An exotic barrier option which has one American-style barrier and one European-style barrier. Conventionally, the American-style barrier is out-of-the-money, while the European-style barrier is in-the-money. Basically, there are two types of a Transatlantic barrier option: (1) a call in which the American-style barrier (up-and-out) is above the strike price, and the European-style barrier (down-and-out) is lower, or equal to, the strike price, (2) a put in which the American-style barrier (up-and-out) is above, or equal to, the strike price, the European-style barrier (down-and-out) is lower than the strike price.