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Explanation:
Correct answer: A
A down-and-in put only becomes active if the underlying price falls to or below the barrier. With and , the barrier has not been breached at inception, so the option is not immediately equivalent to a vanilla put.
Why the others are true:
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Question-413.1. Let (p) be the value of a standard (non-exotic or vanilla) put option with a strike price of $16.00, where the underlying current underlying stock price, S(0), is $18.40. Consider an exotic knock-in barrier put option (aka, down-and-in put) also with a strike price of (K) of $16.00. Each of the following it true about the down-and-in put, EXCEPT which is false?
A
If the barrier (H) is $17.00, then the value of this down-and-in put option, p(di), is equal to the value of the vanilla put option; p(di) = p
B
If the barrier (H) is $14.00, then the value of this down-and-in put option, p(di), is equal to the value of the vanilla put option minus the value of an equivalent down-and-out put; p(di) = p - p(do)
C
The vega of the down-and-in put, p(di), is generally lower than the vega of the corresponding vanilla put; vega(di) < vega(p)
D
As we increase the frequency with which we observe the asset price in determining whether the barrier is reached, the value of the down-and-in put increases