Finance

i need help with a couple exercises on duration an convexity of bullet bond and immunization. can you do that?



Exercise CW1.1: Duration and convexity of a bullet bond

Consider a three-year bond with face value of $100, which pays semi-annual coupons of $2.25. The rst coupon is due in two months. The bond matures in two years and eight months. The interest rate, annually compounded, is 3%.
(a) Compute the present value of the bond.
(b) Compute the Macaulay duration of the bond.
(c) Compute the convexity of the bond.
(d) Use your answers to (a){(c) to approximate the eect of an increase of the interest rate of one percent point on the price of the bond.


CW1.2: Immunization
A company has to pay $25,000 in six years and $35,000 in eight years. It sets up an investment funds consisting of ve-year and ten-year zero-coupon bonds with a face value of $100 in order to meet these requirements. The current interest rate, continuously compounded, is 4%.
(a) How many ve-year and ten-year bonds should the company buy based on immu-
nization?
(b) Suppose that, instead of ve-year and ten-year bonds, the company uses ve-year
and n-year bonds for some value of n. Construct a portfolio of ve-year and n-year
bonds such that the present value and duration of the portfolio matches the present
value and duration of the liabilities.
(c) For which values of n can the conditions of Redington immunization be satised?