Hull, Chapter 7 Swaps-Calculate the value of a plain vanilla interest rate swap

[idcnik01]

Hi All,

Referring to Page 104 example (See attached for details.
In the solution I am not able to understand, in the receiving cash flow why will we receive $2 (Which is semi annual interest) after 3 month and similarly the outgoing cashflow is after 3 months (Why?)

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We assume a notional principal of $100 million (L = $100 million). In this case, we will
receive fixed-rate payments at 4% per annum. The LIBOR rates at 3-months, 9-months, and
15-months are, respectively, 5%, 6% and 7%. The 6-month LIBOR is 5.5% and our company
is going to “pay floating” such that the first floating payment is based on this six-month
LIBOR. The swap expires in 15 months. We’ll assume the LIBOR curve does not shift over
time.

First, we compute the present value of the (received or incoming) fixed cash flow
stream. That requires us to discount the $2 (1/2 of the 4% per annum) to be received
in three months (4% annual = $2 semi-annual) and again in nine months; finally, we
discount the lump sum to be received in fifteen months ($102). The present value of
the fixed cash flow stream is $97.34.

idcnik01

 

[ShaktiRathore]

Hi,
Here the swap is already initiated before so that the payments are based on the 6 months rates and we are here finding the value of the swap when swap has 15 months left to expire.

thanks

 

[David Harper CFA FRM]

Hi @idcnik01 It's what @ShaktiRathore said. This is Hull's (prior edition) example. The swap expires in 15 months and it pays every six moths (six month LIBOR). So you could induce backwards: the final payments swap in 15 months, so there will be a prior swap in 15 - 6 = 9 months, and the next swap must be in 9 months - 6 = +3 months. We actually are not told when the swap initiated, and we do not need to know! In case it's easier to grok, I just updated all of Hull exhibits for our upcoming, revised note, here is this swap in the new XLS format https://www.dropbox.com/s/b5kjspev38ch3xn/0331-hull-swap.xlsx?dl=0 (screen below):