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Answer: Yes, and it is exploited with a bear spread
Yes, an arbitrage is possible, and it is associated with a **bear put spread**. For European puts with the same maturity and no dividends, the price difference should satisfy: \[ 0 \le p(K_2) - p(K_1) \le (K_2 - K_1)e^{-rT} \] Here: \[ p(45) - p(40) = 25.20 - 18.20 = 7.00 \] and \[ (45 - 40)e^{-0.04 \times 1} = 5e^{-0.04} \approx 4.80 \] Since **7.00 > 4.80**, the observed spread is too wide, so arbitrage exists. The relevant option structure is a **bear spread** in puts (long the higher-strike put and short the lower-strike put). If that spread is overpriced, it can be shorted to lock in arbitrage profit.
Author: Manit Arora
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Question-726.3. A non-dividend-paying stock currently trades at a price of $21.00 while the risk-rate is 4.0%. The stock’s is highly uncertain, with a volatility of 50.0%. Two deeply in-the-money one-year European put options on this stock are trading at the following prices:
$40.00 has a price (premium) of $18.20$45.00 has a price (premium) of $25.20Is an arbitrage possible?
A
No
B
Yes, and it exploited with a straddle
C
Yes, and it is exploited with a bull spread
D
Yes, and it is exploited with a bear spread
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