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?
A)$74,250
B)-$70,760
C)-$11,250
D)$103,790

Question

Quizplus · Accepted Answer

The forward rates for the floating payment at time 9 months is 6.14%.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 3.07% of the principal at 3 months and 9 months.The value of the swap to the party receiving fixed is therefore 1,000,000(0.025-0.02425)e^-0.053×0.25+1,000,000(0.025-0.0307)e^-0.058×0.75 = –$70,760

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