Consider a consol with an annual cash-flow of $1 (with the first payment in one year from now) and a two-year bond with an annual coupon rate of 5% and face value $100. The first coupon is due in on year from now. Suppose that the term structure is flat at 4%.There is no risk of default.
a) Calculate the prices of the consol and the coupon-bond.
b) Calculate the Macaulay duration, modified duration and convexity of the two bonds.
c) Suppose that the term structure moves down to 3.9% in a parallel way. Calculate the exact price changes after the change in the term structure. Calculate the approximate price changes using a first order and second-order approximation useful? Explain.
d) There are also two zero-coupon bonds traded in the market. The first bond has a maturity of one year, and the second bond has a maturity of two years, with face values $100. Their prices are S1 =96.154 and S2=93.163 respectively. Given the coupon-bond price you calculated in (a) and the prices of these two zero-coupons is there an arbitrage in the market and if so how would you profit from it?