A semi-annual pay interest rate swap where the fixed rate is 5% (with semi-annua

Question

A semi-annual pay interest rate swap where the fixed rate is 5% (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 paying a floating rate of interest?

Explanation / Answer

Forward LIBOR rates between 3 and 9 months is 6.14%.

Value of swap can be valued by assuming that the fixed payments are 2.5% (5% is semi-annual compounding) 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. T

Value of swap for the party receiving fixed is

$ 15,000,000 (0.025 - 0.02425) e - 0.053 × 0.25 +$ 15,000,000 (0.025 - 0.0307) e - 0.058 × 0.75=

($ 70,760) is the correct answer.

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