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Answer: -43,824.76
**Swap Valuation Calculation:** **Cash Flows:** - **Pounds Paid:** 3% semi-annual on £1,000,000 = £15,000 every 6 months - **Euros Received:** 2% semi-annual on €1,100,000 = €11,000 every 6 months - **Principal exchange:** £1,000,000 vs €1,100,000 at maturity **Valuation Process:** 1. **Convert Euro cash flows to Pounds using forward rates:** - 6 months: €11,000 / 1.1443 = £9,614.26 - 1 year: €11,000 / 1.1387 = £9,660.15 - 1.5 years: €11,000 / 1.1330 = £9,708.74 - 2 years: (€11,000 + €1,100,000) / 1.1275 = €1,111,000 / 1.1275 = £985,365.85 2. **Discount Pound cash flows:** - Semi-annual discount rate: 2.5%/2 = 1.25% - PV(Pounds Paid) = £15,000 × (1/1.0125 + 1/1.0125² + 1/1.0125³ + 1/1.0125⁴) + £1,000,000/1.0125⁴ - PV(Euros Received in Pounds) = sum of discounted converted euro cash flows 3. **Swap Value = PV(Euros Received in Pounds) - PV(Pounds Paid)** After calculations, the value is approximately -£43,824.76, indicating the swap has negative value from the pound-paying perspective.
Author: LeetQuiz Editorial Team
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Consider a currency swap where interest on British pounds at the rate of 3% is paid and interest on euros at 2% is received. The British pound principal is 1.0 million pounds and the euro principal is 1.1 million euros. The most recent exchange has just occurred and the interest is exchanged every six months. There are two years are remaining in the life of the swap. The current exchange rate is 1.15 (1.15 euro per pound). Suppose that the forward exchange rates (euro per pound) for year 0.5, 1, 1.5 and 2 are 1.1443, 1.1387, 1.1330 and 1.1275 respectively. The risk-free rates in pounds are 2.5%. All rates are compounded semi-annually. What is the value of the swap (Pounds Paid) in pounds?
A
-43,824.76
B
+43,824.76
C
-29,591.90
D
+29,591.90
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