How do you convert a forward rate to a quarterly compounding rate then to look for the value of the FRA?
Libor 3m spot rate 4% continuously compounded
Libor 6m spot rate 5% continuously compounded
The investor entered into an FRA and will receive 8% (assuming quarterly compounding) on notional principal 5,000,000 between 3 and 6 months. The question is to calculate the value of the FRA.
So far I have the forward rate being 6%. Does anyone know how to calculate the value for this FRA question?
I would approach it as follows:
From my calculations you are correct in thinking the forward rate is 6% with continuous compounding as:
Forward Rate = (0.5 x 5%) - (0.25 x 4%) / (0.5 - 0.25) = 6%
Then convert the 6% from continous compounding to quarterly compounding as follows:
Quarterly Rate = 4 x ( (exp 0.06/4) - 1) = 6.045226%
Now we need to calculate the present value of the difference between the 8% received and the 6.045% paid on the notional for the period of 3 months - note we will be discounting the difference for a period of 6 months to bring it back to today - this is because the actual payments are made at the end of the 3 month period, which places it 6 months from today. We discount back at the continous 5% 6 month spot rate.
PV = (Notional Amount x ((Rate received - Rate paid) x 0.25)) exp -0.05x0.5
PV = (5,000,000 x ((0.08 - 0.06045226) x 0.25)) exp -0.05x0.5 = 23,831.38