Suppose the 0.5-year zero rate is 6% and the 1-year zero rate is 8%. Consider a 1-year, plain vanilla, semi-annual pay, xed-for-
oating interest rate swap.
(a) What is the swap rate that will make this swap worth zero?
(b) What is the duration of $100 notional amount of this zero-cost swap?
(c) Assume your liabilities have a market value of $100,000 and a duration of 3. Your assets have a market value of $100,000 and a duration of 5. Determine the notional amount of a position in the swap described above that you require to immunize your net position against parallel shifts in interest rates.