Option contracts

What Are Option Contracts?

Option contracts are a type of derivatives that grant the purchaser the right, but not the obligation, to buy or sell an underlying asset at a predetermined strike price on or before a specified expiration date. As financial instruments, options derive their value from the price movements of the underlying asset, which can include stocks, stock indexes, exchange-traded funds (ETFs), or commodities. The seller of an option contract, known as the writer, is obligated to fulfill the contract if the buyer chooses to exercise it.

There are two primary types of option contracts:

• A call option gives the holder the right to buy the underlying asset.
• A put option gives the holder the right to sell the underlying asset.

The price paid for an option contract is called the premium.

History and Origin

The concept of option contracts can be traced back to ancient times, with one of the earliest anecdotes involving the Greek philosopher Thales of Miletus, who reportedly profited from predicting a large olive harvest by securing rights to olive presses. While early forms of options existed for centuries, including during the Dutch tulip mania of the 17th century, their modern, standardized exchange-traded form is a relatively recent development.

A pivotal moment in the history of option contracts occurred on April 26, 1973, with the founding of the Chicago Board Options Exchange (CBOE). Established by the Chicago Board of Trade, the CBOE became the first U.S. exchange to list standardized, exchange-traded stock options, revolutionizing the options market by introducing features like centralized clearing and set contract terms.¹² This standardization significantly increased the liquidity and accessibility of option contracts.

Also in 1973, a groundbreaking academic paper, "The Pricing of Options and Corporate Liabilities," by Fischer Black and Myron Scholes was published.¹⁰, ¹¹ This work, which developed a formula for valuing stock options, along with subsequent contributions by Robert C. Merton, laid the theoretical foundation for the modern derivatives market.⁷, ⁸, ⁹ Merton and Scholes were awarded the Nobel Memorial Prize in Economic Sciences in 1997 for their pioneering work on option valuation.⁵, ⁶

Key Takeaways

• Option contracts provide the holder with the right, but not the obligation, to buy or sell an underlying asset.
• They are a versatile derivatives instrument used for speculation, hedging, and income generation.
• The value of an option is influenced by factors such as the underlying asset's price, strike price, expiration date, volatility, and interest rates.
• The modern options market gained significant traction with the standardization introduced by exchanges like the CBOE and the development of robust pricing models.
• Trading option contracts involves inherent risks, including the potential loss of the entire premium paid.

Formula and Calculation

The most famous and widely used model for pricing European-style option contracts is the Black-Scholes-Merton (BSM) model. While the full formula is complex, it aims to estimate the theoretical price of a call option or put option by considering several key variables.

For a call option, the Black-Scholes formula is generally expressed as:

Where:

• (C) = Call option premium
• (S_0) = Current price of the underlying asset
• (K) = Strike price of the option
• (T) = Time to expiration date (in years)
• (r) = Risk-free interest rate
• (N(x)) = Cumulative standard normal distribution function
• (e) = Euler's number (the base of natural logarithms)

And (d_1) and (d_2) are calculated as:

Where:

• (\ln) = Natural logarithm
• (\sigma) = Volatility of the underlying asset

This formula demonstrates that the theoretical price of an option contract is a function of observable market inputs and the estimated future volatility. A similar formula exists for pricing put options, derived through an concept known as put-call parity.

Interpreting Option Contracts

Interpreting option contracts involves understanding the rights and obligations they confer and how their value changes in response to various market factors. For a buyer, holding an option provides leverage, as a small premium can control a larger quantity of the underlying asset. This means potential for significant percentage gains if the underlying asset moves favorably. However, if the asset moves unfavorably or remains stagnant, the option may expire worthless, resulting in the loss of the entire premium paid.

For a seller (writer) of an option, the interpretation is different. They receive the premium upfront but take on the obligation to buy or sell the underlying asset if the option is exercised. This involves balancing the income received from the premium against the potential for substantial losses if the market moves sharply against their position. The perceived volatility of the underlying asset heavily influences the option's price; higher expected volatility generally leads to higher option premiums, reflecting the increased potential for larger price swings.

Hypothetical Example

Imagine an investor believes that XYZ Corp.'s stock, currently trading at $100 per share, will rise in the next three months. Instead of buying 100 shares directly for $10,000, they decide to buy a call option contract.

Scenario:

• Underlying Asset: XYZ Corp. stock
• Current Stock Price: $100
• Option Type: Call
• Strike Price: $105
• Expiration Date: 3 months from now
• Premium: $3.00 per share ($300 for one contract, as each contract typically represents 100 shares)

Outcome 1: Stock Price Rises
Suppose in two months, XYZ Corp. announces positive news, and its stock price jumps to $115 per share. The investor's call option, with a strike price of $105, is now "in the money" because the market price ($115) is above the strike price. The investor can:

1. Exercise the option: Buy 100 shares of XYZ Corp. at $105 per share (totaling $10,500), and then immediately sell them in the open market at $115 per share (totaling $11,500).
   • Profit from stock: $11,500 - $10,500 = $1,000
   • Net profit (after accounting for premium): $1,000 - $300 = $700
2. Sell the option: The option itself would now be worth more than its $3 premium due to the stock price increase. The investor could sell the option contract on the open market, likely realizing a similar profit without needing to buy the shares.

Outcome 2: Stock Price Falls or Stays Flat
Suppose by the expiration date, XYZ Corp.'s stock price is $102.00. The call option, with a strike price of $105, is "out of the money" because the market price is below the strike price. The investor would not exercise the option, as they could buy the shares cheaper directly in the market. The option expires worthless, and the investor loses the $300 premium paid for the contract.

This example illustrates how option contracts offer potential for magnified gains but also carry the risk of losing the entire investment (the premium).

Practical Applications

Option contracts serve various practical applications in financial markets, ranging from risk management to generating income and enhancing speculative strategies.

• Hedging: Investors and corporations use options to protect existing portfolios or future transactions from adverse price movements. For instance, an investor holding a stock portfolio might buy put options on those stocks to limit potential losses if the market declines. This acts like an insurance policy, capping downside risk.
• Income Generation: Option writing strategies, such as selling covered calls, allow investors to generate income (the premium) on assets they already own. This is a common strategy for investors looking to enhance returns from their long-term holdings.
• Speculation: Traders use option contracts to profit from anticipated price movements of an underlying asset. Due to their inherent leverage, options can provide significant returns on a relatively small capital outlay if the price forecast is accurate.
• Leverage: Options enable investors to control a larger value of an underlying asset with a smaller amount of capital than directly buying or selling the asset. This magnification of exposure can amplify both gains and losses.
• Regulation: The trading of option contracts is subject to extensive regulatory oversight to ensure fair and orderly markets and protect investors. In the United States, key bodies like the Securities and Exchange Commission (SEC), the Financial Industry Regulatory Authority (FINRA), and the Commodity Futures Trading Commission (CFTC) oversee various aspects of options trading.⁴ These regulators establish rules concerning position limits, margin requirements, and disclosure to maintain market integrity. The Cboe Global Markets, Inc., for example, reported 3.8 billion contracts traded across its four options exchanges in 2024, demonstrating the significant scale and activity in this regulated market.³

Limitations and Criticisms

While option contracts offer valuable tools for investors, they also come with inherent limitations and criticisms that warrant careful consideration.

• Complexity: Option strategies can range from simple outright purchases to highly complex multi-leg combinations, requiring a deep understanding of market dynamics, pricing models, and risk profiles. Misunderstanding these complexities can lead to unexpected losses.
• Time Decay (Theta): Unlike direct ownership of an underlying asset, option contracts have a finite life. As the expiration date approaches, the time value component of the option's premium erodes, a phenomenon known as "time decay." This works against option buyers and can make it challenging to profit unless the underlying asset moves significantly and quickly.
• Volatility Risk: Options prices are highly sensitive to changes in the implied volatility of the underlying asset. An unexpected drop in volatility can negatively impact the value of purchased options, even if the underlying asset's price moves favorably.
• Leverage Amplifies Losses: While leverage can amplify gains, it equally amplifies losses. For option buyers, the maximum loss is typically limited to the premium paid, but this can still represent a 100% loss of the capital invested in the option. For option sellers, especially those writing uncovered options, the potential for losses can be theoretically unlimited.
• Liquidity Concerns: While major options on highly traded stocks or indexes typically have good liquidity, options on less popular securities may have wide bid-ask spreads, making it difficult to enter or exit positions efficiently without significant transaction costs.
• Regulatory Scrutiny: Due to their leveraged nature and potential for rapid value changes, option contracts are subject to strict regulatory oversight by bodies such as the U.S. Securities and Exchange Commission (SEC). The SEC provides educational resources to help investors understand the basics and risks associated with options trading.² However, despite regulation, instances of misuse or aggressive speculation can still occur, leading to significant financial setbacks for uninformed participants.

Option Contracts vs. Futures Contracts

Option contracts and futures contracts are both types of derivatives, meaning their value is derived from an underlying asset. However, a key distinction lies in the obligation they impose on the holder.

The fundamental difference is the "right versus obligation." An option buyer can walk away from the contract if it's not profitable, only losing the premium paid. Conversely, a futures contract holder is obligated to fulfill the contract, either by taking delivery of the underlying asset or making a cash settlement, unless the position is closed out before expiration. This makes futures generally riskier for the initial holder due to the mandatory commitment. Both are used for hedging and speculation but involve different risk profiles and capital requirements.

FAQs

1. What is the difference between a call option and a put option?

A call option gives the holder the right to buy an underlying asset at a specific price, while a put option gives the holder the right to sell the underlying asset at a specific price. Both have an expiration date and require paying a premium.

2. Can I lose more than the premium I pay for an option?

If you buy an option, your maximum loss is typically limited to the premium you paid for the contract. However, if you write (sell) an option, especially an "uncovered" or "naked" option where you do not own the underlying asset, your potential losses can be theoretically unlimited.

3. What does "in the money," "at the money," and "out of the money" mean for options?

• In the money (ITM): For a call option, the underlying asset's price is above the strike price. For a put option, the underlying asset's price is below the strike price.
• At the money (ATM): The underlying asset's price is equal to or very close to the strike price.
• Out of the money (OTM): For a call option, the underlying asset's price is below the strike price. For a put option, the underlying asset's price is above the strike price. OTM options generally have no intrinsic value and rely solely on time value.

4. How are option contracts regulated?

In the United States, option contracts are primarily regulated by the Securities and Exchange Commission (SEC), which oversees securities markets, and the Commodity Futures Trading Commission (CFTC), which oversees commodity and futures contracts. Additionally, self-regulatory organizations like the Financial Industry Regulatory Authority (FINRA) and individual exchanges like Cboe Global Markets enforce rules to protect investors and ensure market integrity.¹

5. What are some common uses of option contracts?

Option contracts are commonly used for speculation, allowing investors to profit from anticipated price movements with leverage. They are also widely used for hedging to mitigate portfolio risk, and for generating income through various selling strategies.