Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. The 0.5-year zero rate is 7% and the 1-year zero rate is 9%.
a. What is the price of:
i. $1 par of a 0.5-year zero?
ii. $1 par of a 1-year zero?
iii. $100 par of a 1-year 10%-coupon bond, in the absence of arbitrage?
b. What is the dollar duration of:
i. $1 par of a 0.5-year zero?
ii. $1 par of a 1-year zero?
iii. 100 par of a 1-year 10%-coupon bond?
c. What is the duration of:
i. $1 par of a 0.5-year zero
ii. $1 par of a 1-year zero?
iii. $100 par of a 1-year 10%-coupon bond?
d. Use dollar duration to estimate the change in value of $1,000 par of the 1-year 10%-coupon bond if all zero rates rise 100 basis points.