Interest Rate Swap with Maturity Mitchmatch

[rahul.goyl]

Hi David,
I got another Problem on IRS ? I think this is tricky one to solve. Always appreciate for your quick respond.

A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, six month LIBOR is exchanged for 12% per annum (compounded semi-annually). The average of the bid-offer rate being exchanged for six-month LIBOR in swaps of all maturities is currently 10% per annum with continuous compounding. The six-month LIBOR rate was 9.6% per annum two months ago. What is the current value of the swap to the party paying floating?
Choose one answer.
a. $ 2.064 million
b. $ 10.245 million
c. (-) $ 2.064 million
d. $ 1.964 million

Thanks
Rahul

 

[David Harper CFA FRM]

Hi Rahul,

I did this exact problem (Hull 07.03) on the blog a few days ago.
See http://forum.bionicturtle.com/viewthread/1519/

David

 

[rahul.goyl]

I have a question, :-/

Why in the floating we are just having one cash flow 104.8M compare to fixed where we have 2 cash flow 6m + 106M discounted at PV.
Would appreciate if you can provide your feedback

Thanks
Rahul

 

[David Harper CFA FRM]

Rahul,

...because the floater must be worth par at the time of the next coupon; we can use the par value, at that time, as it prices in all subsequent cash flows
(we could still build them out, should get same answer)....

see http://sheet.zoho.com/public/btzoho/floater-worthpar

and note that you can change the three LIBOR rates (i.e., floater) and, since they are used to discount, the price will always still be par

related: duration of floater is time to next coupon for the same reason! at the next coupon, floater price = par and there's no market risk

David

 

[Brian_no9]

Hi David,

In your sample questions for Hull Chapter 7, question number 175.2

A $50 million interest swap has a remaining life of 14 months. Under the swap, 6-month LIBOR is exchanged for 5.0% per annum with semi-annual compounding. Four months ago (t - 4/12 years) the 6-month LIBOR was 4.0% and, currently the swap rate curve is flat at 4.0% per annum, with continuous compounding, for all maturities. What is the current value of the swap to the PAY FLOATING counterparty?

The value of the fixed-rate bond position = $1.25 MM * EXP(-4%*2/12) + $1.25 MM * EXP(-4%*8/12) + $51.25 * EXP(-4% * 14/12) = $51.37

How did you determine the maturities in calculation of the fixed rate bond? Sorry if this is a simple question, i just can't wrap my head around how you got the periods 2/12 and 8/12?

Many thanks for any insight you can offer.
Brian

 

[David Harper CFA FRM]

Hi Brian_no9 good question, this is somewhat typical of FRM-style swap question (only because if follows Hull) so it's good to get comfortable with this. You first want to identify the settlement periods (i.e., how often are the cash flows netted). In this case, my question is not exactly overt, it gives just enough information to convey six-month settlement periods. You have to realize that 6-month LIBOR and semi-annual compounding imply settlement every six months. Then you can work backwards:

• If the swap matures in 14 months, then the final settlement (exchange) much occur in 14 months; such that:
• the settlement before that must be in 14-6 = +8 months from today (valuation), such that:
• the settlement before that must be in 8-6 = +2 months from today.

Mathematically, it's a mod or remainder function; i.e., in excel = MOD(14,6) = 2 months until the next cash flow. Then 2+6 = 8. I was going to link you to wikipedia entry on the remainder (mod) function but it's almost incomprehensible to me (yikes!): http://en.wikipedia.org/wiki/Modular_arithmetic

I hope that explains,

 

[Brian_no9]

Thats great David.
Really appreciate it,
Brian