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Answer: $22.60
A protective put costs: \[ \text{Stock price} + \text{put premium} \] We are given the call price and can use **put-call parity** for a non-dividend-paying stock: \[ C + Ke^{-rT} = P + S_0 \] Where: - \(C = 3.00\) - \(S_0 = 20.00\) - \(K = 20.00\) - \(r = 4\%\) - \(T = 0.5\) First compute the present value of the strike: \[ Ke^{-rT} = 20e^{-0.04 \times 0.5} \approx 19.60 \] Then solve for the put price: \[ P = C + Ke^{-rT} - S_0 = 3.00 + 19.60 - 20.00 = 2.60 \] Total initial cost of the protective put: \[ 20.00 + 2.60 = 22.60 \] So the correct answer is **$22.60**.
Author: Manit Arora
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Q-183.5. The current price of a non-dividend-paying stock is $20.00 and the price of a six-month European call option on the stock with a strike price of $20.00 (ATM) is $3.00. The riskfree rate is 4.0%. What is the total initial cost to enter a protective put if we assume the trade includes a six-month ATM put?
A
$3.60
B
$16.70
C
$22.00
D
$22.60
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