0:02

In this module we're going to introduce you to swap contracts, introduce you to

Â the ideas why these swap contracts are

Â constructed, what is the advantage of swap contracts.

Â And also show you how to price a

Â very simple interest rate swap using a no-arbitrage principle.

Â 0:24

A plain vanilla swap transforms a fixed interest rate cash

Â flow into a floating interest rate cash flow.

Â A commodity swap, swaps or exchanges floating price of, for

Â the commodity for a fixed price for the same commodity.

Â Examples include gold swaps, oil swaps, and so on.

Â Currency swaps allows you to swap a cash flow

Â in one currency for a cash flow in another currency.

Â 1:08

Company A, were it to borrow in the fixed

Â interest rate market would be charged 4% per annum.

Â If it were to borrow in the floating rate market, it would have to pay LIBOR

Â plus 0.3%.

Â LIBOR stands for the London Interbank Offer Rate, and that's the

Â rate which is used as the base for floating, floating interest rates.

Â 1:30

Company B, were it to borrow in the fixed interest-rate market, would be charged 5.2

Â percent, and in the floating interest-rate market,

Â it could borrow at LIBOR plus one percent.

Â 1:39

So company A is clearly superior to company B, both in the fixed

Â interest rate market as well as the floating interest rate market.

Â However, company B is relatively stronger in the floating rate market.

Â The difference between the rate for company A and

Â B is only 0.7% in the floating rate market.

Â Whereas it's one point two percent in the fixed rate market.

Â 2:02

So these companies, could take advantage of

Â the difference of their relative strengths in

Â the true markets to create an, an instrument which lets them borrow at the

Â better rate than they could have individually

Â borrowed in either of the two markets.

Â Company A, which is stronger in the fixed-rate market,

Â borrows in the fixed-rate market, company B, which is stronger

Â in the floating-rate market, borrows in the floating-rate market, and

Â then they construct a swap in order to make an

Â additional product or a derivative product.

Â Which is going to be better than each of

Â these individual deals that are available to this company.

Â So here's company A, it borrows at

Â 4%, which means that it's going to

Â pay out 4%. Here's company B,

Â which borrows at libor plus 1%. And then we

Â construct a swap, we have company A, B is company

Â B LIBOR and company B pays company A 3.95%.

Â And if you see what the net effect of this swap is to each of these companies.

Â Company

Â A now ends up paying LIBOR plus

Â 0.05%, which is better than what it could have borrowed in the

Â floating rate market, and company B ends up paying 4.95%.

Â Which is better than what it could have gotten in the fixed-rate market.

Â So by constructing this swap, these two

Â companies are able to leverage their relative strength

Â to get a deal which is better than what they could

Â have achieved in, either the fixed-rate market or the floating-rate market.

Â Both of them end up gaining.

Â 4:02

The details of how to the 3.95% gets set depends on supply and demand.

Â But there is an inplicit assumption that is being made in this

Â particular example, and that's that company A and company B continue to exist.

Â That neither of them is going

Â to default.

Â 4:32

So most of the times when swaps are constructed.

Â You don't make a swap with a counterparty directly because

Â you don't want to be exposed to the counterparty default risk.

Â You would

Â rather make it with an intermediary, a financial intermediary,

Â that is able to take on the counterparty risk,

Â 4:57

So here's how, these swaps get, set up.

Â The same two companies, A and B, and

Â now there's a financial intermediate that contracts the swap.

Â Company A

Â borrows in the fixed market at 4%, swaps with an intermediary and pays LIBOR and

Â receives 3.93%. So, 0.02% less.

Â Company B borrows in the floating rate market at

Â LIBOR plus 1%. Constructors swap with an intermediary,

Â receives LIBOR and pays, 3.97%. So 0.02% more,

Â or this is the same thing as saying two basis

Â points less, two basis points more.

Â 6:02

Why does it get that?

Â This is the compensation for taking on the counter party risk.

Â If either of these two companies default, the financial intermediary's on

Â the hook, to provide the cash flow necessary for the surviving party.

Â And it also constructs

Â a service in the sense that, typically, in the

Â market, company A and company B don't know that they

Â exist, and their relative strengths are different so, by creating

Â a swap, they would be able to better position themselves.

Â So financial intermediary is able to bring these

Â two parties to the table and construct a

Â swap that is going to mutually beneficial, and

Â ends up getting paid for providing this service.

Â 6:48

And let's consider a swap whose cash flows at time little

Â t equal to 1 through capital T is given as false.

Â Company A, which takes on the long position in the swap, receives a

Â notional principal n, times the random interest

Â rate prevailing at time t minus 1.

Â So the cash flow that it receives at time

Â t is given by the notional principal n. Times the interest rate at time T minus 1.

Â And it pays the same notion of principal n times a fixed interest rate x.

Â 7:18

Company B, which nominally takes on a short

Â position on the swap, receives the fixed interest

Â rate payment n times capital X, and pays the floating payment n times rt minus 1.

Â 7:37

So there are two pieces to the cash flow to company A.

Â It receives the cash flow, the principle, n times r 0, r 1, r 2 and so on

Â up to r T minus 1 at times 1, 2, 3, 4 up to capital T minus 1.

Â This is precisely the cash flow associated with the floating weight bond,

Â minus the face value.

Â So in a floating weight bond, at the expiration capital T, in

Â addition to the coupon payment, you have received the notional principle back.

Â This time you do not get the notional principle.

Â And therefore, the value of the swap to company A consists of two elements.

Â This is the value,

Â 8:48

We know that the value of a floating rate bond is directly equal to the principle.

Â But we don't get the face value back, so I have to subtract from that value n times

Â d, 0, t, which is the discounted value of

Â the principal which was received at time capital T.

Â What happens to the value of the fixed-rate payment?

Â Every period, I get n times x. I have to discount that from time t equal

Â to 1 through capital T. So this is simply the discount values.

Â 9:17

How is this x set?

Â This is this x set, in a similar manner as we had done for former contracts.

Â We set at, at a value such that the va is exactly equal to 0 at time t equal to 0.

Â If you set it up, p equal to 0 implies that

Â x must be equal to 1 minus d, 0, t divided

Â by the sum of little t going from 1 to capital T to 0 T.

Â This is the interest rate that you would have to set up, so that

Â the value of the swap is exactly equal to company, zero for company A.

Â And it's also equal to zero for company B.

Â So, the two companies going into this swap, are eq,

Â are, indifferent between taking a long position or a short position.

Â