Hi David,
I feel there is some discrepancy in the Derivatives 1 screencast relating to the valaution of an IRS. In the screencast you have said that the swap has 15 months to maturity. The Libor rates given are 3,6,9,12. Which means standing today we donot have the Libor rates as of the end of the 15th month. Hence I am a little confused as to how the 12 month rate has been used to discount the 15th month cash flow.

Also while calculating the cashflow for the floating leg it is said that we knew about that the 6 month Libor rate from the beginning of the period hence a cash flow of 2.75 (5.5/2) needs to be taken. But my question is why the same rate (5.5%) has not been used to discount the fixed cashflows.

I hope I was able to make some sense. If my question is not clear please let me know.

Hi Aminesh,

First, I think you are referring to the 2007 version (Derivatives 1). I just want to make sure you are aware there is an 2008 version (Market A)? I leave last years tutorials published because we have not finished the 2008 AIMS, and several customers like this…

Regarding the 15-month rate, in the 2007 version, I did do that and you are right to be confused.
In the 2008 version, which you probably want to be viewing anyhow, i remedied this by assuming a LIBOR curve:

3 months @ 5.0%
6 months @ 5.5%
9 months @ 6.0%
12 months @ 6.5%
15 months @ 7.0%

So in the most recent, I believe i applied this upward-sloping line. But of course, in both cases, they are merely input assumptions.

“But my question is why the same rate (5.5%) has not been used to discount the fixed cashflows. “
This gets to the potentially confusing part of the valuation. Interest rates are being used in two different ways:

1. To compute the floating coupon - this is a 6 month LIBOR in arrears. If we were to extend the floating leg analysis, it may be helpful to note, that under the *naive* assumption of an unchaning LIBOR curve, all of the floating coupons would be at the SAME 5.5%

2. To discount future cash flows. The first fixed coupon arrives in 3 months, not 6 months, so we discount at 3 month rate. My example is not orginal, i just tweaked Hull’s 7.2 and I think it is a good example precisely b/c it teases out the different between the 6 month coupon rate and the discount rates.

David

I guess that the example becomes more obvious when stating that the interest rate at 0 months is 5.5%. It is then the 0 month libor (i.e. not the 6 month libor) from which the interest rate is taken which is the moment of the last coupon payment. The fact that 3 months later the interest rate has dropped to 5% and 3 months later it rose back up to 5.5% is just a coincidence. Do I interpret that correctly?

George

Hi George,

I don’t think so. We are valuing the swap at T0 where the last coupons swap @ T-3 months and the next coupons swap @ T+3 months. The *simplistic* assumption is a static yield curve:

T-3 months: 5%, 5.5% (six month LIBOR), 6%, 6.5%, 7%
T0 today: 5%, 5.5% (six month LIBOR), 6%, 6.5%, 7%

At valuation (T0), the next floating coupon is known. It was based on the 6 month LIBOR at T-3 (i.e., 5.5%). The rate is determined at the beginning of the 6 month period (T-3) for the floating coupon paid at the end (T+3). So a 0 month rate never enters.

At valuation, we need

1. the cash flow pattern. In regard to fixed, it is known (no yield curve needed). In regard to floater, we only need the next coupon, which is determined by the 6-month LIBOR at beg of period (T-3)

2. the T0 yield curve to discount the cash flows

David