Answer-first summary for fast verification
Answer: Yes, regardless
Yes, there is an arbitrage opportunity **regardless of the future spot rate**. A simple way to see this is to compare: - **Long the call**: pay $0.08 now, then at maturity receive `max(S(T) - 1.10, 0)`. - **Short the forward**: at maturity you receive the benefit of selling EUR at $1.20 instead of the market price. Consider the combined payoff at maturity: - If `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`. - If `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**.
Author: Manit Arora
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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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