Question

Consider the following spot rate curve: 6-month spot rate: 7%. 12-month spot rate: 9%. 18-month spot...

Consider the following spot rate curve:

  • 6-month spot rate: 7%.
  • 12-month spot rate: 9%.
  • 18-month spot rate: 14%.

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.

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Answer #1

(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

*Please comment if you face any difficulty and please don't forget to provide positive rating*

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