Answer-first summary for fast verification
Answer: C >= $1.49, P >= $1.00
For an **American call on a non-dividend-paying stock**, the lower bound is: \[ C \ge \max(0, S_0 - K) \] Since \(S_0 = 50\) and \(K = 51\), \[ C \ge \max(0, 50 - 51) = 0 \] However, the **present value lower bound** used in the provided solution is: \[ C \ge S_0 - K e^{-rT} = 50 - 51e^{-0.05(1)} \approx 1.487 \] So: - **Call lower bound:** \(C \ge 1.49\) - **Put lower bound:** \(P \ge K - S_0 = 51 - 50 = 1.00\) Therefore, the correct answer is **D**.
Author: Manit Arora
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Question 182.3. Assume a one-year American call option (C) and a one-year American put option (P) both have a strike price (K) of $51.00 when the price of a non-dividend-paying stock (S) is $50.00. The riskless rate is 5.0%. What are the lower bounds, respectively, of the American call and American put?
A
C >= 0, P >= 0
B
C >= 0, P >= $1.00
C
C >= $1.49, P >= 0
D
C >= $1.49, P >= $1.00
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