Answer-first summary for fast verification
Answer: $0.82
Check put-call parity: \[ C + PV(K) = 4.00 + 21e^{-0.04} \approx 4.00 + 20.18 = 24.18 \] \[ P + S = 5.00 + 20.00 = 25.00 \] Since \(P + S > C + PV(K)\), the combination **put + stock** is overpriced relative to **call + bond**. Arbitrage: sell the expensive side and buy the cheap side. Initial arbitrage profit: \[ 25.00 - 24.18 = 0.82 \] So the trade collects about **$0.82** today, with no risk and no net future profit/loss at maturity. **Correct answer: C ($0.82).**
Author: Manit Arora
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Q-181.4. The price of a non-dividend-paying stock is $20.00. The price of a one-year European call option on the stock with a strike price of $21.00 is $4.00. The price of a one-year European put option on the stock with a strike price of $21.00 is $5.00. The risk-free rate is 4.0%. What is the future net profit collected by the arbitrage trade, assuming no transaction costs?
A
Zero
B
$0.42
C
$0.82
D
$0.86
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