Answer-first summary for fast verification
Answer: The corresponding knock-out (aka, down-and-out) must have a price of about $6.10
Under standard knock-in/knock-out parity, the price of the corresponding knock-out is approximately the regular call price minus the knock-in price: \[ 6.32 - 0.22 = 6.10 \] So statement **A** is consistent with parity. Statements **B** and **C** are also consistent: raising a down-and-in barrier from $18 to $22 makes activation more likely, so the knock-in value increases and the knock-out value falls. Statement **D** is also consistent under the standard convention for a down-and-in option: if the barrier is raised above the current stock price, the barrier has effectively already been breached, so the knock-in behaves like the regular call and the corresponding knock-out is worthless. **Note:** this item appears somewhat flawed because all four statements are consistent with standard barrier-option conventions. The source still presents it as an EXCEPT question, so the extracted answer field follows the provided structure, but there is no uniquely false statement under the usual interpretation.
Author: Manit Arora
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Q-730.2. Consider a one-year barrier call option on a non-dividend-paying stock with a volatility of 30.0% per annum when the stock’s price is $25.00 and the option’s strike price is $20.00. The risk-free rate is 3.0%. The price of a regular call (i.e., without the barrier) in this case is $6.32. This barrier option has a barrier at $18.00 such that, if it is a knock-in (aka, down-and-in) its price is only $0.22. Each of the following statements is true (or at least plausible!) EXCEPT which statement must be false?
A
The corresponding knock-out (aka, down-and-out) must have a price of about $6.10
B
If the barrier is increased to $22.00, then the price of this knock-in must be higher than $0.22
C
If the barrier is increased to $22.00, then the price of the corresponding knock-out must be lower than $6.10
D
If the barrier is increased to $28.00, then the price of this knock-in will be $6.32 and the price of the corresponding knock-out will be zero
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