CDS & Option

7/28/2019 CDS & Option

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A Beginners Guide to the Black-Scholes Option Pricing Formula (Part 1)

Filed under:beginners guide,Black-Scholes,derivatives,made easy,options,pricing,tutorialTags:beginners guide,Black-Scholes,derivatives,made easy,options,pricing,tutorialrichnewman @ 10:28 pm

Preface

Firstly let me apologize to the .NET developers perusing this blog, as this article is a little off-topic. However, my interests range over both .NET and derivatives, and I will be posting on bothtopics in the future.

Introduction

The Black-Scholes model for pricing stock options was developed by Fischer Black, MyronScholes and Robert Merton in the early 1970s. It is arguably the most important result infinancial engineering, and is certainly a rich source of interview questions in the financial

services industry.

I was recently askedby a friend if I could provide a written explanation in laymans terms ofhow the Black-Scholes options pricing formula works. This isnt necessarily all that easy as theformula involves some relatively complex mathematics. However, I think it is possible to get anintuitive understanding of what the various parts of the formula mean. This article is an attemptto explain that.

Note that to keep things simple here I am only going to discuss European call options on non-dividend paying stock. It doesnt matter for the purposes of this article if you dont know whatthat means.

What is an Option?

Firstly a reminder of what a European call option is. If I ask this in an interview I usually get thetextbook answer: the right but not the obligation to buy an asset at a predetermined price at apredetermined date. My next question is always what does that actually mean?
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Consider a European call option on a Microsoft share (the asset), with a strike of 30 (thepredetermined price) and maturity of one year from today (the predetermined date). If I pay toenter into this contract I have the right but not the obligation to buy one share at 30 in a yearstime. Whether I actually exercise my right clearly depends on the share price in the market at thatdate:

- If the share price is above 30, say at 35, I can buy the share in the contract at 30 and sell itimmediately at 35, making a profit of 5. Similarly if the share price is 40 I make a profit of 10.- If the share price is below 30, say at 25, the fact that I have the right to buy at 30 is worthless: Ican buy more cheaply in the open market.

Thus we get the classic hockey stick payoff diagram as below. This shows how the amount ofmoney I make on my contract varies with the value of Microsoft stock at the end of the year.

So if I enter into this contract I make money if the stock price finishes above 30, but dont loseanything if it finishes below 30. Because I cant lose, I have to pay to enter into the contract (thisis the price of the contract, orthe premium). This premium is usually paid upfront at the start ofthe contract. The question is how much this premium is going to be?

The Basic Idea


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So were trying to find the value today of a contract whose ultimate value depends on the valueof the Microsoft stock price in one years time. Furthermore, the contract has different valuesdepending on whether that stock price goes up or goes down: the payoff curve above is notsymmetrical.

So intuitively we are going to need some measure, or measures, of the probabilities of the stockprice ending up at various values after one year.

If we have that it may be possible to apply an expected value calculation to get to a price for thecontract. This is explained further inpart 2.

Expected Value

Suppose theres a competition I can enter for free where I have a 50% chance of winning$1,000,000, and a 50% chance of receiving nothing. Obviously Im going to enter as many timesas possible. Suppose I enter 1,000 times: what will I expect to win?

On average Im going to win $500,000 per entry ($1,000,000 x 50%), so Id expect to winaround $500,000,000 from 1000 entries.

We say that the expected value of playing the game is $500,000. Its what we expect to winon average if we play many times.

Similarly if the game has a 50% chance of winning $1,000,000, a 20% chance of winning$200,000 and a 30% chance of winning $-500,000 we can say the expected value of playing is:

50% x 1,000,000 + 20% x 200,000 + 30% x -500,000 = $390,000

And if I play 1000 times I expect to win around $390,000. Notice that to do this we aremultiplying the percentage probability of each value by the amount we make in each case, andthen adding it all up.

So to value our option contract using an expected value calculation we would:

Work out the percentage probability of each value of the stock price in a years time Work out how much profit we make in each case (from the payoff graph) Multiply the percentage probability of each value by the amount we make and add them

up to get an expected value for the contract.

This can then be considered as the basis of the price of the option, although theres also the timevalue of money to consider, which I will discuss later.

Continuity

In the discussion above I implied that to calculate the expected value of our option we wouldconsider a series of distinct values of the price of the stock at maturity. In fact the Black Scholes
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method assumes that the stock price can take ANY value continuously between minus infinityand plus infinity at maturity. This actually makes the maths easier, although possibly moredifficult for non-mathematicians to understand. Nevertheless the basic concepts remain the same.

Time Value of Money

Another concept that you need to understand is the time value of money. If I receive a cash flowof $1,000,000 in one years time then that is worth LESS to me than if I receive $1,000,000today. This is intuitively obvious if you consider that if I receive $1,000,000 today I can buy agovernment bond and earn interest on it for a year. At the end of the year Ill have more than$1,000,000.

The difference between the two values clearly depends on the interest rate that I can get over theyear. If I can get an interest rate of i% then at the end of the year my $1,000,000 will be worth$1,000,000 x (1+i%). Equally if I am due to receive $1,000,000 x (1+i%) in a years time, I cansay that that is worth $1,000,000 to me today. If I receive $1,000,000 in a years time that is

worth $1,000,000 / (1+i%) to me today.

In general if I am going to receive $y in a years time I can say that that is worth y / (1+i%) to metoday. In this case we call the 1/(1+i%) a discount factor. Its what we discount (multiply) thefuture cash flow by to get its current value.

Note that here i% is the interest rate I can get for investing in something with very little or norisk for a whole year. A different rate may apply if my cash flow is due in six months time (andclearly Ill only be getting six months of interest at the different rate, so the calculation changesas well). A different discount factor will apply.

To avoid some of the difficulties of interest rates over different periods the Black-Scholesmethod assumes initially that interest rates are constant. It also uses what are calledcontinuously compounded interest rates. I will explain these in more detail in another article.All you need to know for the purposes of this article is that if r is our continuously compounded

interest rate for a period of T years then the discount factor will be .

Black-Scholes

The easiest way to understand the Black-Scholes formula intuitively is to consider what happensif we exercise the option. This has two parts:

i) Value of the Cash to Buy the Option

Firstly, if the option is exercised we pay the strike price (30 in our example). We pay the strikeprice only if the underlying stock price is above the strike at maturity. So to work out theexpected value of this we need the probability simply that the stock price is above the strike atmaturity. Lets call this probability N(d2), and the strike price K. Then the expected value of thisis just KN(d2). What N() means, and the value of d2, will be discussed later.


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KN(d2) is the value of the cash flow at maturity. As discussed above, to get the value of this cash

flow today we need to discount it, and the discount factor is .

So the value of the cash to buy the option today is KN(d2) .

ii) Value of the Stock Received if any

Secondly, if the option is exercised we get a unit of the stock. This is clearly worth whatever thestock price is in the market at maturity. But this again only happens if the underlying stock priceis above the strike at maturity.

It turns out that the expected value of this valued as at today is proportional to S, the stock pricetoday, and can be written as SN(d1). That is to say, SN(d1) is the expected value of somethingthat is equal to the final stock price if the final stock price is above the strike, and equal to zero ifthe final stock price is below the strike.

This is continued in part 3.

Volatility

If you know a little about options already you will probably be aware that their values depend onsomething called volatility. Volatility is usually not needed to price derivatives that are notoptions.

Technically volatility is defined as the annualized standard deviation of the return on an asset (inour case Microsoft stock). They are expressed as percentages.

However, its easier to think of it intuitively as the amount that the price will swing around in agiven period. Stocks with a high level of uncertainty surrounding them will have high volatilities.An example currently might be the stock of small Russian oil companies. Stocks that arerelatively stable (e.g. Microsoft) will have lower volatilities.

Why does volatility affect the price of an option? Again this is because our payoff graph is notsymmetrical. A stock that has a high volatility is more likely to swing around, and hence morelikely to have a very high value or very low value at maturity. A stock with a low volatility ismore likely to be close to its current value at maturity.

Now if the stock price at maturity is below our strike price we dont care if its just slightly

below or massively below. In both cases we dont exercise the option and dont make anymoney.

But if the share price at maturity is above our strike we really want it to be as far above the strikeas is possible, since we make more money the higher the volume is.

So an option with a high volatility is more likely to make us lots of money if the price goes up,but wont lose us lots of money even if the price goes down hugely.
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As a result options with high volatility are more valuable than options with low volatility.

As we will see below both d1 and d2 in the values discussed above depend on volatility.

The Formula

Finally, note that if I have bought the call I am paying the cash amount in i) above and receivingthe value of the stock ii). So we can say that the value, c, of a European call option on a non-dividend paying stock is:

d1 and d2

As mentioned in the introduction the mathematics behind the calculation of the probabilities inthe Black-Scholes formula is fairly complex. It turns out that if N() is the cumulative normal

function (a statistical operator) then d1 and d2 canbe expressed as below. Ill just present theresults without explanation here. Note that whilst these formulas are complicated, you can justplug in the underlying values and get a result: this is what is known as a closed form solution.

Here sigma () is volatility, as discussed above.

Actual Derivation of the Formula

This article has attempted to provide an intuitive interpretation of the Black-Scholes formula,without going into the mathematics behind it. Such an interpretation inevitably glosses oversome of the details. I have glossed over risk neutrality considerations above, for instance.

In particular the actual derivation of the Black-Scholes formula was not done directly using theintuitive ideas discussed here. I will discuss this in future articles.

References

John C. Hull. Options, Futures and Other Derivatives (Sixth Edition)


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A Beginners Guide to Credit Default Swaps (Part 1)

Filed under:.net,beginners guide,bonds,cds,credit default swap,derivatives,introduction,tutorialTags:beginners guide,cds,credit default swap,introduction,tutorialrichnewman@ 6:21 pm

Introduction

On our team at work we occasionally employ developers who know nothing about derivatives. Itusually falls to me to give these guys a general introduction to the credit derivatives business. Aspart of that we usually have a session on what a credit default swap is and why its important.This article is based on what I say in that session, and as such is an attempt to explain the productto someone who knows very little about the financial services industry.

Government Bonds

It isnt really possible to understand a credit default swap without having a basic understandingof bonds, so well start with a discussion of what bonds are and why someone might invest inone.

Imagine I have some cash and I want to invest it for a long period. Furthermore assume thatinterest rates are high and I want to ensure I get a high rate of interest for the period. I wouldideally like a fixed interest rate. One way of doing this would be to go to my bank and see whatthey have on offer. However, most banks dont offer very generous fixed rate deposits,especially over long periods. They prefer to offer you a variable rate.

An alternative is to buy a bond from the government. To raise money almost all governmentsperiodically issue these bonds. The way they work is that you give your money to thegovernment. The government then pays a fixed rate of interest periodically (usually every sixmonths) on the money you give them. The government does this for a fixed period, usually ofseveral years. At the end of the fixed period they will give you your money back. The end of thefixed period is called the maturity of the bond. The amount they pay interest on is called theface value, the notional value or the principal of the bond.

What makes this even more attractive as an option is the fact that there is a secondary marketfor bonds. What that means is that there is someone who will buy the bond from me should I notwant to hold it to maturity. This is like the stock market. You can buy stocks from individual

companies when they issue them, and then (usually) sell them on a stock exchange when you nolonger wish to hold the stock. In both cases the price you get will depend on market conditions atthe time. Clearly the current level of interest rates will have a major impact on the price you canget when you come to sell your bond. Of course you can buy your bond in the secondary marketin the first place, rather than buying it directly from the government.

Should you actually want to do this most of the major stockbrokers will also allow you to tradegovernment bonds, although some cheap online brokers wont.
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So for example, if I look on theUS TreasuryDirect siteright now I can see that on the 15thAugust 2007 the US government issued a bond that has a maturity of 15th May 2037 with aninterest rate of 5% per year. This is paid every six months (so I get 2.5% of the face value of thebond every six months).

Note that in the United States government bonds issued with a period to maturity of between tenand thirty years are called Treasury bonds, whilst government bonds issued with a period tomaturity of two to ten years are called Treasury notes. However, these instruments all behaveas described above, and are often just referred to as government bonds.

Corporate Bonds

Its not only governments that issue bonds, companies do so as well. This is a way of raisingmoney for them, the other alternative being to issue stock. These corporate bonds are typicallyvery like the government bonds discussed above: the company will pay you a fixed interest rate

on your money for a fixed period. Theres also a secondary market for these bonds as describedabove for government bonds.

If you are given the choice between a 10-year corporate bond issued by, say, General Motors (acar company) and a US government bond, which one would you prefer? If the interest rates werethe same youd be wise to go for the US government bond. This is because theres almost nochance that the US government wont pay you back your money. Its going to take a world waror something similar for the US government to be in such trouble that it cant repay (and in thatcase youd probably have bigger worries than your bonds). However, companies can get intofinancial trouble, even big ones (think of WorldCom, or Enron). If a company goes bankrupttheres a chance you wont get all the money youve given them for the bond back.

For this reason companies are forced to pay a higher rate of interest on their bonds than the USgovernment. Otherwise no-one will give them the money for their bonds. How much bigger therate of interest has to be depends on how risky the company is perceived to be.

For example General Motors has issued a bond that matures on the 15th July 2033 paying8.375%. Whilst this interest rate isnt directly comparable with that on the US Treasury bonddiscussed above, if you do work out the numbers you will find that you are getting much moreinterest from the General Motors bond. This article isnt going to go into the details of how to dothis, as it isnt strictly relevant to understanding credit default swaps.

Further Reading on Bonds

The sections above have given a very simple overview of bonds. These sections have notdescribed how the secondary markets work, how we price bonds, what a yield is or what yieldcurves are. If you are interested in such things there are some more details at the links below:

http://www.investopedia.com/university/bonds/http://www.riskworx.com/resources/Yield%20Curves_RiskWorX.pdf
http://www.treasurydirect.gov/RI/OFNtebndhttp://www.treasurydirect.gov/RI/OFNtebndhttp://www.treasurydirect.gov/RI/OFNtebndhttp://www.investopedia.com/university/bonds/http://www.investopedia.com/university/bonds/http://www.riskworx.com/resources/Yield%20Curves_RiskWorX.pdfhttp://www.riskworx.com/resources/Yield%20Curves_RiskWorX.pdfhttp://www.riskworx.com/resources/Yield%20Curves_RiskWorX.pdfhttp://www.investopedia.com/university/bonds/http://www.treasurydirect.gov/RI/OFNtebnd


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Credit Default Swaps (CDS)

Suppose that we have invested in the General Motors bond mentioned above. Suppose ourinvestment is $10,000,000. Suppose also that we have become worried that General Motors maybe getting into financial trouble. What can we do about it? Obviously we could just sell our bond

position in the secondary market. However, we can also enter into a credit default swap. Theeasiest way to think of a credit default swap is as an insurance contract. We are insuring againstthe possibility that a company might get into financial trouble and cause us to lose money on ourbond position.

To enter into this insurance contract we have to find someone prepared to insure us. Note thatthis is NOT General Motors. The big banks are usually the people to go to.

What we can do is to pay the bank a periodic small amount of money known as a premium(which is like an insurance premium). This is calculated as a percentage of the face value of thebond we are insuring against, which is $10m in our case. This amount (the $10m) is known as

the notional principal. The premium is paid every few months (usually every three or sixmonths) throughout the life of the contract.

In return for the premium the bank does nothing unless General Motors gets into financialdifficulty. In that case the bank will pay us an amount equal to the amount we have lost on ourbond position. This is likely to be a big sum relative to the small premiums that we will pay.Once this happens the contract will terminate. Otherwise the contract carries on for an agreedperiod (usually five years). In picture form this looks a bit as below:

Here the Big Bank is the protection seller: its receiving money in return for providingprotection against our bonds falling in value. Similarly we are protection buyers.

Clearly there are a few things that need to be sorted out before we enter into this contract. Sincethe Big Bank is going to make us a large payment if General Motors gets into financial difficultywed better define what financial difficulty means very clearly. Wed also better sort outexactly how were going to calculate the amount that will be paid.

Physical Settlement and Cash Settlement

The amount to be paid is slightly the easier of the two to define. We know which bond we want

insurance on (the one we are holding), and we know we want to get the reduction in its value as aresult of General Motors getting into trouble. There are two ways of handling this. The first isknown as physical settlement. Here we give the bond to the Big Bank, and the Big Bank givesus the full face value of the bond in return (i.e. the amount that was originally paid to GeneralMotors for it). The bank will then try to dispose of the bond in the market. Note that it will beworth much less than the full face value. This is because General Motors is in difficulty andhence unlikely to pay back the full face value at maturity. So from our point of view weve given


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up our bond but been paid face value for it: weve been compensated for the reduction in thevalue.

The second method is known as cash settlement. Here we try to work out the reduction in valueof the bond, and this is just paid from the Big Bank to us in cash. To work out the reduction in

value usually a calculation agent is appointed in the CDS contract. The calculation agent willgo into the market and get a selection of quotes for the bond from which a price for settlementwill be calculated in an agreed way. Often the calculation agent is the seller of protection (theBig Bank in our example).

Credit Events

Defining financial difficulty is more problematic, and indeed has led to several lawsuitsalready. We dont usually call it financial difficulty, by the way. Its referred to as a creditevent, or a default. We say a credit default swap contract is triggered if a credit event occurs,meaning the Big Bank has to pay up in our example.

There are three broad categories of credit events that are put into the documentation of creditdefault swap contracts:

1. BankruptcyIf a company goes into Chapter 11 (in the US) then that is a clear indicator that thecompany is in serious financial difficulty and that the bondholders may not get all theirmoney back. This is an obvious thing to have trigger the payment in a CDS contract.

2. Failure to PayIf a company fails to make payments it should be making, including coupon payments onthe bonds, then this can be documented as a credit event.

3.

RestructuringThis is where a company changes the payment schedules it makes on its bonds, usuallywith the agreement of the bondholders. Its usually not to the bondholders advantagewhen this happens, and hence CDS contracts can be documented to cover this kind ofrestructuring as a credit event.

Of these, restructuring is the one that has proved the most problematic for the market. There arenow four separate standard definitions for restructuring that can be used in CDS contracts.

Size of Premium Payment is Bigger if the Company is More Likely to Default

One question that has been asked is how large the premium will be in general (see thecomments).

The Big Bank in our example is providing us with protection against the default of a company(General Motors). We are paying them the premium for this protection. Clearly if the companybeing referred to is more likely to default the Big Bank will want us to pay them moremoney. So the premium rate is higher for riskier companies than for safe ones.


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The Big Bank will decide which companies it thinks are risky, and hence what premium itshould charge, based on a number of factors. However, theres already a market that reflectshow risky a company is. This is the bond market as described earlier in this article. In theexample there General Motors had to pay a higher interest rate on its bonds than the USGovernment because of the risk that the investor wouldnt get their money back if General

Motors defaulted.

Size of Premium Payment and How it Relates to Bond Prices

Now consider the case where we buy a General Motors bond. We then enter into a credit defaultswap to the maturity of the bond as well. This acts as insurance against General Motorsdefaulting on the bond. We receive interest from the General Motors bond, but pay some of itaway in insurance on the credit default swap.

In simple terms we now have overall a bond position where we dont lose anything if GeneralMotors defaults. If a default occurs we get our money back from the credit default swap. We

can then invest in another bond.

We can think of this as a risk-free bond position. This is in many ways equivalent to a positionin US Government bonds (which we can assume wont default at all). Wed expect ouroverallinterest rate to be similar to that of a US Government bond. Our overall interest rate is the rateon the General Motors bond less the premium on the credit default swap.

Now suppose the interest rate on a US Government bond is 5% and the interest rate on a GeneralMotors bond of the same maturity is 8%. Wed expect the premium on a credit default swap onGeneral Motors for the same period to be about 3%. Note that the 3% premium is also called thespread on a credit default swap, since it is the spread between the government bond and the

corporate bond interest rates.

Note that this is a very simplistic analysis. It is broadly accurate but there are reasons why itdoesnt work exactly in practice.

Some Other Terminology Relating to Credit Default Swaps

(i) Reference Entity and Reference Obligation

Note above that General Motors is not directly involved in the credit default swap contract.General Motors as a company will not even know the contract exists. The contract is between us

and the Big Bank. General Motors is just an entity that is referred to in the contract, and hence isknown as the reference entity.

Similarly the contract refers to the specific bond we are insuring (General Motors 8.375%maturing 15th July 2033 in our example). However the bond isnt directly involved in thecontract. Indeed if the contract is cash settled we dont even have to be holding the bond at anytime: we can just enter into the CDS contract without it. The bond is just an obligation beingreferred to in the contract, and hence is known as the reference obligation.


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You should know that, at least in technology, everyones favourite interview question aboutcredit default swaps is whats the difference between a reference entity and a referenceobligation?

(ii) Bond Seniority

Bonds have a hierarchy of importance when a company is unable to pay its debts. Somebondholders will get their money back before others. (They ALL get their money back before theshareholders.) The exact place in the pecking order depends on the documentation of the bonds.Typically bonds are classified according to seniority. They are assigned to one of seniorsecured, senior unsecured, senior subordinated, subordinated and junior subordinated senioritycategories. The list is in order of seniority: senior secured is the highest, junior subordinated thelowest. This means if we hold a senior secured bond we are more likely to get our money back ifthe company goes bankrupt than if we hold a junior subordinated bond.

When a company is being wound up the bondholders get paid in seniority order out of the cash

that is remaining to the company. The bondholders with the highest seniority debt get paid first,then the bondholders with the next level of seniority debt, and so on. Bondholders will get paidin full in each seniority category until the money runs out. If at any stage the money isinsufficient to pay the current seniority of bondholder in full, every bondholder of thatseniority gets paid the same percentage of the face value of their bond. So, for example, themost senior bondholders may get paid in full, one category of more junior bondholders will onlyget a percentage payout, and the most junior bondholders may get nothing.

(iii) Recovery Rates

The recovery rate is the percentage of the face value of our bond that we get back if theres acredit event. For example, suppose we hold $10m of bonds in a company, and it goes bankrupt.Assume we get $4m back for our bonds from the company after the bankruptcy. We would sayour recovery rate is 40% (4m/10m as a percentage).

Recovery rates are also one of the inputs into pricing a CDS contract (working out its value toeither counterparty) prior to maturity. To price a CDS one of the things we need to know is howmuch the bond we are insuring will reduce in value if a credit event occurs. This is obviouslyimportant since it determines the size of the payment made as a result of the credit event. Clearlywe cant know exactly how much the bond will be worth after a credit event before the creditevent has happened, so we estimate a recovery rate.

Most pricing methodologies estimate recovery rates in a very simplistic way: a percentage isassigned to the seniority of the debt of a company. So we might say General Motors SeniorUnsecured debt has a recovery rate of 40%, and then use that number for pricing all GM seniorunsecured credit default swaps.


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Uses of Credit Default Swaps

As described above it sounds like the credit default swap is a very niche product since itsprimary use is to hedge bond positions against default. However, the credit default swap markethas taken off and is huge. The reason is that there is a wide range of ways CDS can be used. In

recent years pure speculation, largely by hedge funds, seems to have been the main driver of themarket.

Geoff Chaplins excellent book Credit Derivatives: Risk Management, Trading and Investingcites the following uses of CDS:

Directional Trading/Relative Trades (speculation on individual companies) Debt Hedging (hedging bond positions as described above) Sector/Portfolio Trades (speculation on groups of companies) Income Generation (we can just sell protection and receive premium, provided were

confident we wont face defaults (credit events))

Regulatory Capital Reduction (if a bank has lent to a company that uses regulatory capitalwhich can be reduced by buying CDS protection)

Issues

Below are a few further issues relating to credit default swaps:

The description of CDS as insurance is not technically accurate. Insurance contracts areregulated in a different way, the documentation is different, and usually an insurancecontract would require us to actually own the bond to be valid for a claim, which is notthe case for a CDS.

As mentioned above, theres no reason for either party to a CDS contract to actually beholding a bond (reference obligation) of the reference entity. CDS can be entered intopurely as speculative positions. Even with physical settlement the buyer of protection canjust go into the market and buy the appropriate bond at the time of a credit event, anddoesnt need to hold it through the life of the contract.

CDS contracts are usually not entered into with retail investors. You or I couldntactually execute a CDS on our bond position; we dont have big enough positions tomake it worthwhile in general. Hedge funds, pension funds, fund managers and insurancecompanies tend to be the counterparties to the banks on these contracts (as well as otherbanks).

Credit default swaps are usually documented such that a range of bonds can bedelivered (handed over in physical settlement or used to calculate losses in cashsettlement). The text above implied that only one bond was ever relevant. The referenceobligation cited in the contract simply defines the type of bond that can be delivered (itsseniority). Usually any bond of the same seniority or higher seniority can be delivered.CDS can be traded without any reference obligation being cited: usually this means thatany senior unsecured debt can be delivered.

This is a zero-cost instrument. The two parties to the contract just agree the details upfront, and the contract starts without any initial payment being necessary. If you are a


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seller of protection you just get premium in without having to do anything, which can beattractive.

Summary

In summary, a credit default swap is a contract where one party to the contract pays a smallperiodic premium to the other, in return for protection against a credit event (financial difficulty)of a known reference entity (company).

This article was written in 2007. Since then there have been a few developments in the creditdefault swap market. A discussion of these developments can be found inpart 2 of this series ofarticles.

Introduction

Part 1 of the Beginners Guide to Credit Default Swapswas written in 2007. Since that time we

have seen what many are calling the greatest financial crisis since the Great Depression, and aglobal recession.

Rightly or wrongly, some of theblame for the crisis has been attributed to credit derivativesandspeculation in them. This has led to calls for a more transparent and better regulated creditdefault swap (CDS) market. Furthermore the CDS market has grown very quickly, and by 2009it had become clear that some simple changes to operational procedures would benefit everyone.

As a result many changes in the market have already been implemented, and more are on theway. This article will discuss these changes. It will focus primarily on how the mechanics oftrading a credit default swap have changed, rather than the history of how we got here or why

these changes have been made. Ill also briefly discuss the further changes that are on the way.

Overview of the Changes

The first thing to note is that nothing has fundamentally changed from thedescription of a creditdefault swap in part 1. A credit default swap is still a contract that provides a kind of insuranceagainst a company defaulting on its bonds. If you have read and understood part one then youshould understand how a credit default swap works.

The main change that has happened is that credit default swap contracts have been standardized.This standardization falls into three broad categories:

1. Changes to the premium, premium and maturity dates, and premium payments thatsimplify the mechanics of CDS trading.

2. Changes to the processes around identifying whether a credit event has occurred.3. Changes to the processes around what happens when a credit event has occurred.

Items 2 and 3 are extremely important, and have removed many of the problems that werediscussed in part 1 relating to credit events. However, they dont affect the way credit default
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swaps are traded as fundamentally as item 1, and are arguably more boring, so well start withitem 1.

The Non-Standard Nature of Credit Default Swaps Previously

If I buy 100 IBM shares and then buy 100 more I know that I have a position of 200 IBMshares. I can go to a broker and sell 200 IBM shares to get rid of (close out) this position.

One of the problems with credit default swaps (CDS) as described in part 1 of this series ofarticles is that you couldnt do this. Every CDS trade was different, and it was consequentlydifficult to close out positions.

Using the description in part 1, consider the case where I have some senior IBM bonds. I havebought protection against IBM default using a five year CDS. Now I decide to sell the bondsand want to close out my CDS. Its difficult to do this by selling a five year CDS as describedpreviously. Even if I can get the bonds being covered, the definition of default, the maturity date

and all the premium payment dates to match exactly its likely that the premiums to be paid willbe different from those on the original CDS. This means a calculation has to be done for bothtrades separately at each premium payment date.

Standardization

To address this issue a standard contract has been introduced that has:

1. Standard Maturity Dates

There are four dates per year, theIMM datesthat can be the maturity date of a standard

contract: 20th March, 20th June, 20th September, and 20th December. This means that if todayis 5th July 2011 and I want to trade a standard five-year CDS I will normally enter into a contractthat ends 20th September 2016. It wont be a standard CDS if I insist my maturity date has to be5th July 2016.

2. Standard Premium Payment Dates

The same four dates per year are the dates on which premiums are paid (and none other). As aresult three months of premium are paid at every premium payment date.

Note that the use of IMM dates for CDS maturity and premium payment dates was already

common when I wrote part 1 of the article.

3. Standard Premiums

In North America, standard contracts ONLY have premiums of 100 or 500 basis points perannum (1% or 5%). In Europe, Asia and elsewhere a wider range of premiums is traded onstandard contracts, although this is still restricted. How this works in practice will be explainedin part 3.
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4. Payment of Full First Coupon

Standard contracts pay a full first coupon. What this means is that if I buy a CDS midwaybetween the standard premium payment dates I still have to pay a full three months worth ofpremium at the next premium date. Note that coupon here means premium payment.

For example, if I enter into a CDS with face value $100m on 5th July 2011 with a premium of5% I will have to pay 3 months x 5% x 100m on the 20th September. This is in spite of the factthat I have not been protected against default for the full three months.

Note that for the standard premiums and the payment of full first coupon to work we now haveupfront fees for CDS. Again this will beexplained in more detail in part 3.

Impact of these Changes

What all this means is that we have fewer contract variations in the market. The last item in

particular means that a position in any given contract always pays the same amount at everypremium date: we dont need to make any adjustments for when the contract was traded.

In fact, in terms of the amount paid EVERY contract with the same premium (e.g. 500 bps) paysthe same percentage of face value at a premium date, regardless of reference entity. This clearlysimplifies coupon processing. It also allows us to more easily net positions in credit defaultswaps in our systems.

Conclusion

One of the major changes in the CDS market sincepart 1was written is that contracts have been

largely standardized. More detail on this and other changes will be given inpart 3.

Introduction

Part 1 of this series of articlesdescribed the basic mechanics of a credit default swap.

Part 2started to describe some of the changes in the market since part 1 was written. This partwill continue that description by describing the upfront fee that is now paid on a standard CDScontract, and the impact of the changes on how CDS are quoted in the market.

Standard Premiums mean there is a Fee

Part 1 discussed how CDS contracts have been standardized. One of the ways in which theyhave been standardized is that there are now standard premiums.

Now consider the case where I buy protection on a five-year CDS. I enter into a standardcontract with a premium of 500 basis points (5%). It may be that the premium I would have paidunder the old nonstandard contract for the same dates and terms would have been 450 basispoints. However, now Im paying 500 basis points.
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Clearly I need to be compensated for the 50 bps difference or I wont want to enter into the tradeunder the new terms.

As a result an upfront fee is paid to me when the contract is started. This represents the 50 basispoints difference over the life of the trade, so that I am paying the same amount overall as under

the old contract.

Note that in this case I (the protection buyer) am receiving the payment, but it could easily bethat I pay this upfront fee (if, for example, the nonstandard contract would have traded at 550bps).

Upfront Fee Calculation

The calculation of the fee from the old premium (spread) is not trivial. It takes into accountdiscounting, and also the possibility that the reference entity will default, which would mean thepremium would not be paid for the full life of the trade. However, this calculation too has been

standardized by the contracts body (ISDA). There is a standard model that does it for us.

The Full First Coupon means there is a Fee

In the example in part 1 I discussed how I might pay for a full three months protection at the firstpremium payment date for a CDS trade, even though I hadnt had protection for three months.

Once again I need compensation for this or I will prefer to enter into the old contract. So onceagain there is a fee paid to me when I enter into the trade.

This is known as an accrual payment because of the similarity to accrued interest payment for

bonds. Here the calculation is simple: its the premium rate applied to the face value of the tradefor the period from the last premium payment date to the trade date.

That is, its the amount Ill be paying for protection that I havent received as part of the firstpremium payment. Note no discounting is applied to this.

Upfront Fee/Accrual Payment

So in summary the new contract standardization means that a payment is now always made whena standard CDS contract is traded.

Part of the payment is the upfront fee that compensates for the difference between the standardpremium (100 or 500 bps in North America) and the actual premium for the trade. This can be ineither direction (payment from protection buyer to seller or vice versa). Part of the payment isthe accrual payment made to the protection buyer to compensate them for the fact that they haveto make a full first coupon payment.

How CDS are Quoted in the Market


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Prior to these changes CDS were traded by simply quoting the premium that would be paidthroughout the life of the trade.With the contract standardization clearly the premium paid through the life of the trade will notvary with market conditions (it will always be 100 or 500 bps in North America, for example), soquoting it makes little sense.

Instead the dealers will quote one of:

a) Points UpfrontPoints upfront or just points refer to the upfront fee as a percentage of the notional. Forexample, a CDS might be quoted as 3 points upfront to buy protection. This means the upfrontfee (excluding the accrual payment) is 3% of the notional. Points upfront have a sign: if thepoints are quoted as a negative then the protection buyer is paid the upfront fee by the protectionseller. If the points are positive its the other way around.

b) Price

With price we quote like a bond. We take price away from 100 to get points:That is, points = 100price. So in the example above where a CDS is quoted as 3 points to buyprotection, the price will be 97. The protection buyer still pays the 3% as an upfront fee ofcourse.

c) SpreadDealers are so used to quoting spread that they have carried on doing so in some markets, evenfor standard contracts that pay a standard premium. That is they still quote the periodic premiumamount you would have been paying if you had bought prior to the standardization. As alreadymentioned, there is a standard model for turning this number into the upfront fee that actuallyneeds to be paid.

Conclusion

This part concludes the discussion of the changes in the mechanics of CDS trading since2007. As you can see, in many ways the standardization of the CDS market has actuallymade it more complicated. The things to remember are that premiums, premium and maturitydates, and the amounts paid at premium dates have all been standardized in a standardcontract. This has meant there is an upfront fee for all standard CDS, and that they are quoteddifferently in the market from before. It has also meant that CDS positions can be more easilynetted against each other, and that the mechanics of calculating and settling premiums have beensimplified.

Part 4 of this serieswill examine some of the other changes since 2007, and changes that arecoming.

Introduction

This post continues the discussion of changes in the credit default swap (CDS) since 2007. Part2andpart 3of this series of articles discussed changes in the mechanics of CDS trading. This
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part will discuss changes around how credit events are handled, and future changes in themarket.

Changes in the CDS Market re Credit Events Since 1997

Determination committees (DCs) have been set up to work out if a credit event hasoccurred, and to oversee various aspects of dealing with a credit event for the market. Adetermination committee is simply a group of CDS traders of various kinds, althoughoverseen by ISDA (the standards body). The parties to one of the new standard contractsagree to be bound by the committees decisions.

Auctions are now conductedto determine the price to cash-settle credit default swapswhen there is a credit event. For this we need to determine the current price of the bondsin default. To do this we get a group of dealers to quote prices at which they are preparedto trade the bonds (and may have to), and then calculate the price via an averagingprocess. This can get quite complicated. The determination committees oversee theseauctions.

Classes of events that lead to credit events have been simplified. In particular whetherrestructuring is a credit event has been standardized (although the standards aredifferent in North America, Asia and Europe). Restructuring means such things aschanging the maturity of a bond, or changing its currency.

There is now a lookback period for credit events regardless of when a CDS istraded. What this means is that credit events that have happened in the past 60 days(only) can trigger a contract payout. This simplifies things because the same CDS tradedon different days is now treated identically in this regard.

Terminology and a Little History

The changes described so far in this article were introduced in 2009. For North America, whichwent first, this was known asCDS Big Bang. The standard contract terms thus introducedwere known as the Standard North American CDS Contract or SNAC (pronouncedsnack). The later changes in Europe were known as theCDS Small Bang. The finalstandardization of Asian contractsoccurred later still.

Much more detail on all of this can be found on the links to the excellent MarkIt papers above.

Future Changes

Further standardization in the credit default swap market will occur as a result of theDodd-FrankAct in the USA. This mandates that standard swaps (such as standard CDS) be traded through aswap execution facility (SEF). It further mandates that any such trades be cleared through acentral clearing house. Europe is likely to impose a similar regulatory regime, but is behind theUnited States. More detail on SEFs and clearing houses is below.

The primary aims of these changes are:
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1/ Greater transparency of trading. Currently many swaps are traded over-the-counter with nodisclosure other than between the two counterparties. This makes it different to assess the size ofthe market, or the effects of a default.

2/ Reduced risk in the market overall from the bankruptcy of one participant.

The exact details of these changes are still being worked on by the regulators.

Swap Execution Facilities (SEFs)

At the time of writingits not even clear exactly what a SEF is. The Act defines a SEF as afacility, trading system or platform in which multiple participants have the ability to execute ortrade Swaps by accepting bids and offers made by other participants that are open to multipleparticipants. That is, a SEF is a place where any participant can see and trade on current prices.There are some additional requirements of SEFs relating to providing public data relating toprice and volume, and preventing market abuses.

In many ways a SEF will be very similar to an existing exchange. As mentioned the exact detailsare still being worked on.

A number of the existing electronic platforms for the trading of CDS are likely to become SEFs.

Clearing Houses

Central clearing housesare another mechanism for reducing risk in a market.

When a trade is done both parties to the trade can agree that it will be cleared through a clearing

house. This means that the clearing house becomes the counterparty to both sides of the trade:rather than bank A buying from bank B, bank A buys from the clearing house, and bank B sellsto the clearing house.

Obviously the clearing house has no risk from the trades themselves. The clearing house isexposed to the risk that either bank A or bank B goes bankrupt and thus cant pay its obligationsfrom the trade. To mitigate this the clearing house will demand cash or other assets from bothbanks A and B. This is known as margin.

The advantage of this arrangement is that the clearing house can guarantee that bank A will beunaffected even if bank B goes bankrupt. The only counterparty risk for bank A is that the

clearing house itself goes bankrupt. This is unlikely since the clearing house will have no marketrisk, be well capitalized, and demands margin for all transactions.

Clearing houses and exchanges are often linked (and may be the same entity), but they aredistinct concepts: the exchange is the place where you go to get prices and trade, the clearinghouse deals with the settlement of the trade. Usually clearing houses only have a restrictednumber of members who are allowed to clear trades. Anyone else wanting clearing services hasto get them indirectly through one of these members.
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At the time of writing there are already a few central clearing houses for credit default swaps inoperation, and more are on the way.

Conclusion

Since 1997 contracts for credit default swaps have been standardized. This has simplified theway in which the market works overall: its reduced the scope for difficulties when a credit eventhappens, simplified the processing of premium payments, and allowed similar CDS contracts tobe netted together more easily. At the same time it has made understanding the mechanics of themarket more difficult.

Further changes are in the pipeline for the CDS market to use swap execution facilities andclearing houses.

CDS & Option

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