A barrier option in which in which the payoff is contingent on whether a specific level has been crossed or not during the entire life of the option. That means, any time during the option’s life that level is crossed, its payoff becomes automatically payable. For example, an up-and-out call option with a strike price of K, and with barrier of B will pay:
Payoff= max [ST – K, 0]
That holds true unless at any time during the option’s life the value of the underlying remains below the barrier B. This option is, thus, a knock-out option, i.e., it becomes inactive once the barrier is hit or crossed, otherwise it would expire worthless.
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