The six month LIBOR is 15% per annum with continuous compounding for all maturit

Question

The six month LIBOR is 15% per annum with continuous compounding for all maturities. Under the terms of an interest rate swap, SABIC Financial has agreed to pay 8% per annum and to receive six-month LIBOR in return on a notional principal of $150 Million with payments being exchanged every six months. The swap has a remaining life of fifteen months. The six-month LIBOR at the last payment date was 6% per annum.

1) When was the last (i.e., most recent) payment made?

2) What are the remaining payment dates?

3) What is the value of the fixed-rate bond?

4) What is the value of the floating-rate bond?

5) What is the value of the swap to SABIC Financial?

Explanation / Answer

1)

Last payment made on 3 months back

2)

1st - 3 months from now

2nd - 9 months from now

3rd - 15 months from now

3)

Fixed payments = 0.5*15%*150 = 11.25

Fixed value = 11.25*EXP(-0.5*8%*3/12) + 11.25*EXP(-0.5*8%*9/12) + (11.25+150) *EXP(-0.5*8%*15/12) = 175.4413

4)

float payment = 0.5*6%*150 = 4.5

float value = (150+4.5)*EXP(-6%*3/12) = 152.1998

5)

value = 175.4413 - 152.1998 = 23.24152

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