Equity option

What Is Equity Option?

An equity option is a type of options contract that grants the holder the right, but not the obligation, to buy or sell a specified number of shares of an underlying stock at a predetermined price, known as the strike price, on or before a specific expiration date. As a derivative, its value is derived from the price movement of the underlying equity. Equity options fall under the broader category of financial instruments, specifically derivatives, which are used for various purposes including hedging, speculation, and income generation.

History and Origin

The concept of options has roots extending back centuries, with unlisted, bilaterally negotiated options traded in the United States as early as the 1790s. For many decades, the options market remained small and largely unregulated, with over-the-counter (OTC) options being the primary form of trading. These OTC options involved direct links between buyers and sellers and often had complex terms of sale¹³.

A significant transformation occurred in 1973 with the establishment of the Chicago Board Options Exchange (CBOE). The CBOE introduced the first U.S. listed options market, standardizing contract terms, centralizing liquidity, and creating a dedicated clearing entity, the Options Clearing Corporation (OCC), to guarantee contract fulfillment¹²,,¹¹. This standardization and centralization were pivotal in making equity options more accessible and transparent. Trading commenced on April 26, 1973, in a space that was formerly the Chicago Board of Trade's smoking lounge, marking the beginning of the modern listed options market¹⁰,.

Key Takeaways

• An equity option provides the holder the right, but not the obligation, to buy or sell an underlying stock.
• The primary types are call options (right to buy) and put options (right to sell).
• Options have a fixed strike price and an expiration date, after which they become worthless.
• The price of an option, known as the premium, is influenced by factors such as the underlying stock price, volatility, and time to expiration.
• Equity options can be used for strategies ranging from income generation to managing portfolio risk.

Formula and Calculation

The most renowned model for pricing European-style equity options is the Black-Scholes Model, developed by Fischer Black and Myron Scholes in 1973. This model provides a theoretical value for a European call option (C) and a European put option (P), taking into account several key variables.⁹

For a call option:

For a put option:

Where:
[
d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma \sqrt{T}}
]
[
d_2 = d_1 - \sigma \sqrt{T}
]

Variables:

• (C): Theoretical call option price
• (P): Theoretical put option price
• (S_0): Current price of the underlying asset (stock)
• (K): Strike price of the option
• (T): Time to expiration date (in years)
• (r): Risk-free interest rate (annualized)
• (\sigma): Volatility of the underlying asset's returns
• (N(\cdot)): The cumulative standard normal distribution function
• (e): Euler's number (approximately 2.71828)
• (\ln): Natural logarithm

This formula helps assess the fair value of an equity option under certain assumptions, including that the stock price follows a log-normal distribution and that no dividends are paid during the option's life⁸,⁷.

Interpreting the Equity Option

The interpretation of an equity option depends on whether one is the buyer (holder) or the seller (writer) and whether it's a call option or a put option.

For a buyer of a call option, the expectation is that the underlying asset's price will rise significantly above the strike price before expiration. The higher the stock price goes above the strike, the more profitable the option becomes. Conversely, if the stock price remains below the strike, the option will expire worthless, and the buyer loses only the initial premium paid.

For a buyer of a put option, the expectation is that the underlying stock price will fall significantly below the strike price. The lower the stock price drops below the strike, the more the put option gains value. If the stock price stays above the strike, the put option expires worthless.

Sellers (writers) of options have different motivations. A call option writer expects the stock price to stay below the strike, while a put option writer expects it to stay above the strike. The seller receives the premium upfront but takes on the obligation to buy or sell the stock if the option is exercised. Understanding the relationship between the option's premium, the underlying asset's price, and the time remaining until expiration is crucial for successful options trading.

Hypothetical Example

Consider an investor, Alice, who believes that Company XYZ's stock, currently trading at $50 per share, will increase in value. She decides to purchase a call option on XYZ with a strike price of $55 and an expiration date three months from now. The premium for this equity option is $2.00 per share, meaning each contract (representing 100 shares) costs her $200 ($2.00 x 100 shares).

Scenario 1: Stock Price Rises
Two months later, Company XYZ's stock price jumps to $65 per share. Alice's call option is now "in the money" because the stock price ($65) is above her strike price ($55). She can exercise her option to buy 100 shares at $55 each and immediately sell them on the open market at $65.

• Value of shares purchased: 100 shares * $55 = $5,500
• Value of shares sold: 100 shares * $65 = $6,500
• Gross profit from exercise and sale: $6,500 - $5,500 = $1,000
• Net profit (after deducting premium paid): $1,000 - $200 = $800

Alternatively, Alice could sell her equity option on the open market before expiration, as its value would have increased due to the rise in the underlying asset.

Scenario 2: Stock Price Falls or Stays Flat
If, by the expiration date, Company XYZ's stock price remains below or at $55 (e.g., $53), Alice's call option would expire worthless. In this case, she would not exercise the option, and her total loss would be limited to the initial premium paid, which is $200.

Practical Applications

Equity options serve various purposes for investors and traders in real-world financial markets:

• Income Generation: Investors can sell (write) equity options, such as covered calls or cash-secured put options, to collect the premium from buyers. This strategy can generate regular income, particularly in sideways or moderately trending markets.
• Risk Management (Hedging): Options can be used to protect existing stock positions. For example, an investor holding shares of a stock can buy put options on that stock to protect against a potential price decline, similar to buying insurance. This form of hedging limits potential losses while allowing for upside participation.
• Speculation: Traders can use equity options to speculate on the price direction of an underlying asset with a potentially smaller capital outlay compared to buying the shares outright. Options offer leverage, meaning a small change in the underlying stock price can lead to a significant percentage change in the option's value. Reports indicate that "zero-day to expiry" options, a highly speculative form of equity option, have recently accounted for over 60% of all S&P 500 options trading activity⁶.
• Portfolio Diversification: While not a primary means of portfolio diversification in the traditional sense, options can be used to add different risk/reward profiles to a portfolio or to gain exposure to sectors or market movements without direct stock ownership.
• Arbitrage: Experienced traders may use options to exploit small price discrepancies between different markets or related securities, engaging in arbitrage strategies.

Regulatory bodies such as the Securities and Exchange Commission (SEC) and the Financial Industry Regulatory Authority (FINRA) oversee options markets to ensure fair and orderly trading, protect investors from fraud, and enforce securities laws⁵,.

Limitations and Criticisms

Despite their utility, equity options come with significant limitations and criticisms:

• Complexity: Options trading involves complex strategies and terminology, which can be challenging for inexperienced investors. Understanding concepts like the "Greeks" (delta, gamma, theta, vega) and various multi-leg strategies requires considerable knowledge and experience⁴.
• Time Decay (Theta): Unlike stocks, options have a finite life and are subject to time decay. As an equity option approaches its expiration date, its extrinsic value erodes, meaning its price can fall even if the underlying asset remains stable. This inherent characteristic makes options a depreciating asset for buyers.
• Leverage and Amplified Losses: While leverage can amplify gains, it can also significantly amplify losses. For option buyers, the entire premium paid can be lost if the option expires out-of-the-money. For option writers (sellers), especially of uncovered options, theoretical losses can be unlimited if the underlying asset moves sharply against their position³.
• Volatility Risk: The value of an equity option is highly sensitive to changes in the underlying stock's volatility. Unexpected changes in volatility can significantly impact option prices, making them more unpredictable than direct stock ownership.
• Regulatory Scrutiny: Due to their complexity and potential for significant losses, options trading is highly regulated. Investors are often required to be approved by their brokerage firm for specific options trading levels based on their experience and financial situation. The SEC and FINRA impose rules on position limits, margin requirements, and reporting standards to safeguard investors and maintain market integrity²,¹,.

Equity Option vs. Futures Contract

While both equity options and futures contracts are derivatives used for speculation and hedging, they differ fundamentally in their obligations and characteristics.

The key point of confusion often arises because both allow investors to gain exposure to an underlying asset's price movements without owning the asset directly. However, the critical distinction lies in the optionality versus the obligation. An equity option provides flexibility, while a futures contract mandates a transaction.

FAQs

What does it mean if an equity option is "in the money"?

An equity option is "in the money" if exercising it would result in a profit. For a call option, this means the underlying asset's current price is above the strike price. For a put option, it means the underlying asset's current price is below the strike price.

How is the premium of an equity option determined?

The premium of an equity option is determined by several factors, including the current price of the underlying asset, the strike price, the time remaining until expiration date, the expected volatility of the underlying asset, and prevailing risk-free interest rates. Market supply and demand also play a role.

Can an equity option be exercised before its expiration date?

Most standardized equity options traded on exchanges are American-style options, which means they can be exercised at any time up to and including the expiration date. European-style options, in contrast, can only be exercised on the expiration date itself. The type of option determines when it can be exercised.