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96

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

A.$74,250

B.−$70,760

C.−$11,250

D.$103,790

Answer: B

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

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

Flashcard info:

Author: CoboCards-User

Main topic: Finance & Investment

Topic: Derivatives

Published: 27.10.2015