Problem 3.1. A financial institution has agreed to pay 4% per annum and to receive three- month LIBOR in return in an interest rate swap. The notional principal is $80 million and payments are exchanged every three months. The swap has a remaining life of 11 months. Three-month forward LIBOR for all maturities is currently 4.8% per annum. The three- month LIBOR rate one month ago was 4.4% per annum. OIS rates for all maturities are currently 4.5% with continuous compounding. All other rates are compounded quarterly. What is the value of the swap? Problem 3.2. A U.S. company wants to borrow sterling at a fixed rate of interest. A British company wants to borrow U.S. dollars at a fixed rate of interest. They have been quoted the following interest rates (per annum): US company British company US Dollars 9.4% 8.8% Sterling 8.8% 7.6% Design a swap that will net a bank, acting as intermediary, 10 basis points per annum and that will produce a gain of 25 basis points per annum for each of the two companies. Problem 3.3. Suppose that the term structure of risk-free interest rates is flat in the United States and Australia. The USD interest rate is 5% per annum and the AUD rate is 6% per annum. The current value of the AUD is 0.65 USD. Under the terms of a swap agreement, a financial institution pays 5% per annum in AUD and receives 4% per annum in USD. The principals in the two currencies are $13 million USD and 20 million AUD. Payments are exchanged every year, with one exchange having just taken place. The swap will last two more years. What is the value of the swap to the financial institution? Assume all interest rates are continuously compounded. Problem 3.4. A company wants a swap where it receives semiannual payments at 6.5% per annum with semiannual compounding on a principal of $5 million. The five-year swap rate with semiannual cash flows is 6% per annum with semiannual compounding. The OIS zero curve is flat at 5% per annum with continuous compounding. How much should a derivatives dealer charge the company