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Asked Oct 19, 2019

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Question 2. Suppose the current ZCB prices for maturity in two years and in five years are 0.8 and 0.7, respectively. Suppose the two-year forward three-year libor rate is 4%. Determine if there is an arbitrage opportunity. If so, find an arbitrage portfolio. Make sure that you verify the portfolio is an arbitrage portfolio.

Hint: In your arbitrage portfolio you will need to include a forward rate agreement.

Step 1

If P_{n} is the price of ZCB with maturity of n years and S_{n} is the spot rate for year n then,

P_{n} = (1 + S_{n})^{-n}

Hence, (P_{n})^{-1/n} = (1 + S_{n})

Hence, S_{n} = (P_{n})^{-1/n} - 1

Step 2

Hence,

S_{2} = (P_{2})^{-1/2} – 1 = 0.8^{-1/2} – 1 = 11.80%

S_{5} = (P_{5})^{-1/5} – 1 = 0.7^{-1/5} – 1 = 7.39%

Step 3

two-year forward three-year libor rate = 2F3 = 4%

Hence, no arbitrage five year spot rate, S should follow the following equation:

(1 + S)5 = (1 + S2)2 x (1 + 2F3)3 = (1 + 11.80%)2 x (1 + 4%)3 = 1.40608

Hence, ...

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