Skip to main content
diversification.com
← Back to E Definitions

European options

What Are European Options?

A European option is a type of options contract that can only be exercised on its expiration date. This restriction on exercise stands in contrast to other types of options, such as American options, which permit exercise at any time before or on the expiration date. European options are foundational instruments within the broader category of financial derivatives, allowing investors to speculate on or hedge against price movements of an underlying asset without owning the asset itself.

History and Origin

The concept of options trading has roots stretching back to ancient times, with early forms mentioned by Aristotle. However, the modern, standardized exchange-traded options market, which includes European options, began with the establishment of the Chicago Board Options Exchange (CBOE) in 1973. Prior to this, options were primarily traded over-the-counter (OTC) with unstandardized terms22, 23. The CBOE's innovation was to standardize options contracts, making them more transparent and liquid.21

A pivotal moment in the pricing of European options, and derivatives in general, occurred in 1973 with the publication of "The Pricing of Options and Corporate Liabilities" by Fischer Black and Myron Scholes in the Journal of Political Economy.18, 19, 20 This groundbreaking paper introduced what became known as the Black-Scholes model, providing a mathematical framework for valuing options, particularly European options. Robert C. Merton also contributed significantly to the model's development and extensions.16, 17 The development of this model, coupled with the standardization of exchange-traded options, greatly expanded the derivatives market and facilitated the widespread use of options by investors.14, 15

Key Takeaways

  • European options can only be exercised on their specified expiration date, unlike American options which can be exercised at any time up to and including expiration.
  • They are a fundamental type of financial derivative used for both speculation and hedging.
  • The pricing of European options is famously modeled by the Black-Scholes formula.
  • European options typically trade at a lower option premium compared to their American counterparts due to the restricted exercise feature.
  • Their simpler exercise characteristic makes them more amenable to mathematical modeling.

Formula and Calculation

The most well-known formula for pricing a European option is the Black-Scholes model. This model calculates the theoretical fair value of a European call or put option by considering several variables: the current price of the underlying asset, the option's strike price, the time until expiration, the risk-free rate, and the volatility of the underlying asset.

For a European call option ($C$), the formula is:

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

For a European put option ($P$), the formula is:

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

Where:

  • (S_0) = Current price of the underlying asset
  • (K) = Strike price of the option
  • (T) = Time to expiration (in years)
  • (r) = Risk-free interest rate (annualized)
  • (\sigma) = Volatility of the underlying asset's returns (annualized standard deviation)
  • (N(x)) = The cumulative standard normal distribution function
  • (e) = Euler's number (approximately 2.71828)

And (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}

This formula assumes that the option is European-style and can only be exercised at expiration, among other conditions such as constant volatility and no dividends during the option's life13.

Interpreting the European Option

Interpreting a European option involves understanding its value components and how market factors influence its price. The premium of a European option consists of two main parts: intrinsic value and time value. Intrinsic value is the immediate profit if the option were exercised (though European options cannot be exercised early). For a call option, it's the underlying price minus the strike price (if positive, otherwise zero). For a put, it's the strike price minus the underlying price (if positive, otherwise zero).

The time value represents the additional premium paid for the potential for the option to increase in intrinsic value before expiration. It accounts for the time remaining until expiration and the expected volatility of the underlying asset. As a European option approaches its expiration date, its time value erodes, a phenomenon known as time decay or theta decay. By expiration, a European option's value is purely its intrinsic value, if any; otherwise, it expires worthless.

Hypothetical Example

Consider a European call option on ABC stock with a strike price of $100 and an expiration date three months from now. The current market price of ABC stock is $98. The option premium is $3.

  1. Purchase: An investor buys one European call option contract (representing 100 shares) for $300 ($3 premium x 100 shares).
  2. Market Movement: On the expiration date, ABC stock is trading at $105.
  3. Exercise Decision: Since the stock price ($105) is above the strike price ($100), the option is "in-the-money." The investor exercises the option.
  4. Outcome: The investor buys 100 shares of ABC stock at $100 per share, totaling $10,000. They can immediately sell these shares in the market at $105 per share, receiving $10,500.
  5. Profit Calculation:
    • Proceeds from selling shares: $10,500
    • Cost of buying shares (exercise): $10,000
    • Initial option premium paid: $300
    • Net Profit = $10,500 - $10,000 - $300 = $200

If, on the expiration date, ABC stock was trading at $99, the option would be "out-of-the-money" and would expire worthless, resulting in a loss of the initial $300 premium.

Practical Applications

European options are primarily used by investors for two main purposes: hedging and speculation within the realm of options trading.

  • Hedging: Portfolio managers and investors use European options to protect existing positions from adverse price movements. For example, an investor holding shares of a stock might buy a European put option to limit potential losses if the stock price falls. This acts as a form of insurance, with the cost of the put option being the premium.
  • Speculation: Traders use European options to profit from anticipated price changes in an underlying asset. A trader bullish on a stock might buy a call option, believing the stock price will rise above the strike price by expiration. Conversely, a bearish trader might buy a put option. The leverage inherent in options allows for potentially significant returns from relatively small capital outlays, though it also amplifies potential losses.

Regulatory bodies such as the Securities and Exchange Commission (SEC) and the Financial Industry Regulatory Authority (FINRA) oversee options trading in the U.S. to ensure market integrity and investor protection.12 Before trading options, investors must typically be approved by their brokerage firm, often requiring them to fill out an options agreement that assesses their financial knowledge and risk tolerance.11

Limitations and Criticisms

While widely used, the Black-Scholes model, a cornerstone for pricing European options, has several recognized limitations stemming from its underlying assumptions. One significant criticism is its assumption of constant volatility over the life of the option. In reality, market volatility is dynamic and changes over time, often exhibiting "volatility smiles" or "skews" where implied volatilities differ for options with the same expiration but different strike prices.8, 9, 10

Other assumptions that may not hold true in real-world markets include:

  • No Dividends: The original Black-Scholes model assumes the underlying asset does not pay dividends. While extensions address this, it's a limitation for dividend-paying stocks.7
  • Constant Risk-Free Rate: The model assumes a constant, known risk-free interest rate, whereas interest rates fluctuate.6
  • Lognormal Distribution of Returns: It assumes that the underlying asset's price follows a lognormal distribution, implying that asset returns are normally distributed. However, actual asset returns often exhibit "fat tails" (more extreme events than a normal distribution would predict) and skewness.3, 4, 5
  • No Transaction Costs or Taxes: The model assumes a frictionless market without transaction costs, taxes, or restrictions on short selling.

These simplifications, while making the model mathematically tractable, can lead to deviations between the model's theoretical prices and actual market prices, especially during periods of market stress or high uncertainty.1, 2

European Options vs. American Options

The primary distinction between European options and American options lies in their exercise rights. A European option can only be exercised on its expiration date. This means the holder must wait until the specified date to either buy (for a call) or sell (for a put) the underlying asset at the strike price.

In contrast, an American option grants the holder the right to exercise the option at any time between the purchase date and the expiration date, including the expiration date itself. This early exercise feature gives American options greater flexibility.

Due to this added flexibility, American options typically command a higher premium than comparable European options. The ability to exercise early holds potential value, especially for dividend-paying stocks (where exercising a call before a dividend ex-date might be advantageous) or in situations where interest rate changes make early exercise beneficial for a put option. However, for most non-dividend-paying stocks, a rational investor would generally not exercise a call option early, as it means forfeiting the remaining time value.

FAQs

Can European options be traded before expiration?

Yes, European options can be bought and sold in the secondary market at any time before their expiration date, even though they can only be exercised on the expiration date. This allows investors to close out their positions or realize profits/losses without exercising the option.

Why are European options simpler to price than American options?

European options are simpler to price because their exercise event is fixed at a single point in time (expiration). This removes the complexity of considering optimal early exercise strategies, which is a significant factor in pricing American options. Models like Black-Scholes are specifically designed for European-style options.

Are European options only traded in Europe?

No, the term "European option" refers to its exercise style, not its geographic location. European-style options are traded on exchanges worldwide, including in the United States. Many index options and some equity options traded on U.S. exchanges are European-style.

Do European options always expire worthless if they are out-of-the-money?

Yes, if a European call option's strike price is above the underlying asset's price at expiration, or a European put option's strike price is below the underlying asset's price at expiration, the option will expire worthless. There is no intrinsic value to be realized, and since it cannot be exercised early, the entire premium paid is lost.