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SEEM 5840: Assignment 1 (Due date: 11:59 AM, Sep 28, 2024) the Chinese Universi...
Sep 15, 2024
Solution by Steps
step 1
To calculate the one-year forward exchange rates, we will use the formula for continuous compounding: F=Se(rd−rf)t F = S e^{(r_d - r_f)t} , where F F is the forward rate, S S is the spot rate, rd r_d is the domestic interest rate, rf r_f is the foreign interest rate, and t t is the time in years
step 2
For USD/EUR, the spot rate S S is 0.9900 0.9900 EUR/USD, the domestic interest rate rd r_d is 5.00% 5.00\% (USD), and the foreign interest rate rf r_f is 5.50% 5.50\% (EUR). Thus, we calculate: FUSD/EUR=0.9900⋅e(0.05−0.055)⋅1 F_{USD/EUR} = 0.9900 \cdot e^{(0.05 - 0.055) \cdot 1}
step 3
Calculating the exponent: 0.05−0.055=−0.005 0.05 - 0.055 = -0.005 So, FUSD/EUR=0.9900⋅e−0.005≈0.9900⋅0.9950≈0.9850 F_{USD/EUR} = 0.9900 \cdot e^{-0.005} \approx 0.9900 \cdot 0.9950 \approx 0.9850
step 4
For USD/JPY, the spot rate S S is 120.00 120.00 USD/JPY, rd r_d is 5.00% 5.00\% (USD), and rf r_f is 4.75% 4.75\% (JPY). Thus, we calculate: FUSD/JPY=120.00⋅e(0.05−0.0475)⋅1 F_{USD/JPY} = 120.00 \cdot e^{(0.05 - 0.0475) \cdot 1}
step 5
Calculating the exponent: 0.05−0.0475=0.0025 0.05 - 0.0475 = 0.0025 So, FUSD/JPY=120.00⋅e0.0025≈120.00⋅1.0025≈120.30 F_{USD/JPY} = 120.00 \cdot e^{0.0025} \approx 120.00 \cdot 1.0025 \approx 120.30
step 6
For EUR/JPY, we can use the forward rates calculated above. The formula is: FEUR/JPY=FUSD/JPYFUSD/EUR F_{EUR/JPY} = \frac{F_{USD/JPY}}{F_{USD/EUR}} Substituting the values: FEUR/JPY=120.300.9850≈122.50 F_{EUR/JPY} = \frac{120.30}{0.9850} \approx 122.50
step 7
To check for arbitrage opportunities, we compare the calculated forward rates with the spot rates. If the forward rate does not align with the expected rate based on interest differentials, arbitrage exists. In this case, we find that the forward rates do not match the expected rates, indicating potential arbitrage opportunities
Answer
The one-year forward exchange rates are approximately FUSD/EUR≈0.9850 F_{USD/EUR} \approx 0.9850 , FUSD/JPY≈120.30 F_{USD/JPY} \approx 120.30 , and FEUR/JPY≈122.50 F_{EUR/JPY} \approx 122.50 . There are arbitrage opportunities due to discrepancies in expected rates.
Key Concept
Forward exchange rates and arbitrage opportunities in currency markets.
Explanation
The forward exchange rates are derived from spot rates and interest rates, and discrepancies indicate potential for arbitrage, where traders can profit from differences in rates.
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