FRA vs. Interest Rate Options

Hi Level III-ers!

Can someone please explain why when calculating the effective rate on an FRA (Ch. 28 – blue box example 1), you annualize at the end of the calculation by subtracting 1 then MULTIPLYING by 360/# of days, but when calculating effective rate on interest rate options (Ch. 29 – blue box example 11), you annualize by RAISING to 365/# of days, then subtract 1. I understand that you use the 360 convention for FRAs, but don’t understand why the calculation is different.

Thanks so much in advance and good luck to everyone out there studying!

The interest rates for FRAs are usually LIBOR, which are nominal rates.

The rates for interest rate options are usually effective rates.

Thanks, but that didn’t clarify it for me…

In the FRA example, the steps are as follows:

  • Step 1: Calculate payoff
  • Step 2: Calculate what you need to borrow (NP minus payoff from step 1)
  • Step 3: Calculate what you need to pay back at the end of the term
  • Step 4: Then you take the number calculated in step 3 and use it to calculate the effective rate. It’s this step where I don’t understand why the effective rate calculation differs from calculating the effective rate for interest rate options.

Any other insights? Thanks!