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In a fixed-for-fixed currency swap, 4% on a US dollar principal of $160 million is received and 5% on a British pound principal of 100 million pounds is paid
In a fixed-for-fixed currency swap, 4% on a US dollar principal of $160 million is received and 5% on a British pound principal of 100 million pounds is paid. The current exchange rate is 1.55 dollars per pound. Interest rates in both countries for all maturities are currently 6% (continuously compounded). Payments are exchanged every year. The swap has 2.5 years left in its life.
Find the value of the swap in terms of a portfolio of forwarding contracts.
Expert Solution
We will calculate the net payment received at each swap reset date. Since we have 2.5 years left, there are 3 swap payment dates, the first one after 0.5 years, the second one after 1.5 years and the third after 2.5 years.
Net payment received = (4% on a US dollar principal of $160 million) - (5% on a British pound principal of 100 million pounds) * Exhcange rate = 4% * 160 Mn - 5%*100 * 1.55 = - $1.35 Mn
Since the value is negative, there is a net out flow of $1.35 Mn.
Value of swap = Present value of payments made after 0.5 years, 1.5 years and 2.5 years =
Swap payment / (1 + r)^n
where r = Int rate in both countries = 6%.
Since the interest rate in both the contries is same for all the duration, the currency exchange rate stays constant each year.
Substitute the given values:
Value of swap = 1.35 / (1+0.06)^(0.5) + 1.35 / (1+0.06)^(1.5) + 1.35 / (1+0.06)^(2.5) = 3.715246223
Answer: Value of swap = $3.715246223 Million
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