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.
$100 par of a 0.5-year 10%-coupon bond has a price of $102.
$100 par of a 1-year 12%-coupon bond has a price of $105.
a. What is the price of $1 par of a 0.5-year zero?
b. What is the price of $1 par of a 1-year zero?
c. Suppose $100 of a 1-year 8%-coupon bond has a price of $99. Is there an arbitrage opportunity? If so, how?
d. What is the 0.5-year zero rate?
e. What is the 1-year zero rate?
f. What is the 1-year par rate, i.e., what coupon rate would make the price of a 1-year coupon bond equal to par?
g. Considering the shape of the yield curve, should the yield on the 1-year 12%-coupon bond be higher or lower than the 1-year par rate?