The half-year LIBOR rate is 3.5% and the one-year LIBOR rate is 6%. Suppose that some...

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.

Solutions

Expert Solution

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

jeff jeffy answered 2 years ago

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