You are given the following data concerning a 6×12 FRA.The first six-month period is 182 days and the second is 183 days.The Libor rate for six months is 5% and for one year is 6%.The arbitrage-free price of the 6×12 FRA,assuming the Actual/360 day-count convention,is
A)5.50%
B)6.22%
C)6.55%
D)6.82%

Question

Quizplus · Accepted Answer

Straightforward computation using the formulae in the text.The calculations are as follows:
> d1=182
> d2=183
> r1=0.05
> r2=0.06
> B1 = 1/(1+d1*r1/360)
> B2 = 1/(1+(d1+d2)*r2/360)
> B1
[1] 0.9753454
> B2
[1] 0.9426551
> f = function(x){ B2*(1+d2*x/360)-B1 }
> uniroot(f,c(0,1))
$root
[1] 0.06822088

You Are Given the Following Data Concerning a 6×12 FRA