Consider the following spot rate curve:
What is the forward rate for a one-year zero coupon bond issued 6 months from today? Equivalently, the question asks for f21, where 1 time period consists of 6 months.
(1 + 6 month rate/2) * (1 + forward rate one year from now/2)^2 = (1 + 18 month rate/2)^3
(1 + 0.07/2) * (1 + 1 year forward rate 6 months from now/2)^2 = (1 + 14%/2)^3
1.035 * (1 + 1 year forward rate 6 months from now/2)^2 = 1.07^3
(1 + 1 year forward rate 6 months from now/2)^2 = 1.225043 / 1.035
(1 + 1 year forward rate 6 months from now/2)^2 = 1.183616
1 + 1 year forward rate 6 months from now/2 = 1.087941
1 year forward rate 6 months from now = 0.1759
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