
Explanation:
Cost of the swap = 1.0% + 2.6% + 0.4% = 4.0%
Note: The Sterling pound Libor is negative (-2.6%); thus, counterparty B will also have to pay for it, hence the reason why we add it.
Detailed Explanation
Counterparty A is exchanging pounds for dollars. In other words, it's giving out pounds to receive dollars. Both parties pay interest on the currency they receive (because they have technically borrowed that currency). In our case, A should pay the dollar LIBOR (1%) plus the cross-currency basis (-0.4%). Because B has “borrowed” the pound from A, it should pay the pound LIBOR (-2.6%) to A. But here's the problem: this rate is negative, and just like in any other scenario where the interest rate is negative, it would be the lender and not the borrower, who pays the interest. Counterparty A would have to pay pound interest to B.
At the end of the day, therefore, the total theoretical cost of the Pound/USD currency swap to A is 1% + 0.4% + 2.6% = 4.0%
If the pound LIBOR was +2.6%, party A would have actually received interest on the pound. A’s cost would have been 1% + 0.4% - 2.6% = -1.2%; it would receive a net rate of interest of 1.2% from B.
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Q.4184 Counterparty A wants to carry out a cross-currency swap where it will exchange the sterling pound for the U.S. dollar with counterparty B. Today, the U.S. Libor rate is 1.0% while the sterling pound Libor rate is -2.6%. A dollar shortage occurs, and counterparty B quotes a basis of -40 bps. Compute the cost of the swap for counterparty A. (Assume that both parties pay interest on the currency they receive.)
A
4.0%
B
2.0%
C
2.6%
D
3.2%