You are developing a strategy to manage interest rate risk of your portfolio using options on a bond.

a) You do not know if interest rates will go up or down, but it can change only by 1 per cent. Show how to hedge interest rate risks over the two-year period using a 6 per cent 10-year T-bond, which is priced at par, $1000 and call options on 100 thousand $ with a strike price of 105$ and intrinsic value $1000. (changes in interest rates that will happen only at year end every year.)

b) Using results from part a) compute an option premium if a discount factor is 4 per cent.