Question

An interest rate swap where the annual fixed rate is 6.00% has a remaining life of one year. Both floating and fixed rates are paid every six months. The floating payments are indexed on the six-month LIBOR rate. The six-month LIBOR rate observed today is 7% with semi-annual compounding. Today’s LIBOR rates for 6-month and 12-month deposits are 7.5% and 8.0%, respectively. These two rates are annual and continuously compounded.

a) Calculate the forward LIBOR rate for the period between six and twelve months assuming semi-annual compounding.

b) If the swap has a principal value of $50,000,000, what is the value today of the swap to the party receiving the floating rate of interest?

Answer 1

Answer :

a) Calculation of Forward LIBOR rete :

6 month LIBOR rate = 7.5% + ( 7.5 / 2 ) * 7.5%

LIBOR rate = 7.5% + 0.28%

LIBOR rate = 7.78%

12 month LIBOR rate

LIBOR rate = 8% + ( 8 / 2 ) * 8%

= 8% + 0.32%

6 month LIBOR rate = 8.32%

12 month LIBOR rate = 8.32% + ( 8.32% / 2 ) * 8%

LIBOR rate = 8.32% + 0.33%

LIBOR rate = 8.65%

b) Calculation of Interest

6 month = Principle * Interest rate

= 50,000,000 * 7.78% / 2

= 3,890,000 / 2

= 1,945,000

12 month = 50,000,000 * 8.65%

= 4,325,000