Question: 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 current price of $1 par of a zero maturing at time 2 is $0.97
a. What is the 2-year spot rate?
b. What is the dollar duration of $1 par of the 2-year zero? The current price of $1 par of a zero maturing at time 3 is $0.92
c. What is the 3-year spot rate?
d. What is the dollar duration of $1 par of the 3-year zero? You can enter into a forward contract today to buy, at time 2, $1 par of a zero maturing at time 3. The price you would pay at time 2 is the forward price. The cost today of entering into this contract is zero.
e. Construct a portfolio of 2- and 3-year zeroes that synthesizes this forward contract.
f. What is the no arbitrage forward price?
g. What is the dollar duration of the forward contract?