A down-and-out option is a type of exotic option known as a barrier option. These...

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A down-and-out option is a type of exotic option known as a barrier option. These options define the payout conditions based on whether the price falls enough from the exercise price to reach a designated barrier price. What happens at the barrier depends on whether the option is knock-in or knock-out. A down-and-out option is a knock-out barrier option. Specifically, if the price falls to the knock-out price the option is terminated with zero value. Consider a down and out perpetual American call option on a non-dividend-paying stock. The option has an exercise price of K and a knock-out price of N, where N

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