Credit Default Swaps

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From the course by Columbia University

Financial Engineering and Risk Management Part I

1366 ratings

Columbia University

Financial Engineering and Risk Management Part I

1366 ratings

Financial Engineering is a multidisciplinary field drawing from finance and economics, mathematics, statistics, engineering and computational methods. The emphasis of FE & RM Part I will be on the use of simple stochastic models to price derivative securities in various asset classes including equities, fixed income, credit and mortgage-backed securities. We will also consider the role that some of these asset classes played during the financial crisis. A notable feature of this course will be an interview module with Emanuel Derman, the renowned ``quant'' and best-selling author of "My Life as a Quant". We hope that students who complete the course will begin to understand the "rocket science" behind financial engineering but perhaps more importantly, we hope they will also understand the limitations of this theory in practice and why financial models should always be treated with a healthy degree of skepticism. The follow-on course FE & RM Part II will continue to develop derivatives pricing models but it will also focus on asset allocation and portfolio optimization as well as other applications of financial engineering such as real options, commodity and energy derivatives and algorithmic trading.

From the lesson

Term Structure Models II and Introduction to Credit Derivatives

Calibration of term-structure models; the Black-Derman-Toy and Ho-Lee models. Limitations of term-structure models and derivatives pricing models in general. Introduction to credit-default swaps (CDS) and the pricing of CDS and defaultable bonds.

Credit Default Swaps18:28

Meet the Instructors

Martin Haugh
Co-Director, Center for Financial Engineering
Industrial Engineering & Operations Research
Garud Iyengar
Professor
Industrial Engineering and Operations Research Department

This module is the first of two modules on Credit Default Swaps.

In this module, we are going, we are going to introduce you to the details of

what a Credit Default Swap is. Talk about, on an intuitive level, of how

Credit Default Swaps give you some information about the default

probability. And how these quantities can be used for

hedging, can be used for investment, can be used for speculation.

And how Credit Default Swaps have played an important role in the financial crisis

and also the sovereign debt crisis that is currently going on in Europe.

The seller of a Credit Default Swap, CDS, agrees to compensate the buyer in the

event of a loan default or some other credit event on a reference entity.

The reference entity could be a corporation, it could be a sovereign

that's a country, in return for periodic premium payments.

So, the dynamics are as follows. This is what happens to the buyer.

So, the buyer pays periodic premiums and what is a premium?

It's some coupon rate S, which is also called the spread.

d is in a year, it's a fraction of a year.

So, d times S is the total coupon that has been accumulated over the years.

N is a notional principal. So, there's a certain amount of principal

that has been protected. In order to protect that principal, you

have to pay a spread or a coupon S times N.

It has to be paid every d fraction of the year.

So, every coupon payment is going to be d times S times N.

And this keeps on going until some kind of a credit event happens.

Maybe the corporation defaults on the bond, maybe the country is not able to

make an interest payment, and so on. It's, we going to talk about credit

events later on and talk about the fact that defining whether a credit event has

happened or not in itself, a difficult problem.

So, once that credit event happens, two things happen.

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.

Another way CDS has started to be used is to arbitrage between the reference bond

and the CDS price. It's not coupon, but a reference bond and

the CDS spreads, gave another opportunity to find an investment opportunity to make

the difference. CDSs have been blamed for the financial

crisis and the debt crisis. And there are many reasons why this

happened. CDS positions are not transparent.

The riskiness of financial intermediaries, therefore cannot be

accurately evaluated, because they don't, these positions don't show up on a

balance sheet. And because of that, because of the fact

that you could not accurately evaluate the riskiness of financial

intermediaries, it threatened the trust in all counter parties.

Since no one knew who faced losses when a crisis event happened, all the counter

parties were suspect and entire trading came to a halt.

CDS were treated on an OTC market and because of that, because impossible for

any dealer to know what previous deals a customer had made.

Resulting in situations where some dealers could make lots of CDS deals

without putting up enough collateral. So, AIG was able to leverage its high

credit rating to sell approximately $500 billion worth of CDSs, without putting up

the enough collateral. Because it was in the OTC market and

because they were, because these trades were opaque, it allowed a small number of

CDS traders to take on huge amounts of risk.

And it also allowed them to be very severely interconnected in terms of their

obligations. And as a result of this

interconnectedness, the dealers led to worries about contagion.

CDSs also have been blamed during the financial crisis to adversely affect the

cost of borrowing of a firm in a country. And recently, more so in the European

debt crisis, CDS have been blamed for the fact that the cost of borrowing of

countries have gone tremendously high. So, the story here is that speculated

purchase CDS, without holding the underlying debt, sometimes called a naked

CDS. Once a lot of these speculators actually

start buying these naked CDS, this drives the spread higher.

And when the spread goes high, because the market perceives the spread as the

riskiness of a particular company or a particular country, the firms start

appearing risky. And the cost of borrowing of the firm

increases. The cost of borrowing of the sovereign

increases. And this can lead to collapse.

Various policy decisions have been made in the recent past to try to correct all

of these problems. Try to get CDS positions and balance

sheets. Trying to move the CDS, at least, to a

clearing house. And then, to an exchange credit

situation. this allow naked CDSs.

Many of these are things that are in, in place, some of them completed, some of

them are still being discussed. But CDSs have played their role and will,

unless something is done, will continue to be a risky part of the economy.

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