Explanation:
Yes, there is an arbitrage opportunity regardless of the future spot rate.
A simple way to see this is to compare:
$0.08 now, then at maturity receive max(S(T) - 1.10, 0).$1.20 instead of the market price.Consider the combined payoff at maturity:
S(T) > 1.10, the call payoff is S(T) - 1.10, and the short forward payoff is 1.20 - S(T). Net payoff = 0.10.S(T) <= 1.10, the call payoff is 0, and the short forward payoff is 1.20 - S(T) >= 0.10. Net payoff is at least 0.10.After subtracting the initial call premium of 0.08, the strategy locks in at least 0.02 profit with no downside, assuming no transaction costs and ignoring the time value of money.
Therefore, the correct answer is C. Yes, regardless.
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Question 139.2. Assume the USD/EUR spot exchange rate is $1.40/EUR, and the 180-day forward rate is $1.20 USD/EUR. You can purchase a 180-day European call option to buy 1 EUR for $1.10 with a (premium) cost of $0.08. Is there an arbitrage opportunity if we assume no transaction costs and ignore the time value of money?
A
No, because the call option premium eliminates the profit
B
No, because there is not a gain if the future spot exchange rate is less than $1.1 USD/EUR
C
Yes, regardless
D
Yes, if the future spot exchange rate S(t) is greater than $1.1 USD/EUR
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