Consider two paths A and B for stock prices in a barrier option setting that result in the same terminal price. Paths A and B will have different payoff consequences for the barrier option if
A) Path A crossed the barrier before maturity while Path B did not.
B) Both paths crossed the barrier prior to maturity but Path A re-crossed it while Path B did not.
C) Neither path crossed the barrier prior to maturity.
D) All of the above.

Question

Quizplus · Accepted Answer

The barrier option only comes into play if the stock price crosses the barrier before maturity. If both paths do not cross the barrier, then the barrier option has no effect. If both paths do cross the barrier, but only one re-crosses it, then the option may still be in the money if the other path has not crossed the barrier at all. However, if only one path crosses the barrier and the other does not, then the barrier option will have very different consequences for each path. Therefore, the correct choice is A, as it describes the scenario where the payoff consequences for the barrier option would be different for each path.

Consider Two Paths a and B for Stock Prices in a Barrier