Answer-first summary for fast verification
Answer: Knock-out call
The barrier level is **above** the current stock price, so it is an **up-barrier**. For an **up-and-out call** with barrier $43 and strike $45, any path that ends above the strike must first cross the barrier. Under standard continuous monitoring, that means the call gets knocked out before it can finish in the money. So the **knock-out call** is the cheapest, and in many textbook conventions it is effectively worth zero. The put variants retain more value because a put benefits from lower stock prices, which do not necessarily require the barrier to be touched. Therefore, the **lowest price** is **B. Knock-out call**.
Author: Manit Arora
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Q-730.3. A non-dividend-paying stock with a current price of $40.00 and a volatility of 30.0% per annum when the risk-free rate is 4.0%. Consider a one-year barrier option with a barrier, H = $43.00, and a strike price, K = $45.00. Please note that the corresponding regular (i.e., without the barrier) put option price is $6.75. Which of the following instances of this barrier option has the LOWEST price?
A
Knock-in call
B
Knock-out call
C
Knock-in put
D
Knock-out put
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