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?
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).
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!
