-Scholes model10, 11. This mathematical framework provided a theoretical valuation for European-style options, revolutionizing how these instruments were priced and understood. Robert C. Merton also made significant contributions to the model's development; Black, Scholes, and Merton are widely credited for laying the foundation for modern derivative markets8, 9.

Key Takeaways

  • A call option grants the holder the right, but not the obligation, to buy an underlying asset.
  • It is typically bought by investors who expect the underlying asset's price to rise.
  • The seller (writer) of a call option is obligated to sell the underlying asset if the option is exercised.
  • Call options offer amplified returns (leverage) but also carry the risk of losing the entire premium paid7.
  • Standardized call options began trading on the Chicago Board Options Exchange (CBOE) in 1973.

Formula and Calculation

The theoretical value of a call option, particularly a European-style option, can be estimated using models like the Black-Scholes model. While the full Black-Scholes formula is complex, it considers several key variables:

C=S0N(d1)−Ke−rTN(d2)C = S_0 N(d_1) - K e^{-rT} N(d_2)

Where:

  • (C) = Call option price
  • (S_0) = Current price of the underlying asset
  • (K) = Strike price of the option
  • (r) = Risk-free interest rate
  • (T) = Time to expiration date (in years)
  • (N(x)) = Cumulative standard normal distribution function
  • (e) = Euler's number (the base of the natural logarithm)
  • (d_1) and (d_2) are calculated as: d1=ln⁡(S0/K)+(r+σ2/2)TσTd_1 = \frac{{\ln(S_0/K) + (r + \sigma^2/2)T}}{{\sigma \sqrt{T}}} d2=d1−σTd_2 = d_1 - \sigma \sqrt{T} Where (\ln) is the natural logarithm and (\sigma) is the volatility of the underlying asset.

This formula helps determine the fair premium of a call option, considering factors beyond just the current price and strike price.

Interpreting the Call Option

Interpreting a call option involves understanding its potential profitability based on the underlying asset's price movement relative to the strike price. A call option is considered "in-the-money" when the underlying asset's current market price is above the strike price, meaning it has intrinsic value. Conversely, it is "out-of-the-money" if the underlying price is below the strike price, possessing only time value. If the underlying price is exactly at the strike price, it is "at-the-money."

The value of a call option increases as the underlying asset's price rises, as it offers the right to buy at a lower, predetermined price. The longer the time until the expiration date, the greater the option's time value, reflecting more opportunities for the underlying asset to move favorably. Volatility also significantly impacts a call option's value; higher volatility generally leads to a higher call premium because there's a greater probability of the price moving substantially above the strike price.

Hypothetical Example

Suppose an investor believes that XYZ Corp. stock, currently trading at $50 per share, will increase in value. The investor decides to purchase a call option with a strike price of $55 and an expiration date three months from now. The premium for this call option is $2.00 per share. Since one option contract typically represents 100 shares, the total cost for one contract is $2.00 * 100 = $200.

Scenario 1: XYZ Corp. stock rises to $60 before the expiration date.
The investor can now exercise the call option, buying 100 shares at the $55 strike price and immediately selling them in the market at $60.
Profit per share = $60 (market price) - $55 (strike price) = $5.00
Gross profit = $5.00 * 100 shares = $500
Net profit = $500 (gross profit) - $200 (premium paid) = $300.

Scenario 2: XYZ Corp. stock falls to $45 by the expiration date.
The option is now out-of-the-money, as the market price ($45) is below the strike price ($55). There is no incentive to exercise the option.
The call option expires worthless, and the investor loses the entire $200 premium paid.

Practical Applications

Call options are versatile financial instruments used in various investment strategies. One primary application is speculation. Traders might buy call options to bet on an upward movement in a stock or index, seeking to capitalize on amplified gains due to the leverage inherent in options. For instance, in a bull market environment, purchasing calls can offer significant returns if the underlying asset's price surpasses the strike price.

Beyond outright speculation, call options are also crucial tools for hedging. While typically associated with mitigating downside risk through put options, calls can be used defensively in certain scenarios. For example, a portfolio manager holding a short position in a stock might buy a call option to cap potential losses if the stock's price unexpectedly rises.

Furthermore, call options are integral components of more complex options strategies, such as covered calls, call spreads, and collars. Regulatory bodies like the U.S. Securities and Exchange Commission (SEC) actively oversee the options market to ensure fairness, transparency, and investor protection, enforcing rules on trading practices and disclosures5, 6. These regulations aim to manage the inherent risks associated with call options and other derivative products.

Limitations and Criticisms

While call options offer compelling opportunities, they come with notable limitations and risks. One significant drawback is the finite lifespan of a call option; it has an expiration date, after which it becomes worthless if not exercised or sold4. This "wasting asset" characteristic means that time decay (theta) constantly erodes the option's time value as expiration approaches, even if the underlying asset's price remains stable or moves slightly favorably.

Another major criticism is the amplified risk due to leverage3. While leverage can magnify profits, it can equally magnify losses. An investor can lose 100% of the premium paid for a call option if the underlying asset's price does not move above the strike price by expiration. This makes call options unsuitable for all investors, particularly those with a low risk tolerance or limited capital.

The complexity of options contracts also poses a limitation. Understanding how factors like volatility, interest rates, and dividends affect an option's premium requires a solid grasp of financial concepts and pricing models2. Mispricing or misinterpreting these dynamics can lead to suboptimal trading decisions. Academic research often highlights various financial and non-financial risks in derivatives markets, including liquidity risk, credit risk, and model risk, which can affect options trading1.

Call Option vs. Put Option

A fundamental distinction exists between a call option and a put option, though both are types of options contracts. The primary difference lies in the right they convey to the holder.

A call option grants the holder the right to buy the underlying asset at the strike price on or before the expiration date. Investors typically buy call options when they anticipate a price increase in the underlying asset, aiming to profit from an upward market movement (a bull market outlook).

In contrast, a put option grants the holder the right to sell the underlying asset at the strike price on or before the expiration date. Investors typically purchase put options when they anticipate a price decrease, aiming to profit from a downward market movement (a bear market outlook) or to hedge against potential losses in an existing long position.

The confusion between the two often arises from their inverse relationship to market direction. A call option benefits from rising prices, while a put option benefits from falling prices.

FAQs

What does it mean to "call" an option?

To "call" an option, in the context of a call option, refers to the right it gives the holder to "call away" or buy the underlying asset from the option writer at the predetermined strike price. It signifies the bullish stance of the option buyer.

Can I lose more than my initial investment when buying a call option?

When buying a call option, the maximum loss is limited to the premium paid for the option. However, if you are the writer (seller) of an uncovered call option, your potential losses are theoretically unlimited, as the price of the underlying asset can rise indefinitely.

How does volatility affect a call option's price?

Volatility has a positive correlation with a call option's premium. Higher expected volatility in the underlying asset increases the probability of the price moving significantly above the strike price before the expiration date, thus increasing the call option's value.

What is the "break-even" point for a call option buyer?

The break-even point for a call option buyer is the strike price plus the premium paid per share. For the call option to be profitable, the underlying asset's price must rise above this break-even point by the expiration date.