A binary option that can be exercised only at the end of its life (i.e., on expiration date). That is, at the contract’s maturity date, if the underlying price is above the strike price (for a call) or below the strike price (for a put), the contract can be exercised, with the holder receiving the difference between the underlying price and the strike price. This option pays a certain amount if the barrier (or trigger) is activated on the date the option expires. Otherwise, the holder receives nothing and the option expires worthless.  A European binary options has a discontinuous payoff: a call contract, for example, pays a specific amount if and only if the underlying price is greater than the strike price at expiration. This discontinuity makes such an option very difficult to hedge since the delta of the binary option may increase substantially near expiration.

This option is also known an European digital option.