# Pricing Interest Rate Swaps

##### In todays video we will learn the two methods for pricing interest rate swaps.

Series on swaps. today we’ll learn about two different approaches to pricing first one of my videos you’ve watched, you should check out some of the others. make sure you subscribe if you’d like to get on with it and learn about how we price interest rate swaps. we’ll work derivatives. there’s a link to it in the description below. as explained in my that they can be valued

At zero at inception. this allows the two parties to when the npv or net present value of both cash flows is equal. once the swap value, and that just occurs once the market rates for whatever the two cash if you receive fixed in a swap, the swap cash flows, minus the present value of floating cash flows. if you pay fixed in present value of fixed cash flows. so basically

What i’m saying is that the the present value of whatever it is that for this reason, swaps are amongst the easiest derivatives that there are to there’s no stochastic calculus, no drawing of lattices like in the have to do is lay out the expected cash flows and then present value them. present value of what you get less the present value what you have agreed to whatever

Loss that you might have made on the swap your counterparty will have present value the cash flows. if you’ve ever priced a bond you can because we sometimes lay out the cash flows a little bit differently to how still the same thing we just kind of group it all together into a table with one bond, price the other bond and you you’re receiving less what you’re paying.

In my book i cover two approaches so let’s work through them here. a plain position in one bond and a short position in another bond, or as a coupon interest rates, as it’s assumed that the risk on the cash flows is description of a swap and then we will value it using each of our different that we now are looking to value it assume that it pays floating six month and has

1 and 3/4 years remaining to maturity suppose we know that libor percent for the three-month nine month 15 month and 21 month period we are also is the value of this swap so that’s what we have to solve there are two methods one floating and takes the difference between these present values the other forward rate agreements for each of the upcoming payment periods and then

Taking each upcoming payment period on screen right now you can see the calculations the value to the receive fixed counterparty is the fixed bond valuation million dollars. the opposing counterparty will have the opposite what have we done in there we just put together a table of the expected cash fixed payments are easy enough they’re just two and a half million dollars

Each five million dollars at the last payment to present value those cash flows so the to the discount rate which in the first payment period three months is 6% so we do the same calculation subbing in the different applicable interest rates just multiply those discount rates by the 2.5 million dollar cash flows and that is the value of the fixed-rate bond which you can see

In our example that floating rate bond has the coupon indexed to libor each coupon date the quoted six months earlier at the beginning of the coupon period. so each at the current date the later ones are random thus a floating rate bond is we have a floating rate being discounted at a floating rate so it just comes to all we have to do is discount the upcoming coupon which

We know with question the very last line in the question said we are also aware that the that floating rate bond we know that that payment is coming in three months which the bond will be worth par so that’s all that’s happening in that hundred million times six point two percent over two as it’s a semi-annual coupon giving us \$103.1 million. we then multiply that by the

101.565 million dollars the value to the receive fixed counterparty see that the swap is worth -4.22 million dollars. the we have to do to price our swap next let’s look at valuing the same swap but a’s which stands for forward rate agreement we draw up a table with a lot flows are the same the time periods and discount factors are the same and advance and the remaining

Ones are calculated as shown in row two where or a semi annually compounded in the next column we then work out the the discount rates to get the present value of the net cash flows we sum up dollars the same as the bond method that we just did earlier if you’re having forward rate agreements which will explain the idea of forward rate probably just learn off one method