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Asked Jul 17, 2019
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3. Bonds: The three parts of this problem are related.
By studying prices of zero coupon STRIPS, you have calculated that the 1- ,2- ,3-,
and 4-year spot-rates are: ri-3%, 12-4.5 %, r3-5.5% and r4-7% respectively.
a)
Calculate the forward rates, f23 and f3,4.
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3. Bonds: The three parts of this problem are related. By studying prices of zero coupon STRIPS, you have calculated that the 1- ,2- ,3-, and 4-year spot-rates are: ri-3%, 12-4.5 %, r3-5.5% and r4-7% respectively. a) Calculate the forward rates, f23 and f3,4.

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Step 1

If rn andrSn+1 are the spot rates for the year n and n+1 respectively, then one year forward rate between year n and n+1 is given by fn, n+1 and governed by the following equation:

(1 + rn)n x (1 + fn, n+1) = (1 + rn + 1)n + 1

Step 2

In order to get f2, 3 we need to put n = 2. In that case, the equation becomes:

(1 + r2)2 x (1 + f2, 3) = (1 + r3)3

Or, (1 + 4.5%)2 x (1 + f2, 3) = (1 + 5.5%)3

Or, f2, 3 = (1 + 5.5%)3 / (1+ 4.5%)2 – 1 =  7.5288%

Step 3

In order to get f3, 4 we need to put n = 3. In that case, the equation becomes:

(1 + r3)3 x (1 + f3, 4) = (1 + r4)4

Or, (1 + 5.5%)3 x (1 + f3, 4) = (1 + 7%)4

Or, f3, ...

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