What is the European Option?

A European option can be defined as a type of options contract (call or put option) that restricts its execution until the expiration date. In layman’s terms, after an investor has purchased a European option, even if the price of the underlying security moves in a favorable direction, i.e., an increase in the price of the stock for call options and a decrease in the price of the stock for put options, the investor cannot take advantage by exercising the option early.

Types of European Option

Below are the two types of European options.

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#1 – European Call Option

Holders of such contracts can buy a predetermined quantity of the underlying at the expiration date at a predetermined price, also known as the strike priceStrike PriceExercise price or strike price refers to the price at which the underlying stock is purchased or sold by the persons trading in the options of calls & puts available in the derivative trading. Thus, the exercise price is a term used in the derivative market.read more. The investor is bullish on the market.

#2 – European Put Option

Investors can sell a predetermined quantity of the underlying at the expiration date at the strike price. Investor opinion is bearishBearishBearish market refers to an opinion where the stock market is likely to go down or correct shortly. It is predicted in consideration of events that are happening or are bound to happen which would drag down the prices of the stocks in the market.read more.

The formula of the European Option

Black Scholes Merton Model or BSM model is more suited for pricing European options since one of the assumptions that this model rests on is that the options aren’t exercised early.

Pricing a European Call Option Formula

Where,

  • d1 = [ln(P0/X) + (r+v2/2)t]/v √t  and  d2 = d1 – v √tP0= Price of the underlying securityX= Strike priceN= standard normal cumulative distribution functionr = risk-free rate Risk-free RateA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read morev= volatilityt= time until expiry

Pricing a European Put Option Formula

Where d1 and d2 can be calculated in the same way as in the call option pricing.

Practical Example of European Option

Stock XYZ is trading for $60. The strike price is $60. Volatility is 10%, and the risk-free rate is 5%.

Calculate the value of a 1-year call and put options written on it using the BSM model.

  • Price of the Underlying Security (P0): $60Strike Price (X): $60Volatility (V): 10%Risk-Free Rate (r): 5%Time Until Expiry: 1

Calculation of d1

  • d1 = [ln(P0/X) + (r+v2/2)t]/v √t= LN(60/60)+(5+10^2/21)/(10SQRT(1))=0.55

Calculation of d2

  • d2 = d1 – v √t = 0.55-60*SQRT(1)= 0.45

We got the following values from the normalization table.

So the calculation of the price of the call option using the above table

Price of call= $4.08

calculation of the price of the put option using the above table –

Price of put= $1.16

Prices are also calculated in the solved example excel sheet.

Before we move forward to its advantages and disadvantages, let’s talk briefly about the upper and lower price bounds for European call and put options.

  • Lowest bound for a Call =0 (Option price can never fall below zero)Highest bound for a Call= P0 (Current value of the underlying)Lowest bound for a Put = 0Highest bound for a Put = Xe-rt (Present value of strike price)

How European Options Differs from American Options?

European Options differ from American optionsEuropean Options Differ From American OptionsA European call option gives the option holder the right to buy a stock at a predetermined future date and price. In contrast, an American call option allows the holder to ask for the delivery of the security or stock anytime between the execution date and the expiration date.read more in that American option holdersAmerican Option HoldersAn American option is a type of options contract (call or put) that can be exercised at any time at the holder’s will of the opportunity before the expiration date. It allows the option holder to reap benefits from the security or stock at any time when the safety or supply is favorable. A European option is the exact opposite of an American option wherein the option holder cannot sell the option until the day of expiration, even when it is favorable. In addition, there is no geographical connection concerning the names since it only refers to the execution of the options trade.read more have the liberty of exercising the option anytime, be it on or before the expiration date. However, investors of such options can choose to sell their holdings in the market before the expiration date approaches. Under such circumstances, profit is essentially the difference between the premium earned and the premium paid.

Also, European and American options are mutually exclusiveMutually ExclusiveMutually exclusive refers to those statistical events which cannot take place at the same time. Thus, these events are entirely independent of one another, i.e., one event’s outcome has no impact on the other event’s result.read more in the market. Both aren’t offered simultaneously, so investors don’t have a choice.

Both these options differ on three grounds:

Advantages

  • There is a predetermined time of expiration of the contract that gives the investor some certainty.These options are less expensive than American options. Due to the added flexibility of any time exercise in American options, the upfront cost tends to be higher than in European options.This tends to be less risky, and the pricing complexity is also less due to the availability of limited options for contract execution.

Disadvantages

  • European options though less risky than the American options aren’t devoid of risks. They can be subject to other types of unique risks. A meticulous approach has to be adopted to avoid such risks.One such risk is the trading lapse risk. Trading of European options closes at the end of the business day on a Thursday that falls before the third Friday of the expiration month. This can lead to an unexpected change in the price of the underlying.The settlement price might be tricky to determine due to the risk of a trading lapse.Investors can’t exercise their options to take advantage of a favorable price move.Most such options are traded over the counterOver The CounterOver the counter (OTC) is the process of stock trading for the companies that don’t hold a place on formal exchange listings. The broker-dealer network facilitates such decentralized trading of derivatives, equity and debt instruments.read more, so there isn’t much regulation, adding another degree of risk.The BSM model used for pricing might not be the most accurate due to some unreal assumptions involved in the calculation.

Limitation

  • European options aren’t much accessible because they are traded over the counter.The pricing model makes certain assumptions of dividendDividendDividends refer to the portion of business earnings paid to the shareholders as gratitude for investing in the company’s equity.read more, volatility, and risk-free rate being constant during the entire duration, which is unreal. Hence, prices might be different from the real world.

Conclusion

The naming of European and American options has nothing to do with the respective geographical locations. It simply gives an idea of when an option can be exercised. Most options traded in the US are known to be European options. Due to the difference in the features of the two options, investor expectations also vary. Like, an American option holder would expect the prices to move favorably before the expiration date arrives. However, the same isn’t true for European option holders who hope such changes happen only at expiration.

This has been a guide to what European Option is and its Definition. Here we discuss the formula to calculate the Price of the European Call and Put option and practical examples, advantages, and disadvantages. You can learn more about accounting from the following articles –

  • 5 Examples of Call OptionNon-Qualified Stock OptionsWriting Call Options PayoffWriting Put Options