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Answer: $4.17 and $5.00
For a **non-dividend-paying stock**, the American call equals the European call. Given: - \(C_A = 3.00\) - \(S = 40\) - \(K = 42\) - \(T = 0.5\) - \(r = 4\%\) ### Lower bound For the American put, a useful lower bound is: \[ P_A \ge C_A + PV(K) - S \] Compute: \[ PV(K)=42e^{-0.04\times 0.5}=42e^{-0.02}\approx 41.17 \] \[ P_A \ge 3.00 + 41.17 - 40.00 = 4.17 \] ### Upper bound A standard upper bound is: \[ P_A \le C_A + K - S \] \[ P_A \le 3.00 + 42.00 - 40.00 = 5.00 \] Therefore, the bounds are **$4.17 and $5.00**. **Correct answer: D.**
Author: Manit Arora
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Q-181.5. The price of an American call on a non-dividend-paying stock is $3.00. The stock price is $40.00, the strike price is $42.00, and the expiration date is in six (6) months. The risk-free interest rate is 4.0%. What are the lower and upper bounds for the price of an American put on the same stock with the same strike price and expiration date?
A
$1.17 and $2.00
B
$2.17 and $3.33
C
$3.06 and $5.17
D
$4.17 and $5.00
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