Suppose that you are given the following term structure of zero-coupon yields (spot rates). r Maturity...

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Suppose that you are given the following term structure of zero-coupon yields (spot rates). r Maturity 0.5 0.02 1 0.025 0.03 0.04 1.5 2 Annual interest rates that are semi-annually compounded 1. From the given spot rates, calculate the forward rates, f(0, 0.5, 1), f(0, 1, 1.5), f(0, 1.5, 2), and f(0, 0.5, 2). 2. Calculate the prices of 1-year and 1.5-year zero coupon bonds with face values of $100. 3. Using the zero-coupon bonds in #2, replicate a forward rate agreement where you borrow $100 at t = 1 and pay back $100 plus interest at t = 1.5. 4. Suppose that someone offers you a forward rate of f(0, 1, 1.5) = 4.5%. This should be about 0.5 percentage points higher than what you found in #1. You can either borrow or lend at this rate. Using this rate and your replicating portfolio from #3, construct an arbitrage trading strategy. 5. Suppose that we go back to #1. You enter into a forward rate agreement to lend $100 at t = 0.5 and be repaid at t = 2 at the forward rate of f(0, 0.5, 2). What happens to the value of the forward rate agreement if all interest rates decline by one percentage point in the instant after you enter into the forward rate agreement? Hint: Do not overcomplicate this. Write down the cash flows to the FRA that you enter into. Then, calculate the NPV using the new discount rates. Suppose that you are given the following term structure of zero-coupon yields (spot rates). r Maturity 0.5 0.02 1 0.025 0.03 0.04 1.5 2 Annual interest rates that are semi-annually compounded 1. From the given spot rates, calculate the forward rates, f(0, 0.5, 1), f(0, 1, 1.5), f(0, 1.5, 2), and f(0, 0.5, 2). 2. Calculate the prices of 1-year and 1.5-year zero coupon bonds with face values of $100. 3. Using the zero-coupon bonds in #2, replicate a forward rate agreement where you borrow $100 at t = 1 and pay back $100 plus interest at t = 1.5. 4. Suppose that someone offers you a forward rate of f(0, 1, 1.5) = 4.5%. This should be about 0.5 percentage points higher than what you found in #1. You can either borrow or lend at this rate. Using this rate and your replicating portfolio from #3, construct an arbitrage trading strategy. 5. Suppose that we go back to #1. You enter into a forward rate agreement to lend $100 at t = 0.5 and be repaid at t = 2 at the forward rate of f(0, 0.5, 2). What happens to the value of the forward rate agreement if all interest rates decline by one percentage point in the instant after you enter into the forward rate agreement? Hint: Do not overcomplicate this. Write down the cash flows to the FRA that you enter into. Then, calculate the NPV using the new discount rates.

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In this question you are asked to perform a series of calculations related to forward rates prices of zerocoupon bonds and determining an arbitrage st... View the full answer