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Answer: Lower bound USD 5.00, upper bound USD 5.13
B is correct. The put-call parity in case of American options leads to the inequality: So - K ≤ (C - P) ≤ So - Ke-rT The lower and upper bounds are given by: = 40 - 35 ≤ (C - P) ≤ 40 - 35e^(-0.015 * 3/12) = 5 ≤ (C - P) ≤ 5.13 Alternatively, the upper and lower bounds for American options are given by: Option | Minimum Value | Maximum Value --- | --- | --- American Call | C ≥ max(0, So - Ke^(-rT)) = 5.13 | So = 40 American Put | P ≥ max(0, K - So) = 0 | K = 35 Subtracting the put values from the call values in the table above, we get the same result: = 5 ≤ C - P ≤ 5.13
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A financial analyst working at a hedge fund is currently evaluating the pricing of American-style call and put options, both with an expiry period of three months, on a stock that is currently priced at USD 40 and does not pay any dividends. The strike price for both options is set at USD 35, and the prevailing risk-free interest rate is 1.5%. What are the minimum and maximum possible differences in the costs of these call and put options?
A
LowerboundUSD0.13,upperbound USD34.87
B
Lower bound USD 5.00, upper bound USD 5.13
C
Lower bound USD5.13,upper bound USD 40.00
D
Lower bound USD 34.87, upper bound USD 40.00
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