Valuing an FRA - PEQ Apr 2013, q8

[Benjamin]

Hi,

Past exam question Apr 2013, q8 (revision book 3, q18) is on valuing a forward rate agreement.

I was trying to do this question using either of these two methodologies and did not arrive at the same result as in the revision booklet

- Chapter 11, section 1.5, formula V = L(RK - RF)...etc.
with
RK = 0.07/4
RF = 0.06/4 (derived from the formula on page 10 of the CMP: RF = (R2T1 - R1T1)...Etc
T2 = 0.5 (half a year)
T1 = 0.25 (3mths)
R2 = 0.055 (given)
L = 1mil
Produces V = 2,432.19

- Chapter 11, section 1.9 - treating the FRA as a single leg of a swap
Step1: RF = 0.06/4 as above
Step2: Swap cashflows are then 1,000,000 x each of (0.06/4) and (0.07/4)
= 15,000 and 17,500
Difference is 2,500
Step3: PV (tried discounting at 3 and 6mths respectively etc and could not arrive at the answer provided of 2,322.

Could you please step me through either of those methodologies in this context?

 

[Simon James]

Your RF is not correct. 6% is the continuously compounded forward rate. For valuing the FRA you need an i(4) (ie the same compounding frequency as the FRA rate). Try converting the 6% continuous to an i(4).

 

[Benjamin]

Good point - so with i(4) = 4(e^(0.06/4)-1) = 0.06045, that gives:

V = 1,000,000(0.07 - 0.06045)(0.5 - 0.25)e^(-0.055x0.5)
= 2,322.

Thank you!