Suppose you observe the spot euro at $1.38/€,the U.S.risk-free interest rate of 0.25% (continuously compounded),and the European risk-free interest rate of 0.75% (continuously compounded).Identify the theoretical value of a six month foreign exchange futures contract (select the closest answer).
A)$1.3815/€
B)$1.3765/€
C)$1.3785/€
D)$1.3825/€
E)$1.3755/€

Question

Quizplus · Accepted Answer

The theoretical value of a futures contract depends on the spot rate, interest rates, and time to expiration. In this case, we have:

- Spot euro: $1.38/€
- U.S. risk-free interest rate: 0.25% (continuously compounded)
- European risk-free interest rate: 0.75% (continuously compounded)
- Time to expiration: 6 months

Using the formula:

F = S x e^((r-rf) x t)

where F is the theoretical futures price, S is the spot rate, r is the foreign risk-free interest rate, rf is the domestic risk-free interest rate, and t is the time to expiration in years (we divide 6 months by 12 to get 0.5 years), we can calculate:

F = 1.38 x e^((0.0075-0.0025) x 0.5)
F = 1.3765/€

Therefore, the best choice is B) $1.3765/€.

Suppose You Observe the Spot Euro at $1