This credit event has happened somewhere in between two coupon payments.

There should have been a coupon payment there.

There should have been a coupon payment there.

So, the credit event happened right in between these two coupon payments.

So, at the next coupon payment date, the buyer has to pay the accrued interest

over this interval . And I'm showing this with a smaller arrow

to suggest that the accrued interest is actually less than the full coupon

payment. On the other hand, the seller, the one

who decided to sell the protection on this underlying credit event, after the

credit event has happened at time, at the next coupon date, the seller has to pay 1

minus R, where R is the recovery rate, times the notional payment, N.

Because the buyer pays premiums, this, the premium payments are sometimes called

the premium leg of the CDS. And because the seller always pays the

amount only on default, this is also called the protection leg.

Here's a simple numerical example. So, consider a hypothetical 2-year CDS on

a notional principal N equal to $1 million.

And the spread S equal to 160 basis points, so just about 1.6%.

And lets assume that the payments are quarterly.

Suppose a default occurs in month 16 of a 24-month protection period.

And the recovery rate at that time is 45%.

And now, let's understand what happens to the payments of the buyers and the

sellers. The buyer pays premiums, so he pays

premiums at month 3, 6, 9, 12, and 15, and this is going to be S, the spread,

times the notional principal of $1 million divided by four.

Why? Because these are quarterly payments, so

it's 1 4th of a year. So, the payments in all of these months

is going to be $4000. Now, here's month 15.

The next coupon is going to be on 18. But in month 16, the default has

happened. So, this is the period over which the

interest has accrued. So, the accrued interest that I have,

that the buyer has to pay in month 18, is just 1 3rd of 4,000, so it's $1333.33.

What about the payments from the protection's seller?

Nothing paid up to month 15, because the default has not happened.

Default happens in month 16 and month 18, which is the next coupon date.

The seller has to pay 1 minus R times N. R was 45%, therefore, 1 minus R is 55% of

N, which is $550,000. This is the total protection payment.

Some other names for these payments. We've called them premium payments.

We have called them, another name for the same payment is fixed leg or the fixed

payments. Because the premiums are fixed, except

for the accrued interest amount. The name for the protection sellers

payment is also sometimes called a contingent leg or the contingent payment

because it's contingent on a default happen.

So, the basic model for the CDS cash flow that we're going to be using in this

module is what we saw in this example. There will be a faction, delta, which is

a fraction of a year, times k, would be the times at which the coupon payments

are going to happen. Delta typically is 1 quarter, that is

quarterly payments. And the dates of the payments are also

set. The March 20th, June 20th, September

20th, and December 20th. If the reference entity is not in default

at time tk, the buyer pays the premium delta which is the fraction times S,

which is the spread times N which is the notional principle.

If the reference en, entity defaults at some time tao between tk minus 1 and tk,

the contract terminates at time tk. So, in the example, the default time was

116. This was between the two coupon payments

at month 15 and month 18. The contract terminates at time 18.

The buyer appraised the accrued interest over whatever fraction is left over.

So, one month was what we did in the numerical example.

And the buyer receives or equally the seller pays, 1 minus R times N where R

denotes the recovery rate of the underlying.

We are going to be working with this basic model to price and understand what

is going to happen to the CDS sensitivities.

But the details behind CDSs are enormous. they have been standardized by the

International Swaps and Derivative Association, ISDA, in 1999.

There were changes made in 2003. Then again, changes were made in 2009.

And may yet again, changes be made, once if CDSs become exchange trader.

And the reason there are so many different details in a CDS contract is

there are many difficult issues. How does one define that a credit event

has occurred? was the interest payment just late, did

it not occur at all? It's a problem.

How does one determine the recovery rate? there's often litigation, there's delays

and so on. So, we're not going to be worrying about

that in this module. We are going to assume that the recovery

rate is somehow known. And we're going to price assuming that

this recovery rate is known. But also many, many details.

How is the spread set? How is it set for junk bonds versus

investment grade bonds? What about countries?

How is the spread set for countries? When is the coupon payment done?

In advance or in arrears? How is the spread quoted?

Is the spread quoted in terms of par spread, meaning the value that makes the

net value the CDS equal to 0, or some other standardized spread.

All these details are important when you talk about particular CDS contracts.

But in order to understand the basic mechanisms of how CDSs work, the basic

model that we have introduced is sufficient and it highlights all the main

features. So, we're going to focus on the basic

model to illustrate the details of pricing and the sensitivity to hazard

rates, which are the probabilities of default.

Later on, in the next module, I'm going to show you that the CDS spread, S is

approximately 1 minus R times h, here R is the recovery rate and h is the hazard

rate. So, for a fixed value of R, the CDS

spreads are directly proportional to the hazard rate h.

And the hazard rate is the conditional probability of default.

So, you will end up getting that the conditional probability of default is

approximately equal to S divided by 1 minus R.

And therefore, CDS spreads end up giving you a very good handle on the probability

that a particular company or a particular country, or a sovereign, is going to

default on the next period. So, here, just as an illustration, I'm

showing you what happens to the fove, what happened to the five year CDS spread

for Ford, GM and AIG in the first nine months of 2008.

The, this data up here, is all in basis points.

So, it started around, a thousand basis points, and it went, oh, it started

rising as the dates went by. And it didn't, neither of these companies

actually defaulted. But the probabilities of default are

going very high because the spreads are going high.

AIG went all the way up to 3500 basis points before coming back down because

this is where bail out event started to happen.

The only idea that I wanted to take away from this picture is the fact that CDS

spreads react to news events. AIG was very low.

And then, suddenly, it started to shoot up because there was feeling in the

market that the default is going to happen.

And using the formula that h is approximately equal to S divided by 1

minus R, we can back out what is the probability of default from the spread

rates. In this slide, the y axis is in

percentages and not in basis points. [SOUND] And it gives you a sense of the

credit worthiness of different countries. So, if you look at Greece, Greece, all

the way, went up to 25% default on around, 20, 25% spread around January

12th. So, if the recovery rate is, let's say,

approximately 50%. Then, h, which is S divided by 1 minus R.

Will turn out to be, approximately a 50% default probability.

So, the, the market taught that the probability that Greece is going to

default is going to be very, very high. The next one over is Portugal, but it's

only at around 1.5%, which is the period over here.

And Germany which is exactly flat down here is pretty close to zero.

And so, in some sense its going to be considered the most safe or risk free of

the countries. Just to give you a sense of what the

development of the applications of CDS, I'm going to trace some of the history.

The development of the modern merger CDS is credited to Blythe Masters of JP

Morgan. It was created in 1994 to cover JP Morgan

for the $4.8 billion credit line that it had issued to Exxon to cover the possible

punitive damages in the Exxon Valdez spill.

So, after extending the credit line, JP Morgan protected itself by buying

protection from the European Bank for Reconstruction and Development using a

CDS. The CDS market, since then, has grown

tremendously. By the end of 2007, the CDS market had a

notional value for 62 trillion. Since then, things have become better.

The DTCC estimates of the gross notional amount, gross years stands for the fact

that after netting of, off setting CDS agreements, the notional amount in 2012

was about 25 trillion. So, 2007 was before the financial crisis,

2012 is after the financial crisis and things have started to come down.

CDSs is where initially developed for hedging.

they allow to hedge concentrations of credit risk privately.

So, if, take the example of JP Morgan, Exxon.

JP Morgan makes a loan to Exxon. It wants to protect itself.

So, there are two possibilities. One, it could write the loan off to

somebody else, in this case, the European Bank for Reconstruction and Development.

But that would mean that it would have to inform Exxon that the loan has been

written, written to another corporation. That might affect the relationship of JP

Morgan and Exxon. Instead, you could construct, you could

create a CDS contract and effectively still remove that credit off of your

balance sheet. you can create, you can hedge credit

exposures when no publicly traded debt exists.

And this is because CDSs can be written on anything pretty much, and it's a

contract, it's not really a bond or a cash bond.

And therefore, you can use this construct to hedge against situations where bonds,

or publicly traded debt, is not available.

Although, CDS can be used to protect against losses, it's very different from

an insurance contract. It's a contract that can be returned to

cover anything. You can buy protection even when you

don't hold the underlying debt. In order to buy insurance, you have to

hold the underline quantity. To buy the insurance on a house, you have

to be the owner of the house. To buy insurance on a bond, you need to

hold the bond. You can buy a CDS on a bond without even

holding the bond. CDS is easy to create and until recently

completely unregulated. And because of these reasons, investing,

and in some cases, speculation, became the main application very soon.

CDS has provided an unfunded way to create credit risk.

So, in order to take a credit risk on a particular company, you either have to

take by the bond or you have to short sell the bond.

Now, short selling bonds is very difficult.

On the other hand, by writing a CDS from a particular company, you can expose

yourself with a credit risk. You can tailor the credit exposure to

match the precise requirement. This is because CDS is a contract and you

can precisely define the contract that you want.

CDS has allowed you to take view on the credit quality of the referenced credit.

If you think that the credit quality is going to go down, you're going to buy

protection. If you think that the credit quality is

going to go up, then you're going to sell the protection.

So, in both directions you can take a view, a positive view or a negative view.

Buying protection, which means that when you have a negative view in a market, is

often easier than shorting the asset. So, CDSs are became the real easy way of

taking negative bets on various corporations.