Hi

@David Harper CFA FRM .. My question is not related to the above and I am using this thread because I did not want to start a new one. My question is on Hull 4.6 (Study notes)

Hull 4.6

Assuming that zero rates are as in Problem 4.5 (above), what is the value of an FRA that enables the holder to earn 9.5% for a 3-month period starting in one (1) year on a principal of $1,000,000? The interest rate is expressed with quarterly compounding.

From David: The “holder who earns 9.5%” is the counterparty who is receiving the fixed, paying the floating rate, and who is SHORT the FRA. The buyer (who is long the FRA) is paying the fixed rate and receiving the floating rate.

Answer:

Here is the spreadsheet:

https://www.dropbox.com/s/8dzdxspnk2blh4s/Hull.04.06a.xlsx
The forward rate is 9.0% with continuous compounding or 9.102% with quarterly compounding.

From equation (4.9) the value of the FRA is therefore

[1,000,000 x 0.25 x (0.095 – 0.09102)]e^-0.086 x 1.25 = 893.56 or $893.56

For the period between 1 and 1.25, the continuous forward rate is calculated as 8.8%. Shouldn't that be the forward rate/variable rate for that period? Why is 9% which is the continuous forward rate for the period between 1.25 and 1.5 considered as the forward rate?

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