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

a) Explain how to use the Black-Scholes model for hedging during the period of crisis. 

b) Now you need to consider changes in interest rates that will happen only at year end every year. 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 percent 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. 

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