Consider a 30-year bond with 10% coupon rate (annual payments) and a £100 face value. To ease your computations, you are given that 1.0530 = 4.32 and 1.0529 = 4.12
Required
a) What is the initial price of this bond if it has a 5% yield to maturity?
b) If the yield to maturity is unchanged, what will the price be immediately before the first coupon is paid? (The answer is not the same as above. You also need to consider the first coupon payment in your calculations)
c) If the yield to maturity is unchanged, what will the price be immediately after the first coupon is paid? (The answer is not the same as above. The first coupon payment has already occurred)
d) Assuming duration is 2.78, find the change in the price of the bond if the market yield changes from 7% to 6.5% (notice that YTM is now 7% not 5% as in parts a, b and c). You can use either modified duration or the standard duration formula.
e) Recalculate the change in the price of the bond if convexity is 100. The rest of the information you need remains the same.