1. . A financial institution has agreed to pay three-month LIBOR and to receive 6% per annum in return in an interest rate swap. The notional principal is $50 million and payments are exchanged every three months. The swap has a remaining life of 10 months. Three-month forward LIBOR for all maturities is currently 6.6% per annum. The three-month LIBOR rate two months ago was 6.4% per annum. OIS rates for all maturities are currently 5% with continuous compounding. All other rates are compounded quarterly. What is the value of the swap?

2. . Consider fixed-for-floating swaps with annual exchanges of cash flows and one-year LIBOR as the floating rate. The two-year swap rate and the three-year swap rate are 2% per annum and 2.2% per annum, respectively, both annually compounded. The riskfree zero interest rates are 1% for one year, 1.1% for two years, and 1.2% for three years, each continuously compounded. What is the forward LIBOR rate for the period between 2 years and 3 years? (Hint: Both 2-year and 3-year swaps have value zero so the differences in their cash flows also have value zero. You can assume the principal amount to be $100 million but it does not matter.)