Skip to main content
← Back to E Definitions

European option

What Is a European Option?

A European option is a type of derivatives contract that can only be exercised on its expiration date. Unlike an American option, which can be exercised at any time before or on its expiration date, the European option restricts the buyer's right to exercise until the very end of the contract's life. This characteristic makes European options generally less flexible than their American counterparts, yet they are widely traded in global financial markets as a specific type of financial instrument. European options belong to the broader category of financial derivatives, which derive their value from an underlying asset, such as stocks, indices, or commodities.

History and Origin

The concept of options has existed for centuries, but standardized, exchange-traded options, including the European option, gained prominence with the establishment of the Chicago Board Options Exchange (Cboe) on April 26, 1973. The Cboe was the first marketplace to offer standardized options contracts.12,11,10 This innovation brought greater transparency and market liquidity to options options trading. A pivotal moment in the history of pricing options came with the publication of the Black-Scholes-Merton model in 1973 by Fischer Black, Myron Scholes, and Robert Merton.,9,8 Their groundbreaking work provided a quantitative framework for valuing options, particularly European-style options, which was crucial for the burgeoning derivatives market. Myron Scholes and Robert C. Merton were awarded the Nobel Memorial Prize in Economic Sciences in 1997 for their work, as Fischer Black had passed away.,7,6 This model's development greatly contributed to the expansion and sophistication of options markets worldwide.

Key Takeaways

  • A European option can only be exercised on its specified expiration date.
  • This characteristic distinguishes it from an American option, which can be exercised at any time up to and including expiration.
  • The pricing of European options is significantly influenced by models like the Black-Scholes formula.
  • They are a fundamental type of derivative used for hedging, speculation, and generating income.
  • Despite their exercise restriction, European options are widely traded on exchanges globally.

Formula and Calculation

The most famous model for valuing a European option is the Black-Scholes formula. This complex mathematical model calculates the theoretical premium of a European call options or put options by considering five key inputs: the price of the underlying asset, the strike price, the time to expiration, the risk-free interest rate, and the volatility of the underlying asset.

For a European call option ($C$):

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

For a European put option ($P$):

P=KerTN(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 (annualized standard deviation of returns)
  • ( N(x) ) = 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=d1σTd_2 = d_1 - \sigma\sqrt{T}

This formula highlights the factors that determine an option's value, including its intrinsic value and time value.

Interpreting the European Option

Interpreting a European option primarily revolves around its fixed exercise window. Since a European option can only be exercised on its expiration date, its value leading up to that date is purely theoretical, derived from the probability of the underlying asset's price moving favorably by expiration. Traders and investors using European options must forecast future price movements with this strict exercise constraint in mind. The primary way to profit from a European option before expiration is by selling it in the open market, as its value fluctuates with changes in the underlying asset price, volatility, and time decay. Understanding the probability of the option being in-the-money at expiration is key to its valuation and strategic use.

Hypothetical Example

Consider a hypothetical European call option on Company XYZ stock.

  • Current Stock Price ((S_0)): $100
  • Strike Price ((K)): $105
  • Expiration Date ((T)): 3 months from now (0.25 years)
  • Premium paid: $3.00

Since this is a European option, you cannot exercise it before the expiration date. Let's say on the expiration date, the price of Company XYZ stock is $110.

  1. Check Exercise Condition: On the expiration date, the stock price ($110) is above the strike price ($105), so the option is in-the-money and worth exercising.
  2. Calculate Profit per Share:
    • Value received from exercising: $110 (stock price) - $105 (strike price) = $5 per share.
  3. Calculate Net Profit:
    • Gross profit: $5 per share
    • Less premium paid: $3 per share
    • Net profit: $5 - $3 = $2 per share.

If, on the other hand, the stock price at expiration was $103, the option would expire worthless as the stock price is below the strike price, and you would lose the $3 premium paid.

Practical Applications

European options are widely utilized in various investment strategies across global financial markets. Their primary applications include:

  • Hedging Risk: Investors can use European options to mitigate potential losses in their portfolios. For instance, a portfolio manager holding a significant stock position might buy European put options to protect against a downward movement in the stock's price.
  • Speculation: Traders can speculate on the future price direction of an underlying asset without owning the asset itself. Buying a European call option implies a belief that the asset's price will rise significantly by expiration, while buying a European put option suggests an expectation of a price decline.
  • Income Generation: Strategies like covered call writing, which involves selling European call options against owned shares, can generate income through the collection of premiums.
  • Portfolio Management: Institutional investors and fund managers use European options for more complex strategies, such as creating synthetic positions or altering their portfolio's volatility exposure.
  • Regulatory Compliance: Broker-dealers are required to provide investors with an Options Disclosure Document (ODD), which explains the characteristics and risks of standardized options, including European options, before they engage in options trading.5,4,3 This document, published by the Options Clearing Corporation (OCC), ensures investors are aware of the potential risks and features of these financial instruments.2,,1

Limitations and Criticisms

While European options are fundamental to the derivatives market, they come with specific limitations and criticisms. The primary restriction is their exercise feature: a European option can only be exercised on its expiration date. This lack of flexibility means that if the underlying asset moves favorably well before expiration, the option holder cannot realize profits through exercise until the very end, potentially missing optimal exercise opportunities. Instead, they must close out their position by selling the option in the market if they wish to lock in gains early.

Another criticism revolves around the assumptions of the Black-Scholes model, which, while revolutionary, relies on certain ideal conditions that do not always hold true in real markets. These assumptions include constant volatility and interest rates, and continuous trading, which can lead to discrepancies between theoretical prices and actual market premiums. The model's limitations became more apparent during periods of extreme market turbulence, highlighting the importance of risk management beyond pure mathematical pricing. Furthermore, the complexity of options trading can expose less experienced investors to significant losses if they do not fully understand the risks involved, underscoring the necessity of reading the Options Disclosure Document provided by regulators.

European Option vs. American Option

The key distinction between a European option and an American option lies in their exercise rights. A European option grants the holder the right to exercise the option only on its expiration date. In contrast, an American option provides the flexibility to exercise the option at any time up to and including its expiration date. This difference significantly impacts their valuation and practical use. American options, due to their greater flexibility, typically command a higher premium than comparable European options. However, for certain underlying assets or strategies, the earlier exercise right of an American option may not offer a significant advantage, and European options may be preferred due to their typically lower cost or for specific hedging or income-generating strategies where early exercise is not desired.

FAQs

Can I sell a European option before its expiration date?

Yes, you can sell a European option in the secondary market before its expiration date. While you cannot exercise it early, you can close out your position by selling it to another investor, effectively realizing any gains or losses based on the option's current premium.

Are European options traded on exchanges?

Yes, many European options are listed and traded on major exchanges worldwide, such as the Cboe. Exchange-traded European options benefit from standardization and market liquidity.

Why are European options generally cheaper than American options?

European options are typically cheaper than comparable American options because they offer less flexibility. The restriction on exercising only on the expiration date means the holder cannot capture favorable price movements of the underlying asset before that specific day, reducing their inherent value compared to American options.

Is the Black-Scholes model used for European options?

Yes, the Black-Scholes model is primarily designed for pricing European-style call options on non-dividend-paying stocks. While variations and extensions exist for other types of options, its core application is for European options.