Question

A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual compounding) has a remaining life of nine months.  The six-month LIBOR rate observed three months ago was 4.85% with semi-annual compounding. Today’s three and nine month LIBOR rates are 5.3% and 5.8% (continuously compounded) respectively. From this it can be calculated that the forward LIBOR rate for the period between three- and nine-months is 6.14% with semi-annual compounding.

Can anyone explain the steps to calculate the forward LIBOR rate for the period between three- and nine-months which is 6.14%?

Answer 1

forward LIBOR rate for the period between three- and nine-months = [(EXP(9 Months LIBOR Rate * 9 / 12) / EXP(3 Months LIBOR Rate * 9 / 12)] - 1) * 12/6

forward LIBOR rate for the period between three- and nine-months = ([EXP(5.80% * 9 / 12) / EXP(5.30% * 3 / 12)] - 1) * 12/6

forward LIBOR rate for the period between three- and nine-months = ([EXP(4.35%) / EXP(1.325%)] - 1) * 12/6

forward LIBOR rate for the period between three- and nine-months = ([1.04446/1.013338] - 1) * 12/6

forward LIBOR rate for the period between three- and nine-months = [1.030712 * - 1} * 12/6

forward LIBOR rate for the period between three- and nine-months = 6.14%