Solve any questions here:

Problem 1. [25 points] The current spot interest rates with continuous compounding are as follows: Quarter Maturity (months) Rate (% per annum) 1 3 8.0 2 6 8.2 3 9 8.4 4 12 8.5 5 15 8.6 6 18 8.7 Find the corresponding continuously compounded annual forward rates for the quarters 2 6. Problem 2. [25 points] Assume the continuously compounded spot rates of Problem 1. Find the value of an FRA that enables the holder to pay a xed rate of 9.5%, compounded quarterly, for one quarter starting in 1 year and ending in 15 months, and receive oating rates, on a principal of $2,000,000. Problem 3. [25 points] A financial institution entered into an interest rate swap with company X two years ago to receive 10% fixed rate and pay 6-month LIBOR on a principal of $10 million ending in three years. Thus, the remaining life of the contract today is 1 year. The payments are made semiannually and the rates are quoted with semiannual compounding: The following were the discount factors two years ago when the swap was entered: Time-to-Maturity (months) |Discount factor 6 0.9608 12 0.9231 18 0.8869 24 0.8521 30 0.8187 36= 0.7866 How much did the financial institute pay to or receive from company X two years ago to enter into the swap? [25 points] Problem 4. [25 points] Continuing with the problem above. The following were the historical 6-month Libor rates in the past two years: Time 6-month LIBOR (%) 24 months ago 8.0 18 months ago 9.0 12 months ago 7.8 6 months ago 11.0 Write down the cash flow stream of the financial institution resulting from the swap in the past two years (including the cash flow today)