A European option is an option that can be exercised only on the exercise date and not before. It gives its holder a choice to sell or buy the underlying asset at the specified strike price at the specified exercise date.
Unlike an American option, European option has no flexibility in timing of exercise.
Theoretically a European option has lower value than an otherwise equivalent American option. It is because a European option does not enjoy the convenience that arises from flexibility in timing of exercise.
Value of a European Call Option = max [0, Asset Price − Exercise Price]
Value of a European Put Option = max [0, Exercise Price − Asset Price]
Asset price is the price of the underlying financial asset at the exercise date.
Exercise price is the price at which the option entitles its holder to sell or purchase the underlying financial asset.
Example 1: European Call Option
To differentiate between a European call option and an equivalent American call option, please see the facts given in Example 1 in the article on American option. Assume that Dona used European options instead of American options.
Since Dona purchased European options which she can exercise only on the exercise date i.e. 26th July 20Y3 and not before, her gain per option will be only $1 (i.e. option value at the exercise date = price of underlying asset ($43) minus exercise price ($42). If she had bought American options, she could have exercised them on 25th July 20Y3 (the day it offered maximum gain) for per option gain of $2 [= $44.5 − $42].
Example 2: European Put Option
Please see the facts in Example 2 of article on American option. Assume that Dona bought European options.
Dona will have to let the option expire because at the exercise date the price of BP share is higher than the exercise price of the option.
Option value on day before exercise date = max [0, $60 − $58] = $1
Option value on exercise date = max [0, $60 − $61] = 0