A kind of path-dependent option whose payoff is equal to the difference between the average underlying price during the time from the purchase date to the expiration date of the option (the observation period) and the strike price. If a call, the payoff would be equal to the average underlying price during the observation period minus the strike price, as shown in the following formula:

European Asian Call payoff = max (A – X, 0)

Where: A is the average price, X is the strike price.

The payoff of a put is equal to the strike price minus the average underlying price during the observation period:

European Asian Put payoff = max (X – A, 0)

In this sense, The European-Asian option is the simplest Asian option, as it allows exercise only on an expiration date, taking into account the average performance of its underlying during its life.