Question

Long position in an FRA expiring in 30 days where the underlying is 90-day LIBOR. The notional principle is $ 10,000,000. The term structure of interest rates is 12% for 30 days and 10.5% for 120 days.

Determine the fixed rate on the FRA.

Today is 27 days into the life of the FRA. Given the term structures of L₂₇(3)=10.6% and L₂₇(93)=10.55%, determine the value of the FRA from the point of view of the financial institution.

Answer 1

Forward Rate (FRA Rate)

e^{0.105*120/360}=e^0.12*30/360 × e^z×90/360

1.03562=1.01005 × e^z×90/360

1.025315= e^z×90/360

=ln(1.025315)= ln(e^z×90/360)

= 0.025=z×90/360

=z=0.10=10%

After 27 days the new FRA rate:

e^{0.1055*93/360}=e^0.1060*3/360 × e^z×90/360

1.027629= 1.000884× e^z×90/360

1.026722= e^z×90/360

=ln(1.026722)= ln(e^z×90/360)

= 0.026371 =z×90/360

=z=10.55%

Therefore, gain to long position after 27 days:

=(0.1055-0.10*90/360*10,000,000)e^{-0.1055*93/360}

=$ 13,339.77