Both barrier options and limit options denote the same. By definition, it is an exotic option whose payoff depends on whether the underlying asset price reaches a specified threshold (a predetermined knock-in or knock-out price) or not. A knock-in option comes into existence only when the underlying asset reaches the threshold (the limit or the barrier). To the contrary, knock-out options cease to exist if the asset price reaches the barrier.
If the barrier is hit from below (above), it is called an up-and-in option (a down-and-in option). In contrast, knock-out options cease to exist if the asset price reaches the barrier. So if the option is deactivated from below (above), it is called an up-and-out option (a down-and-out option).
Barrier options (limit options) are essentially European options whose payoffs depend not only on the underlying price on the expiration date, but also on the underlying price reaching a preset level during the option’s life.
The barrier option is alternatively known as a stoption.
