# 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.

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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.

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Step 1

If Pn is the price of ZCB with maturity of n years and Sn is the spot rate for year n then,

Pn = (1 + Sn)-n

Hence, (Pn)-1/n = (1 + Sn)

Hence, Sn = (Pn)-1/n - 1

Step 2

Hence,

S2 = (P2)-1/2 – 1 = 0.8-1/2 – 1 = 11.80%

S5 = (P5)-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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