Question

Find the approximate market value of a long position in an FRA at a fixed rate of 5 percent in which the contract expires in 20 days, the underlying is 180-day LIBOR, the notional amount is $25 million, the 20-day rate is 7 percent, and the 200-day rate is 8.5 percent.

Answer 1

Sol:

Fixed rate = 5%

Contract expiry = 20 days

LIBOR = 180 days

Notional amount = $25 million

20 days interest rate = 7%

200 days interest rate = 8.5%

To determine market value (MV) of a long position in an FRA:

= [((1 + (200 days interest rate x (200/360)) / (1 + (20 days interest rate x (20/360)) - 1] x 360/180

= [((1 + (8.5% x (200/360)) / [1 + (7% x (20/360)) - 1] x 360/180

= [((1 + (0.085 x (200/360)) / [1 + (0.07 x (20/360)) - 1] x 360/180

= [(1.047222 / 1.0038888) - 1] x 360/180

= 0.0863309

Interest difference = ((0.0863309 x (180/360)) - (Fixed rate x (180/360)) x 25,000,000

Interest difference = ((0.0863309 x (180/360)) - ((5% x (180/360)) x 25,000,000

Interest difference = ((0.0863309 x (180/360)) - ((0.05 x (180/360)) x 25,000,000

Interest difference = (0.04316545 - 0.025) x 25,000,000

Interest difference = $454,136.25

Market value for 200 days will be,

Market Value = $454,136.25 / ((1 + (8.5% x (200/360))

Market Value = $454,136.25 / ((1 + (0.085 x (200/360))

Market Value = $454,136.25 / 1.0472222

Market Value = $433,658 (rounded off to nearest cent)

Therefore market value (MV) of a long position in an FRA is $433,658