0:02

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

the ideas why these swap contracts are

constructed, what is the advantage of swap contracts.

And also show you how to price a

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

0:24

A plain vanilla swap transforms a fixed interest rate cash

flow into a floating interest rate cash flow.

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

the commodity for a fixed price for the same commodity.

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

Currency swaps allows you to swap a cash flow

in one currency for a cash flow in another currency.

1:08

Company A, were it to borrow in the fixed

interest rate market would be charged 4% per annum.

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

plus 0.3%.

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

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

1:30

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

percent, and in the floating interest-rate market,

it could borrow at LIBOR plus one percent.

1:39

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

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

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

The difference between the rate for company A and

B is only 0.7% in the floating rate market.

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

2:02

So these companies, could take advantage of

the difference of their relative strengths in

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

better rate than they could have individually

borrowed in either of the two markets.

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

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

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

then they construct a swap in order to make an

additional product or a derivative product.

Which is going to be better than each of

these individual deals that are available to this company.

So here's company A, it borrows at

4%, which means that it's going to

pay out 4%. Here's company B,

which borrows at libor plus 1%. And then we

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

B LIBOR and company B pays company A 3.95%.

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

Company

A now ends up paying LIBOR plus

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

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

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

So by constructing this swap, these two

companies are able to leverage their relative strength

to get a deal which is better than what they could

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

Both of them end up gaining.

4:02

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

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

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

That neither of them is going

to default.

4:32

So most of the times when swaps are constructed.

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

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

You would

rather make it with an intermediary, a financial intermediary,

that is able to take on the counterparty risk,

4:57

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

The same two companies, A and B, and

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

Company A

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

receives 3.93%. So, 0.02% less.

Company B borrows in the floating rate market at

LIBOR plus 1%. Constructors swap with an intermediary,

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

or this is the same thing as saying two basis

points less, two basis points more.

6:02

Why does it get that?

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

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

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

And it also constructs

a service in the sense that, typically, in the

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

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

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

So financial intermediary is able to bring these

two parties to the table and construct a

swap that is going to mutually beneficial, and

ends up getting paid for providing this service.

6:48

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

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

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

notional principal n, times the random interest

rate prevailing at time t minus 1.

So the cash flow that it receives at time

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

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

7:18

Company B, which nominally takes on a short

position on the swap, receives the fixed interest

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

7:37

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

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

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

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

minus the face value.

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

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

This time you do not get the notional principle.

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

This is the value,

8:48

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

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

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

the principal which was received at time capital T.

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

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

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

9:17

How is this x set?

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

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

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

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

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

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

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

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

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

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