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.If the swap has a principal value of $15,000,000,what is the value of the swap to the party receiving a fixed rate of interest? Assume OIS rates are the same as LIBOR rates.
A) $74,250
B) −$70,933
C) −$11,250
D) $103,790

Question

Quizplus · Accepted Answer

The forward rate for the floating payment at time 9 months is 6.05% with continuous compounding or 6.1424% with semiannual compounding.The swap can be valued assuming that the fixed payments are 2.5% of principal at 3 months and 9 months and that the floating payments are 2.425% and 3.0712% of the principal at 3 months and 9 months.The value of the swap to the party receiving fixed is therefore 15,000,000(0.025-0.02425)e^-0.053×0.25+15,000,000(0.025-0.030712)e^-0.058×0.75 = -$70,933

A Semi-Annual Pay Interest Rate Swap Where the Fixed Rate