Estimate the 2-year, 5-year and 10-year key rate durations of a 20-year bond carrying a coupon of 15% on face value $100 paid semi-annually. The given term structure starts with 10.8% spot rate of interest at time zero and rises at a rate of 0.002 (2%) per half year thereafter. Take a 20 basis point (.002) move in each key interest rate to calculate the key rate durations. Interest rates are expressed as annualized rates for the term specified.
A. What is the current fair price of the bond with the given term structure.
B. (i) What is the price change needed to calculate 2-year key rate duration
(ii) What is the price change needed to calculate 5-year key rate duration
(iii) What is the price change needed to calculate 10-year key rate duration
C. What are the 2-year, 5-year, and 10-year key rate durations