A coupon bond has a maturity of 5 years, yield to maturity of 11% (continuously compounded), and pays an 8% coupon at the end of each year. The bond face value $1,000. Assume that you hold this coupon bond worth $10 million. The Treasury bond futures price is currently 91-16 with a face value of $100,000 and the cheapest-to-deliver bond has a duration of 5.6 years at maturity.

Required:

a. Calculate the coupon bonds price. (3 marks)

b. Calculate the coupon bonds duration. (3 marks)

c. If the market interest rate increases by 0.2%, what is the effect on the value of coupon bonds you hold? Calculate the effect by using duration model. (3 marks)

d. How should you immunize your coupon bonds against changes in interest rates over the next year? (3 marks)