In: Finance
The half-year LIBOR rate is 3.5% and the one-year LIBOR rate is 6%. Suppose that some time ago a company entered into an FRA where it will receive 5.8% and pay LIBOR on a principal of $1 million for the period between time 0.5 years and time 1 year in the future (with semiannual compounding). The one-year risk-free rate is 4%. What is the value of the FRA? All rates are compounded continuously unless specified.
Forward LIBOR rate from 0.5 years to 1 year (r) is given by
exp(r*0.5)= exp(0.06*1- 0.035*0.5)
=> r= 2*(0.06-0.0175) = 0.085 or 8.5%
Net amount received by the company in FRA after one year = $1 million * 0.058*0.5- $1 million * 0.085*0.5
= - $13500
Value of FRA today to the Company = -13500*exp(-0.04)
= - $12970.66