interest rate swap

[owen]

Hi David,
Can you explain to me how to solve the following question:

Assume that a bank enters into a USD 100 million, 4-year annual pay interest rate
swap, where the bank receives 6% fixed against 12-month LIBOR. Which of the
following numbers best approximates the current exposure at the end of year 1 if the
swap rate declines 125 basis points over the year?
a. USD 3,420,069
b. USD 4,458,300
c. USD 3,341,265
d. USD 4,331,382

the solution from the book is first calculate fixed rate bond 6/(1+4.75%)+6/(1+4.75%)^2+106/(1+4.75%)^3, then subtract $100 for floating leg.

It is a 4 years bond, but why is it using 3 years to calculate the fixed rate bond present value. Also I don't think it is correct to use 4.75%.

Thanks a lot.

 

[David Harper CFA FRM]

Hi owf_bob,

(FYI, you can change your screen name, see http://forum.bionicturtle.com/threads/we-recommend-you-change-your-screen-name-in-the-forum.5004/)

I input their solution into version of our IRS pricer, so you can see how the $3,420,069 is confirmed: https://www.dropbox.com/s/q6it4yvxpsjf26z/irs_0502.xlsx

I think it's an instructive question (we might quibble the assumptions that LIBOR is initially 6% and a swap rate decline = LIBOR, a little additional precision would help, but i think it is fair enough...)

• It is pricing the swap one year forward, when the swap has only 3 years remaining
• The question implies that a flat 6.0% libor drops by 125 bps to a flat 4.75% libor (see xls).
• Importantly, one year forward, at the first settlement, the floating rate bond will price at par. So, the -$100 deduction.
• Note the clever use of "current exposure:" what is the one-year forward current exposure to the counterparty? is it - 3,420,069? No! To the counterparty, the value will be -3,420,069 but the current exposure will be max[-3,420,069, 0] = 0 b/c they will be OTM. For the back, ITM value will = current exposure.

I hope that helps,