1. 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.
(Part I) At time 0, Investor A enters into a forward contract, at no cost, to buy, at time 2, $100,000 par of a zero maturing at time 3. The forward price this investor locks in to pay at time 2 is $91,000.
a. What forward rate does this investor lock in at time 0, through this forward contract, for lending from time 2 to time 3?
(Part II) At time 1, the spot price of $1 par of a zero maturing at time 2 is 0.95 and the spot price of $1 par of a zero maturing at time 3 is 0.91.
a. At time 1, what is the forward price an investor could lock in to pay, at time 2, for $100,000 par of a zero maturing at time 3?
b. What is the value, at time 1, of Investor A's position in the forward contract from Part I?
2. 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 $0.95
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 $0.90
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?