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Managing Credit Risk

“This ability of structured finance to repackage risks and create “safe” assets from

otherwise risky collateral led to a dramatic expansion in the issuance of structured

securities, most of which were viewed by investors to be virtually risk-free and certifiedas such by the rating agencies. At the core of the recent financial market crisis has been

the discovery that these securities are actually far riskier than originally advertised.”

- !oshua "aval , !akub !urek, #rick $tafford.

IntroductionCredit risk arises from the possibility of default by counterparty. Credit risk lay at theheart of the sub prime crisis. The most important point to note about credit risk is that itis more difficult to model and measure compared to market risk. Unlike market risk,where a lot of data is available in the public domain, data is scanty and sometimes nonexistent in case of credit risk. Moreover, credit risk is far more contextual, i.e., firmspecific compared to market risk. Despite these challenes, there has been sinificant

proress in credit risk modelin in recent years. !n this chapter, we will examine thethree buildin blocks of credit risk manaement " probability of default, exposure at

default and recovery rate. #e will also discuss briefly some of the commonly used creditrisk modelin techni$ues. These techni$ues can help us to estimate the potential loss in a portfolio of credit exposures over a iven time hori%on at a specified confidence level.The aim of this chapter is to provide a hih level understandin of credit riskmanaement.

Pre-settlement and Settlement risk Credit risk can be defined as the likelihood of a counterparty failin to dischare itsobliations. &ny credit transaction typically involves two staes' pre settlement and

settlement.

%re-settlement risk refers to the probability of failure of the counterparty to dischare itsobliation durin the life of the transaction. This includes the possibility of defaultin on bond interest or principal repayment or not makin marin payment in case of aderivative transaction.

$ettlement risk arises at the time of maturity. (uppose a bank fulfils its obliation at thetime of expiry of a contract. Till the time the bank receives its dues from thecounterparty, settlement risk exists. & ood example of such risk is forein currency payments made by two parties in different time %ones.

To deal with settlement risk, banks have developed real time gross settlement systems.(uch systems reduce the time interval between the point a stop payment instruction canno loner be made and the point of receipt of dues from the counterparty. &nothertechni$ue used is netting . !nstead of payin the ross amounts to each other, only the net

) *The +conomics of (tructured inance, arvard /usiness (chool, #orkin 0aper, 12-131, 4115.



amount is paid by one of the counterparties. This reduces the exposure and contains thedamae even if thins o wron. 6$ee box item& 'anaging settlement risk at ()$*

Settlement risk at UBS

(ettlement risk arises in transactions involvin exchane of value when U/( must honor its obliation todeliver without first bein able to determine that the counter-value has been received.

!n 4115, settlement risk on 758 of ross settlement volumes was eliminated throuh risk mitiation. Themost sinificant source of settlement risk is forein exchane transactions. U/( is a member of Continuous9inked (ettlement 6C9(:, a forein exchane clearin house which allows transactions to be settled on adelivery versus payment basis. The proportion of U/(;s overall ross volumes settled throuh C9(increased to <<8 durin 4115 compared to <=8 in 4117.

The avoidance of settlement risk throuh C9( and other means does not, of course, eliminate the credit riskon forein exchane transactions resultin from chanes in exchane rates prior to settlement. (uchcounterparty risk on forward forein exchane transactions is measured and controlled as part of the overallcredit risk on >TC derivatives.

$ource& U/( &nnual ?eports, 4115.

Probability of defaultThe probability of default is a key concern in credit risk manaement. Two kinds offactors must be evaluated to arrive at the probability of default " borrower specific andmarket specific./orrower specific factors include'

collateral

leverae

volatility of earnins@cash flows

reputation.

Market specific factors include' the phase of the business cycle

industry conditions

interest rates

exchane ratesExhibit !"

S#P$s Cor%orate &inance Cumulati'e (efault Rates ")*"-+,,* ./

4

4



+ef ' The Turner ?eview - & reulatory response to the lobal bankin crisis, published by' UA inancial(ervices &uthority, www.fsa.ov.uk@pubs@other@turnerBreview March 4112

Illustration

& portfolio consists of < bonds each with a probability of default of .1). #hat is the probability that there will be no default #hat is the probability that there will be at least

one default #hat is the probability of exactly one default #hat is the probability ofexactly two defaults

0robability of no default E 6.22:< E .2<)0robability of at least one default E ) - .2<) E .1F20robability of exactly one default E <C) 6.22:F 6.1): E .1F510robability of exactly two default E <C4 6.22:= 6.1):4 E .11127

Illustration

The cumulative probability of default of an instrument over two years is <8. The probability of default in the first year is 48. #hat is the probability of default in the

second year

0robability of no default over the two years E ) - 1.1< E 1.2<0robability of no default durin the first year E 1.259et probability of default in the second year be p

!n order that there is no default over the two years, there must be no default at in year ) oryear 4.Then 6.25: 6)- p: E .2<

⇒ p E25.

2<.)− E 1.1=13

(o probability of default' E =.138

0raditional methodsDefault risk models can rane in complexity from simple $ualitative models to hihlysophisticated $uantitative models. 9et us look first at some of the more simple andtraditional ways of estimatin the probability of default. These typically use financialstatement data. Then we will examine some of the more sophisticated models.

1ltman$s 2 Score&ltman;s4 G score is a ood example of a credit scorin tool based on data available infinancial statements. !t is based on multiple discriminant analysis. The G score iscalculated as'

E ).4x) H ).Fx4 H =.=x= H 1.3xF H .222x<

x) E #orkin capital @ Total assetsx4 E ?etained earnins @ Total assetsx= E +arnins before interest and taxes @ Total assetsxF E Market value of e$uity @ /ook value of total liabilities

4. +.! &ltman, *inancial ?atios, Discriminant &nalysis and the 0rediction of Corporate /ankruptcy, !ournal of inance, (eptember )235, pp. <52-312

=

=



x< E (ales @ Total assets>nce G is calculated, the credit risk is assessed as follows'

G I =.1 means low probability of default 6(afe %one:4.7 J G J =.1 means an alert sinal 6Krey %one:).5 J G J 4.7 means a ood chance of default 6Krey %one:

G J ).5 means a hih probability of default 6Distress %one:

& variant of the &ltman score has been used in the case of mortae loans in the U(. Thisis called the !C> score. !C> scores are tabulated by independent credit bureaus usina model created by air !ssac Corporation 6!C>:. & lower !C> score denotes a hiherrisk of default and vice versa. !n mid-4117, the averae !C> scores were 74<, 7=2, 7)4and 345 for aency=, Lumbo, &lt-& and sub prime mortaes.

Estimating %robability of default from market %ricesThe problem with financial statements is that they tend to be backward lookin. & simple but forward lookin way to measure the probability of default is to examine the market

prices of bonds which are traded. (uppose the one year T /ill yields 48 while a one yearcorporate bond yields =8. &ssume that no recovery is possible in case of a default, whatis the probability of default

#e can invest in either the T /ill or the risky instrument. 9et us say we make aninvestment of ) for exactly one year.

!f we assume the probability of default is p, the followin e$uation must hold ood').14 E ).1= 6)- p:

!f this e$uation does not hold, arbitrae is possible by oin lon in one of the

instruments 6which fetches hiher return: and short in the other 6which fetches lowerreturn:.

(olvin we et' p E:1=.)6

:14.)6)− E .1127

E .278

(uppose in the earlier illustration, the recovery in the case of default has been estimatedas <18. This means that in the case of default, <18 of the exposure can be recovered.Then we can rewrite the e$uation as follows'

).14 E 6).1=: 6)- p: H 6).1=: 6 p: 6.<:E ).1= " ).1= p H .<)< p

.<)< p E .1) p E .1)2F

E ).2F8

=. &ency mortaes are backed by annie Mac@raddic Mac. Numbo mortaes as the name suests arelare loans. 9imited documentation is the key feature of &lt-& loans. (ubprime mortaes have the hihest probability of default. or more details, see Chapter =.

F

F



More enerally, let i be the yield of the risky bond, r that of the risk free instrument. 9et p be the probability of default and f the recovery rate, i.e., fraction of the amount whichcan be collected from the debtor in case of a default. Then for a loan of value, ), to prevent arbitrae, the followin condition must hold'

)Hr E 6)Hi* 6)- p* H 6)Hi: pf

or )Hr E ) H i " p " pi H pf Hi pf or i r / p 0 pi pf ipf. !norin pi, ipf, as these will be small $uantities, we et'

i - r / p 1-f*.

(ince f is the recovery rate, 6)-f: is nothin but the loss iven default. 6 i r* is the creditspread. Thus the spread or risk premium e2uals the product of the default probability and

the loss given default. There is nothin surprisin about the result. (ince we haveassumed the loan value to be ), the left side of the e$uation is the excess amount received by investors for the risky loan in comparison to a risk free loan and the riht side is theexpected loss on the risky loan. !n other words, the left side represents the risk

compensation to the investor and the riht side, the expected loss. To prevent arbitrae,the risk compensation must e$ual the expected loss.

Measuring Probability of default at UBS

U/( assesses the likelihood of default of individual counterparties usin ratin tools tailored to the variouscounterparty sements. & common Masterscale sements clients into )< ratin classes, two bein reservedfor cases of impairment or default. The U/( Masterscale reflects not only an ordinal rankin ofcounterparties, but also the rane of default probabilities defined for each ratin class. 6(ee +xhibit 3.4:

Clients mirate between ratin classes as U/(;s assessment of their probability of default chanes.+xternal ratins, where available, are used to benchmark U/(;s internal default risk assessment. Theratins of the maLor ratin aencies are linked to the internal ratin classes based on the lon-term averae

)-year default rates for each external rade. >bserved defaults per aency ratin cateory vary year-on-year, especially over an economic cycle. (o U/( does not expect the actual number of defaults in itse$uivalent ratin band in any iven period to e$ual the ratin aency averae. U/( monitors the lon-termaverae default rates associated with external ratin classes. !f these lon-term averaes chane in amaterial and permanent way, their mappin to the Masterscale is adLusted. &t the !nvestment /ank, ratintools are differentiated by broad sements - banks, sovereins, corporates, funds, hede funds, commercialreal estate and a number of more speciali%ed businesses. The desin of these tools follows a commonapproach. The selection and combination of relevant criteria 6financial ratios and $ualitative factors: isdetermined throuh a structured analysis by credit officers with expert knowlede of each sement,supported by statistical modelin techni$ues where sufficient data is available.

The (wiss bankin portfolio includes exposures to a rane of enterprises, both lare and small- to medium-si%ed 6*(M+s: and the ratin tools vary accordinly. or sements where sufficient default data is

available, ratin tool development is primarily based on statistical models. Typically, these *score cardsconsist of eiht to twelve criteria combinin financial ratios with $ualitative and behavioral factors whichhave proven ood indicators of default in the past. or smaller risk sements with few observed defaults, amore expert based approach is chosen, similar to that applied at the !nvestment /ank. or the (wisscommercial real estate sement, which is part of the retail sement, the probability of default is derivedfrom simulation of potential chanes in the value of the collateral and the probability that it will fall belowthe loan amount. Default expectations for the (wiss residential mortae sement are based on the internaldefault and loss history, where the maLor differentiatin factor is the loan to value ratio " the amount of theoutstandin obliation expressed as a percentae of the value of the collateral.

$ource& U/( &nnual ?eports

<

<



Exhibit !+

$ource& U/( &nnual ?eport - 4115

Illustration

Calculate the implied probability of default if the one year T /ill yield is 28 and a oneyear %ero coupon corporate bond is fetchin )<.<8. &ssume recovery in the event ofdefault is %ero.

9et the probability of default be p+xpected returns from corporate bond E ).)<< 6)-p: H 61: 6p:

+xpected returns from treasury E ).12or ).)<< 6)-p: E ).12 p E ) - ).12@).)<< E .1<3=

E <.3=8

Illustration

!n the earlier problem, if the recovery is 518 in the case of a default, what is the default probability

).)<< 6)-p: H 6.51: 6).)<<: 6p: E ).12or .4=) p E 1.13<

or p E 1.45)FE 45.)F8

3

3



1 brief note on Credit Rating 1gencies3

?atin aencies speciali%e in evaluatin the creditworthiness of debt securities and also the eneral creditworthiness of issuers. The ratin iven by the aencies are a ood indication of the likelihood of allinterest payment and principal repayments bein made on time. #here capital markets have replaced banksas the maLor source of debt capital, ratin aencies have a particularly important role to play. /asle !! refers

to the credit ratin aencies as external credit assessment institutions. The three main ratin aencies in theU( are Moody;s (tandard and 0oor;s and itch.

The oriin of ratin aencies in the U( oes back to )212 when Nohn Moody initiated bond ratins for therail roads. !n )234, Dun and /radstreet ac$uired Moody;s &fter flourishin till the )2=1s, ratin aencies bean to strule as the bond markets were reasonably safe, dominated by overnment debt and investmentrade corporates. /ut in the )271s, the debt markets became more volatile, a landmark event bein the bankruptcy of 0enn Central in )271.

!n the )271s, the ratin aencies also revamped their revenue model, movin away from subscription payin investors to fee payin issuers. The aencies also widened the scope of coverae to include asset backed securities, commercial paper, municipal bonds, insurance companies, etc.

&s credit $uality can chane over time, ratin aencies publish updates on issuers at periodic intervals.#hile issuin ratins, the aencies can indicate whether the outlook is positive, i.e., it may be raised,neative, i.e., it may be lowered or stable, meanin neutral.

The revenue model of ratin aencies remains a source of concern. The independence of ratin aenciesand their role durin the sub prime crisis has been $uestioned. The !nternational orani%ation of (ecuritiesCommissions 6!>(C>: published a code of conduct for the ratin aencies in December 411<.

#hile ratin bonds, the ratin aencies consider various factors. (O0 for example looks at the followinwhile ratin bonds'

/usiness risk

!ndustry characteristics

Competitive positionin

Manaement

inancial risk

inancial characteristics

inancial policies

0rofitability

Capitali%ation

Cash flow protection

inancial flexibility

The aencies compute a number of financial ratios and track them over time. The aencies typically studya rane of public and non public documents related to the issuer and the specific debt issue. They reviewthe accountin practices. Meetins are usually held with the manaement to seek clarifications reardinkey operatin and financial plans and policies. (ome amount of subLectivity in the ratin process, however,

cannot be avoided.

ollowin the sub prime crisis, the ratin aencies have been revisitin the default and loss assumptions, intheir models. They have also been reviewin the assumptions made about correlations across asset classes.The aencies maintain that their approach is transparent. They also swear by their independence. Theaencies, however, have acknowleded that there have been problems with the $uality of information.

F Nohn / Caouette, +dward ! &ltman, 0aul Parayanan and ?obert # N Pimmo, *Manain Credit ?isk "The reat challene for lobal financial markets, Nohn #iley O (ons, 4115.

7

7



They have also acknowleded the need to o beyond ability to pay, to include other factors such asli$uidity.

#hile the role of the ratin aencies is under intense scrutiny, they will continue to play a maLor role in thecapital markets. The aencies, provided they can reinvent themselves, may still provide a transparent,independent and affordable institutional framework for evaluatin credit risk.

Ex%osure at default Pow that we have covered probability of default, it is time to move on to the second buildin block of credit risk manaement " credit exposure. &t the time of default, theamount of exposure determines the extent of losses. The larer the exposure, more thelosses. (o alon with the probability of default, we must also determine the amount ofexposure. The amount of credit exposure at the time of default is called exposure atdefault 6+&D:. !n traditional bankin, the exposure is usually the face value of the loan./ut when derivatives and structured products are involved, the face value is not therelevant parameter. Determinin the exposure is a more involved process. Kuaranteesand commitments further complicate the problem.

!n case of derivative contracts, three situations may arise. The contract may be a liabilityto the bank, an asset to the bank or either of the two.

#here the derivative position is a liability, there is no credit exposure.

#hen the derivative position is an asset, there is credit exposure.

!n the third case, the position can be an asset or a liability dependin on the marketfluctuation. (o there is a possibility of loss when the position is an asset and no losswhen the position is a liability.

Credit exposure can be broken down into two components " current exposure and potential exposure.

Current exposure is the exposure which exists today.

0otential exposure is the likely exposure in case the credit deteriorates.

&dLusted exposure takes into account both current and potential exposure.

Credit exposure can be manaed proactively in various ways. /y markin to market, anyvariations in the position can be settled daily, throuh a marin account, instead ofallowin an accumulation over the life of the contract. Collateral also helps a company to protect itself aainst current and potential exposure. The collateral will typically exceedthe funds owed, by an amount called haircut . Downrade triers can also be used tomodify exposure. & clause can be inserted statin that if the credit ratin of thecounterparty falls below a certain level, the bank has the option to close out thederivatives contract at its market value.

Ex%osure at default at UBS

+xposure at default represents the amounts U/( expects to be owed at the time of default. or outstandinloans, the exposure at default is the drawn amount or face value. or loan commitments and for continent

5

5



liabilities, it includes any amount already drawn plus the additional amount which is expected to be drawnat the time of default, should it occur.

or traded products, the estimation of exposure at default is more complex, since the current value of acontract can chane sinificantly over time. or repurchase and reverse repurchase areements and forsecurities borrowin and lendin transactions, the net amount is assessed, takin into account the impact of

market moves over the time it would take to close out all transactions 6*close-out exposure:. +xposure atdefault on >TC derivative transactions is determined by modelin the potential evolution of thereplacement value of the portfolio of trades with each counterparty over the lifetime of all transactions "*potential credit exposure " takin into account leally enforceable close-out nettin areements whereapplicable.

or all traded products, the exposure at default is derived from a Monte Carlo simulation of potentialmarket moves in all relevant risk factors, such as interest rates and exchane rates. The randomly simulatedsets of risk factors are then used as inputs to product specific valuation models to enerate valuation paths,takin into account the impact of maturin contracts and chanin collateral values, includin the ability tocall additional collateral.

The resultant distribution of future valuation paths supports various exposure measures. &ll portfolio riskmeasures are based on the expected exposure profile. /y contrast, in controllin individual counterpartyexposures, U/( limits the potential *worst case exposure over the full tenor of all transactions, andtherefore applies the limits to the *maximum likely exposure enerated by the same simulations, measuredto a specified hih confidence level.

Cases where there is material correlation between factors drivin a counterparty;s credit $uality and thefactors drivin the future path of traded products exposure " *wron-way risk " re$uire special treatment.!n such cases, the potential credit exposure enerated by the standard model is overridden by a calculationfrom a customi%ed exposure model that explicitly takes this correlation into account.

$ource' U/( &nnual ?eport

4oss gi'en defaultThe third buildin block of credit risk manaement is the loss iven default. !n case of adefault, it may be possible to recover part of the amount owed. The proportion of theamount which cannot be recovered is called loss given default .

The amount which can be recovered depends on various factors.

The first factor is seniority. (enior claims have priority while settlin claims. Thussecured bonds have priority over unsecured ones.

The ease, with which assets can be sold to recover the amounts due, depends on theleal system and bankruptcy procedures.

Collaterali%ation i.e., the amount of collateral backin the loan, is another key factorin determinin the recovery rate.

?ecovery rates are also more sinificantly neatively correlated with default rates. & bad year for defaults is also bad for recovery./efore we take up a couple of simple illustrations, we need to define a few terms. &commitment represents the total amount the bank is prepared to lend to the borrower. >nthe other hand, outstandings refers to the actual amount loaned. Thus the commitmentconsists of two components " the outstandin and the unused portion of the commitment.The undrawn portion is nothin but a borrower;s call option to draw on the full credit linein distress. Durin distress, the borrower will indeed draw on the remainin amount,

2

2



fully or partly. The &dLusted exposure is nothin but the prior exposure adLusted for thisdrawdown. &dLusted exposure is calculated takin into account the bank;s totalcommitment, undrawn amount and the likely draw down in the case of creditdeterioration. /anks of course may put in place covenants that limit such drawdowns.

Ex%ected and unex%ected loss #xpected loss is the averae loss in value over a period of time for a iven exposure.

The expected loss is best handled by buildin it into the product price.

The unexpected loss refers to the variability of potential loan loss around the averaeloss level.

The unexpected loss can be viewed as some multiple of the standard deviation of theexpected loss. The essence of credit risk management is arriving at a good estimateof the unexpected loss. The unexpected loss in turn can be divided into twocomponents.

The statistical losses can be measured usin techni$ues such as Q&?.

3osses in the tails can be estimated by stress testin or by applyin extreme value

theory.

4oss gi'en default at UBS

9oss iven default represents U/(;s expectation of the extent of loss on a claim should default occur. 9ossiven default includes loss of principal, interest and other amounts due and also the costs of carryin theimpaired position durin the work-out process.

!n the !nvestment /ankin roup, loss iven default estimates are based on expert assessment of the riskdrivers 6country, industry, leal structure, collateral and seniority:, supported by empirical evidence frominternal loss data and external benchmark information where available.

!n the (wiss portfolio, loss iven default differs by counterparty and collateral type and is statisticallyestimated usin internal loss data. or the residential mortae portfolio, further distinctions are achieved by statistical simulation based on loan to value ratios.

$ource' U/( &nnual ?eport

+xpected losses (tatistical losses (tress losses

)1

)1



Exhibit !5

Ex%osure to credit risk at UBS

$ource' U/( &nnual ?eport, 4115

Exhibit !3


Ca%turing correlations6 Structural and Reduced &orm Models(o far we have considered simple situations. !n reality, banks face multiple exposures.Correlations may exist amon different exposures. or example, there tends to be hiherdefault rates across all ratins rades durin a recession. To capture correlations amondifferent credit events, there are broadly two approaches' $tructural models and +educed

form models.

))

))



(tructural models try to establish a relationship between default risk and the value of thefirm. or example, e$uity prices can be used to estimate the probability of default of the bond of a company whose shares are listed on the stock exchane. !n structural models,debt and e$uity are viewed as continent claims on firm value. The probability of defaultis calculated from the difference between the current value of the firm;s assets and

liabilities and the volatility of the assets. (tructural models are difficult to apply if thecapital structure is complicated or if the assets are not traded.

(tructural models view a firm;s e$uity as an option on the firm;s assets with a strike pricee$ual to the value of the firm;s debt. >ption pricin models, typically, /lack-(choles areused to identify the fair value of these claims. Two approaches are cited in the literature.The first was developed by the Pobel pri%e winnin economist, ?obert Merton. Thesecond, called AMQ is a modification of Merton;s model by the credit ratin company,Moody;s. 9et us briefly examine these two models.

Merton Model

The value of a firm, Q e$uals the sum of the values of debt, D and e$uity, +. The Mertonmodel attempts to measure the value of D and thus forecast the probability of default. Themodel frames the situation in such a way it reduces to an option pricin problem. The keyassumption in the Merton model is that the firm has made a sinle issue of %ero coupondebt that will be paid back in one shot, at a future point in time. >ther assumptionsinclude perfect financial markets, no bankruptcy costs and no costs to enforce contracts.&ll these assumptions can be suitably modified to extend the Merton Model.

9et us use the followin notations'

Q> E Current value of the company;s assets.QT E Qalue of the company;s assets at time T.+> E Qalue of the company;s e$uity today.+T E Qalue of the company;s e$uity at time T.D E &mount of %ero coupon debt maturin at time T.

σQ E Qolatility of assets.

σ+ E Qolatility of e$uity.

T E Time of maturity of the debt.

Two situations can arise.!f QT J D, the company will default on its debt. Debt holders will receive QT. +$uityholders will not receive any thin, i.e., +T E 1.

!f QT I D, debt holders will receive their full payment, D. +$uity holders will receive QT

" D.

#e can now combine the two possibilities into a more enerali%ed e$uation'+T E max 6QT " D, 1:

)4

)4



&s the minimum value of e$uity is 1 and the maximum value is unlimited, the pay off profile is that of a call option with strike price E D. #e can now apply the /lack (cholesmodel to value the e$uity.

+> E Q1 P 6d): " De-rt P 6d4:

d) E T

T r 45 nl

v

v

σ

σ :4@6:@6 4

1 ++

d4 E d) - σv√T

P refers to the cumulative normal probability. The probability of default on the debt is P

6-d4:. To calculate d4, we need to know the value of Q1 and σv. /oth fiures will in

eneral not be readily available. (o, assumin the company;s shares are listed, we haveto start with +1. There is a relationship available based on !to;s lemma. 6Derivation of

this relationship is beyond the scope of this book.:

σ+ +1 Ed5

d# σv Q1

Usin this relationship we can estimate Q1 and σv.

#e could also approach the problem in a different way by statin that the amountreceived by the debt holders of the company is'

D " Max R6D-QT:, 1S.

D is the pay off obtained by investin in a risk free %ero coupon bond maturin at time Twith a face value of D.

The second term, - Max D-QT, 1 is the pay off from a short position in a put option onthe firm;s assets with strike price, D and maturity date, T.

/y subtractin the value of the put from the risk free debt, we can value risky debt. Thevalue of the put can be calculated by applyin the /lack-(choles formula'

0 E De-r6t: P 6-d4: " Q1 P6-d):

)=

)=



Illustration

#hat is the value of a firm;s e$uity if the total value of the firm is 311 million and thedebt repayment is )11 million #hat will be the value of e$uity if the total value of thefirm drops to 7< million

!n the first case, value of e$uity E 311 " )11 E <11 million!n the second case, value of e$uity E 1 as the value of debt repayment exceeds thetotal firm value.

Illustration

The market value of a firm is 31 million and the value of the %ero coupon bond to beredeemed in = years is <1 million. The annual interest rate is <8 while the volatility ofthe firm value is )18. Usin the Merton Model, calculate the value of the firm;s e$uity.

9et us first calculate the curent firm value, (. ( E 31 x P 6d): " 6<1:e-6.1<:6=: x P 6d4:

d) E

=)1.

:=:64)1.1<6.

<131

4

++nl

E)7=4).

)3<.)54=. +

E 4.11<

d4 E d) - σ √t E 4.11< " 6.):6√=: E 4.11< - .)7=4) E ).5=)5

( E 31 P 64.11<: " 6<1: 6.5317: P 6).5=)5:

E 31 P 64.11<: " 6F=.1=<: P 6).5=)5:

E 631: 6.277<: " 6F=.1=<: 6.233<:E )7.1<7 million

#e can now calculate the current value of the firm;s debt.

Dt E De-r6t: " pt

E <1e-.1<6=: " pt

E F=.1=< " pt

/ased on put call parity0t E Ct

H e-r6t: " Q

>r 0t E )7.1<7 H F=.1=< " 31 E .124Dt E F=.1=< - .124 E F4.2F= million

#e can verify our calculation by addin up the market values of debt and e$uity andnotin that we et the market value of the firm.

)F

)F



7M8 Model

Moody;s AMQ approach adLusts for some of the limitations of the Merton model. TheMerton Model assumes that all debt matures at the same time and the value of the firmfollows a lonormal diffusion process. The AMQ model assumes that there are only twodebt issues. The first matures before the chosen hori%on and the other matures after thathori%on.

The AMQ model uses a concept called distance to default . This is defined as the numberof standard deviations by which the asset price must chane in order for a default tohappen in T years. The distance to default can be calculated as'

T

T r n4l n5 l

v

v

σ

σ :4@6 4

1 −+−

rom the formula we can see that this is nothin but the value of d4 in the /lack (cholesformula. The distance to default is a proxy measure for the probability of default. &s thedistance to default decreases, the company becomes more likely to default. &s thedistance to default increases, the company becomes less likely to default. The AMQ

model, unlike the Merton Model does not use a normal distribution. !nstead, it assumes a proprietary alorithm based on historical default rates.

Usin the AMQ model involves the followin steps'

a: !dentification of the default point, D.

b: !dentification of the firm value Q and volatility σ.

c: !dentification of the number of standard deviation moves that would result in thefirm value fallin below D, thereby leadin to default. This is the firm;s distanceto default, V.

d: ?eference to the AMQ database to identify the proportion of firms with distance-

to-default, V who actually defaulted with a year. This is the expected defaultfre$uency. AMQ takes D as the sum of the face value of the all short termliabilities 6maturity J ) year: and <18 of the face value of loner term liabilities.

Illustration

Consider the followin fiures for a company. #hat is the probability of default

/ook value of all liabilities ' 4.F billion+stimated default point, D ' ).2 billionMarket value of e$uity ' )).= billionMarket value of firm ' )=.5 billion

Qolatility of firm value ' 418

#e first calculate the distance to default.

Distance to default 6in terms of value: E )=.5 " ).2 E )).2 billion(tandard deviation E 6.41: 6)=.5: E 4.73 billion

Distance to default 6in terms of standard deviation: E73.4

2.))E F.=)

)<

)<



#e now refer to the default database. !f = out of )11 firms with distance to default ofF.=) actually defaulted, probability of default is .1=

Illustration

Kiven the followin fiures, compute the distance to default'

/ook value of liabilities ' <.2< billion+stimated default point ' F.)< billionMarket value of e$uity ' )4.F billionMarket value of firm ' )5.F billionQolatility of firm value ' 4F8

Distance to default 6in terms of value: E )5.F " F.)< E )F.4< billion(tandard deviation E 6.4F: 6)5.F: E F.F)3 billion

Distance to default 6in terms of standard deviation:

F)3.F

4<.)FE =.4=

!f in the default database, 4 out of )11 firms with a distance to default of =.4= actuallydefaulted, the probability of default is .14.

Reduced form modelsThese models assume that default events occur unexpectedly due to one or moreexoenous backround factors which are independent of the firm;s asset value. Thesefactors may be observable such as KD0 rowth, interest rates, exchane rates, inflation orunobservable. Correlations arise because these backround factors affect all theexposures. ?educed form models typically assume that default follows a 0oissondistribution or similar ha%ard rate process. Usin the 0oisson distribution, we can

determine the number of default events occurrin durin a specified period of time.

Credit Risk modelsCredit risk models are used by banks to calculate the credit loss for a iven time hori%on.The output of these models is a portfolio loss distribution which describes the potentialcredit losses and their probabilities. & credit loss is nothin but a decrease in the value ofa portfolio over a specified period of time. To estimate credit loss, we need to establishthe portfolio value today and at the end of the time hori%on.

There are two conceptual approaches to measurin credit loss. !n the default mode

paradigm, a credit loss occurs only when there is an actual default. The credit loss is

nothin but the difference between the exposure-at-default and the recovery value. !n themark-to-market paradigm a credit loss occurs if the borrower defaults or if the borrower;s credit $uality deteriorates.

To measure the value of the obliations, two techni$ues are commonly used " discountedcontractual cash flow approach and risk neutral valuation approach. !n the firstapproach, the credit spreads are used to discount cash flows. Chanes in the value of theloan are the result of chanes in market spreads or chanes in credit ratin. !n case of a

)3

)3



default, the future value is determined by the recovery rate. !n risk neutral valuation, weapply risk free rates and risk neutral probabilities.

Credit Risk Plus

The lobal bank, Credit (uisse< has developed a model for estimatin default probabilityand Qalue at ?isk. This model, called Credit ?isk 0lus, is based on actuarial, analyticaltechni$ues and does not use simulation. Credit risk is modeled on the basis of suddenevents. Default rates are treated as continuous random variables.

(uppose there are 6 counterparties of a type and the probability of default by eachcounterparty is p. !f we consider that there are only two possibilities " default or no

default and apply the binomial distribution, the mean number of defaults, µ, for the whole

portfolio is Pp. !f p is small, the probability of n defaults is iven by the 0oissondistribution, i.e, the followin e$uation'

p 6n: EW

e

n

n µ

µ −

The next step is to specify the recovery rate for each exposure. Then the distribution oflosses in the portfolio can be estimated.

Credit ?isk H allows only two outcomes " default and no default. !n case of default, theloss is of a fixed si%e. The probability of default depends on credit ratin, risk factors andthe sensitivity of the counterparty to the risk factors. >nce the probability of default iscomputed for all the counterparties, the distribution of the total number of defaults in the portfolio can be obtained. #hen the probability of default is multiplied successively byexposure at default and loss iven default, we et the credit loss.

Throuh the use of sector analysis, Credit ?isk 0lus can measure the impact ofconcentration risks and the benefits which can be obtained throuh diversification.

Credit Metrics

Credit Metrics, another popular model, has been developed by N 0 Moran. Unlike Credit?isk 0lus, this model does not view credit risk as a binary situation. !nstead, CreditMetrics tries to determine the probability of a company movin from one ratin cateoryto another durin a certain period of time.

Credit Metrics first estimates the ratin class for a debt claim. The ratin may remain thesame, improve or deteriorate, dependin on the firm;s performance. & ratins transitionmatrix, usually provided by the ratin aencies, ives us the probability of the creditmiratin from one ratin to another durin one year.

< The subsidiary of Credit (uisse, Credit (uisse irst /oston pioneered this model.

)7

)7



Exhibit !9

4argest CR1s :lobal Structured &inance " ;ear 0ransition Rates

+ef ' The Turner ?eview - & reulatory response to the lobal bankin crisis, published by' UA inancial(ervices &uthority, www.fsa.ov.uk@pubs@other@turnerBreview March 4112.

Pext, we construct the distribution of the value of the debt claim. #e compute the valuewe expect the claim to have for each ratin in one year. /ased on the term structure of bond yields for each ratin cateory, we can et today;s price of a %ero coupon bond for aforward contract to mature in one year. !f the bond defaults, we assume a recovery rate.!f the miration probabilities are independent, we can compute the probabilities for thetransition of each bond independently and multiply them to obtain the Loint probability./y computin the value of the portfolio for each possible outcome and the probability of

each outcome, we can construct the distribution for the portfolio value. #e can then findout the Q&? at a iven level of confidence.

/ut in eneral, while determinin credit losses, the credit ratin chanes for differentcounterparties cannot be assumed to be independent. & 7aussian "opula 'odel comesin useful here. Kaussian Copula allows us to construct a Loint probability distribution ofratin chanes. The Copula correlation between the ratins transitions for two companiesis typically set e$ual to the correlation between their e$uity returns usin a factor model.& brief explanation of the rationale behind this approach follows.

The historical record of ratin miration can be used to estimate the different Loint

probabilities. owever, this approach is often not enouh. Credit Metrics proposes anapproach based on stock returns. Usin the ratin transition matrix, we know the probability of the firm miratin to different credit ratins. #e use the distribution of thecompany;s stock returns to find out the ranes of returns that correspond to the variousratins. #e can produce stock returns correspondin to the various ratin outcomes foreach firm represented in the portfolio. !n short, the correlations between stock returnscan be used to compute the probabilities of various ratin outcomes for the credits. orexample, if we have two stocks we can work out the probability that one stock will be in

)5

)5



the & ratin cateory and other in &&& cateory. #hen a lare number of credits isinvolved, a factor model can be used.

Correlations and :aussian Co%ula& more detailed explanation of the Kaussian Copula is in order here. /ut before that, we

need to delve into the world of correlations. !n credit risk manaement, correlations areextremely important. Durin a crisis, default correlations across instruments tend toincrease. This is essentially because the underlyin factors are the same. !n the sameindustry, many companies may default simultaneously. More enerally, if a market participant has exposure to two different market variables, the total exposure will be veryhih when there is a stron positive correlation. The exposure will be far less when thereis a %ero correlation and would actually decrease if there is a neative correlation.

!n credit risk manaement, correlations have to be monitored as closely andsystematically as volatility in case of market risk manaement. The coefficient of

correlation between two variables x, y can be written as' y x

y x xy

nσ σ

∑ −)

The covariance between x and y can be written as' ∑ − y x xyn

). !n other words, the

correlation coefficient is nothin but the covariance divided by the product of the twostandard deviations.

#hile the coefficient of correlation is a useful parameter, it does not tell us the full story.!t measures only the linear dependence between two variables. #e need other parametersto understand the non linear dependence. This is where copulas come in handy. #e willcome to copulas a little later.

9et us et back to covariance. ow do we compute covariance 9et us define thecovariance of daily returns per day between two variables, x, y. !f xi , yi are the values of

the two variables at the end of day i , the returns on day i are)

)

−

−−

i

ii

x

x x and

)

)

−

−−

i

ii

y

y y.

The covariance between x, y is ∑ −nnnn

y x y xn

). !f we assume the expected daily

returns are %ero, the same assumption we made while calculatin volatility, "ovn E

∑ nn y x

n

). The variances of xn and yn are ∑

4)n

xn

and ∑ 4)n

yn

.

&s in the case of volatility, we can use an exponentially weihted movin averae model

to et updated values of the covariance. Covn E λCovn-) H 6)-λ: xn-) yn-).

#e could also use a K&?C model to estimate the covariance. !f we use a K&?C

model, we could write' Covn E γ H Xxn-)yn-) H βCovn-).

!t is important that variances and covariances are calculated consistently. or example, ifvariances are calculated by ivin e$ual weiht to the last m data points, the same should

)2

)2



be done for covariances. !f we use an +#M& 6+xponentially #eihted Movin

&verae: model, the same λ should be used for variances and covariances.

Pow we are ready to discuss copulas. 9et us say there are two variables Q), Q4, whichare not completely independent. The marinal distribution of Q) is its distribution

assumin we know nothin about Q4. The marinal distribution of Q4 is its distributionassumin we know nothin about Q).

Country risk management at UBS

Credit risk and country risk are closely related. U/( assins ratins to all countries to which it hasexposure. (overein ratins express the probability of occurrence of a country risk event that would lead toimpairment of U/(;s claims.

or all countries rated three and below, U/( sets country risk ceilins for all exposures to clients,counterparties or issuers of securities from the country, and to financial investments in that country.Country risk measures cover both cross-border transactions and investments, and local operations by U/( branches and subsidiaries in countries where the risk is material. +xtension of credit, transactions in traded

products and positions in securities may be denied on the basis of a country ceilin, even if exposure to thename is otherwise acceptable.

Counterparty defaults resultin from multiple insolvencies or eneral prevention of payments by authoritiesare the most sinificant effects of a country crisis. /ut U/( also considers the probable financial impact ofmarket disruptions arisin prior to, durin and followin a country crisis. These miht take the form ofsevere falls in the country;s markets and asset prices, loner-term devaluation of the currency, and potentialimmobili%ation of currency balances. The potential financial impact of severe emerin markets crises isassessed by stress testin.

U/( also considers the possibility of restrictions on, cross-border transfers of funds which miht prevent ali$uidity surplus in one country bein used to meet a shortfall in another. Unexpected economic stresssituations or soverein defaults, miht induce a overnment to limit or prohibit the transfer of funds outside

the country. U/( assesses the potential impact on its li$uidity position of potential transfer risk events incountries with a one-year probability of default of <8 or more as indicated by U/(;s internal sovereinratin.


41

41



ow do we establish the correlation structure between Q) O Q4 !f the two marinaldistributions are normal, we can assume that the Loint distribution of the two variables isalso normal. /ut when the marinal distributions are not normal, we run into a problem.(o we use the Kaussian Copula. #e map Q) into U) and Q4 into U4 such that U) and U4

are normal variables. To elaborate, the ) percentile point of the Q) distribution is mapped

to the ) percentile point of the U) distribution and so on. (imilar mappin is done between Q4 and U4. Thus copulas enable us to define a correlation structure between Q)

and Q4 indirectly. Copulas can also be used to establish the correlation structure betweenmore than two variables. 9astly, instead of the Kaussian copula, we could also use the tCopula. &s the name suests, the variables U), U4 are now assumed to have a bivariate t

distribution.

Credit Risk Ca%ital6 Basle II frame<ork >ne of the key obLectives of any risk measurement exercise is to understand how muchcapital must be set aside. Three different approaches are available to calculate the creditrisk capital under /asel !! norms. #e shall cover this topic in more detail in a separate

chapter. #hat follows here is a brief account.

$tandardised approach!n the standardi%ed approach, the risk weihts are determined on the basis of ratins provided by an external credit ratin aency. ixed risk weihts are used correspondinto the deree of risk in each asset cateory. /asel ! had only five weihts. /asle !! ismore ranular with )= cateories of risk weihts ranin from 41 to )<18 dependin onthe type of counterparty and ratin status. !n such cases as low rated securiti%ed assets,the weihts can o up to =<18.

8nternal +atings )ased approach

ere, banks can use their own estimates of credit risk. The exposures are cateori%edinto six broad classes of assets " corporate, soverein, bank, retail, e$uity and purchasedreceivables. #ithin the corporate asset class, five sub classes of speciali%ed lendin have been separately identified. (imilarly in case of retail assets, there are three sub classes ofexposures - exposures secured by residential properties, $ualifyin revolvin retailexposures and all other retail exposures.

!?/ is divided into two cateories " oundation and Advanced .

Under the oundation approach, banks estimate the probability of default and rely onsupervisory estimates for other risk components.

!n the advanced method, banks provide their own estimates of probability of default,

loss iven default and exposure at default. To use the !?/ approach, banks mustmeet various criteria laid down by the reulatory authorities.

Credit deri'ati'es>n paper, banks manae their credit risk throuh diversification. /ut there are limits todiversification. or example, banks may not like to turn down customers with whom theyhave a valuable relationship even if the exposure has crossed prudent limits. &ssinmentof loans to another counterparty is also not that easy. Customers may not like their loans

4)

4)



bein sold off by the bank to another entity. Due to these reasons, the concentration ofcredit risk on the bankin books is often much hiher than desirable.

Credit derivatives have emered to deal with such problems. 8n simple terms, a credit

derivative can be defined as an instrument that allows one party to transfer an asset9s

credit risk to another party without passing on the ownership of the asset. The two partiesin a credit derivative transaction are the protection buyer who pays a premium and protection seller who stands ready to provide compensation in case of a credit event. Theinstrument or roup of instruments with respect to which the credit risk is bein traded iscalled referenced obligation. The reference obliation is sometimes called reference assetor reference credit. Credit derivatives till now have been privately neotiated, over-the-counter 6>TC: instruments. /ut now there are proposals from reulatory authorities inthe U( and +urope to establish central clearin arranements for various >TCderivatives.

Thanks to credit derivatives, banks can continue to make loans and hede the risks

involved. &t the same time, the counterparty which oes short on the credit derivativecan ain access to an exposure which seems to make business sense. !ndeed, creditderivatives can be used to create almost any desired risk profile. (ay the bank is finewith the credit exposure to a specific client but is worried about a downturn in theindustry. & suitable credit derivative can be structured. Credit derivatives also help inincreasin the li$uidity for banks. /y limitin the bank;s downside risk, banks will bemore willin to lend more to many businesses. This will ensure healthy rowth of credit,so vital to maintain economic rowth.

rom a systemic point of view, credit derivatives represent an efficient way of separatinand tradin credit risk by isolatin it from other risks such as market risk and operationalrisk. Thanks to the !nternational (waps O Derivatives &ssociation, !(D&, credit defaultareements have become standardi%ed. (o buyin and sellin credit protection has become easy and straihtforward.

Credit derivatives also have a useful sinalin value. They provide an additional sourceof market based information about the company;s financial health. There is an arumentthat Credit Default (wap 6CD(: prices because they are market determined convey betterinformation about the probability of default, than credit ratins which only reflect theviews of an aency.

Credit derivatives support market completion by providin access to credit exposure inways that would not have been possible otherwise. or example, a bank may not actuallylend to a company but by oin short on the CD(, it can assume an e$uivalent riskexposure. &nd even if a company;s bonds are not traded, synthetic exposures can becreated.

Credit derivatives have also helped in the interation of different sements of financialmarkets. or example, the dividin line between bonds and loans has becomeconsiderably thinner, thanks to CD(.

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44



0he rise and fall of credit deri'ati'esThe oriin of >TC credit derivatives can be traced back to bond insurance whichinvolves compensation in the event of a default. /ond insurance has been around forseveral decades now, but credit derivatives have become popular only in the past )< years

or so. !n )22=, transactions bean to be structured which involved a periodic fee payment by the banks. !nvestors would pay compensation in case of a credit event. Thefirst synthetic credit derivatives product was launched by N 0 Moran in )227. Theoutstandin notional value of credit derivatives rew from )51 million in )227 to morethan ) trillion in 411), reachin < trillion at the end of 411F. The credit derivativesmarket exploded in the build up to the sub prime crisis, reachin a notional value of 34trillion at the peak. (ince then due to nettin and *trade compression, the value hascome down. /ut even now the fiure is sinificant.

Credit derivatives played an important role in the subprime crisis. &!K collapsed due tohue credit default swap positions it built on its books. Pot surprisinly reulators and

economists have expressed deep concerns about the indiscriminate use of creditderivatives. ?ather than sereate and transfer credit risk, economists arue that theseinstruments seem to have added to the systemic risk. 9et us understand the basis forthese concerns.

/anks which lend to clients but offload their credit risk by purchasin credit derivatives,have little incentive to monitor their clients, even thouh they are the best e$uipped to doso in several respects. This has a neative impact on the way credit risk is manaed at asystem level. The protection seller in a CD( may have the motivation but is not as welle$uipped as the bank to monitor credit risk. The net effect is less monitorin oversihtthan what is desirable. !t also leads to the moral ha%ard problem as far as borrowers are

concerned. #hen they know that they are not bein actively monitored, borrowers canafford to indule in imprudent risk takin.

!n the case of +nron, which went bankrupt in a spectacular way, N0 Moran Chase,Citiroup and other banks had lent billions of dollars. /ut they had simultaneously usedcredit derivatives to limit their credit exposure. &ccordin to one estimates, the banksused 511 swaps to lay off 5 billion of +nron risk.

&nother perverse incentive which seems to have developed is that buyers of CD( on acompany;s bonds may be more keen on the company filin for bankruptcy rather thanrevivin it durin a crisis. The CD( compensation is likely to be received immediately

whereas restructurin initiatives are lon drawn out, cumbersome and uncertain in termsof outcome. !n other words, CD( buyers actually have a stron incentive to support valuedestruction. This phenomenon has by no means been uncommon in the aftermath of thesub prime crisis as many companies have run into trouble.

The CD( markets have also been heavily critici%ed for their opa$ueness. The marketsare of the >TC type and unreulated. (o the $uality of disclosure by the players involvedis clearly not ade$uate. Moreover, a party can unwind its position by offloadin it to

4=

4=



another counterparty without informin the oriinal counterparty. &s rank 0artnoy ODavid (keel mention3, *!f suppliers, bond holders or other stakeholders do not knowwhether the bank is heded, the informational content of the bank;s actions will bemuddied. This uncertainty is itself an important cost of the credit default swap market.

Many investors place hihly leveraed bets on CD(. (o even a relatively small chane inthe market position can trier a crisis. !f there is a rush by market participants tounwind a vast array of interconnected contracts, there would be a serious li$uidity crisis.(uch concerns were serious when /ear (tearns and 9ehman /rothers approached bankruptcy. That also probably explains why the U( Treasury was desperate to save&!K.

Credit derivatives are relatively less li$uid instruments compared to currency or interestrate derivatives. This is because of the uni$ue nature of individual reference credits./ecause of the lack of li$uidity, the protection sellers can face problems if they try tohede their derivative position. !n many situations, the credit derivative may also be

vulnerable to basis risk. There may be an imperfect correlation between the referenceobliation and the underlyin risk.

!n case of Collateralised Debt >bliations 6CD>s:, there is another serious problem " themispricin of credit. (imilar assets should have similar values. !f CD>s are able tocreate value by repackain assets, it means there must be some inefficiencies in thecorporate debt market. /ut this mispricin should loically be removed by the buyinand sellin of bonds. &rbitrain opportunities rarely persist unless there is aninformation asymmetry or a reulatory issue. The investors in CD> tranches are usuallysophisticated people. &nd there is no reulatory explanation that can be offered forsynthetic CD>s.

#hat seems to be the case is that the complex arbitrary and opa$ue ratin methodoloiescreate arbitrae opportunities without actually addin any real value. !n short the *valuemay be the result of errors in ratin the assets, errors in calculatin the relationship between the assets and the tranche payouts or errors in ratin the individual CD>tranches.

&s 0artnoy O (keel mention7, *0ut another way, credit ratin aencies are providin themarkets with an opportunity to arbitrae the credit ratin aencies; mistakesY The process of ratin CD>s becomes a mathematical ame that smart bankers know they canwin. & person who understands the details of the model can tweak the inputs,assumptions and underlyin assets to produce a CD> that appears to add value, eventhouh in reality it does not. !n other words, there is a very stron arument emerinthat CD>s have been used to convert existin fixed income instruments that are pricedcorrectly into new ones that are overvalued.

0y%es of credit deri'ati'es

3 *The promise and perils of credit derivatives, #orkin 0aper, University of (an Dieo (chool of 9aw.7 *The promise and perils of credit derivatives, #orkin 0aper, University of (an Dieo (chool of 9aw.

4F

4F



The term credit derivatives may have been coined in recent decades. /ut many traditionalinstruments have carried features of credit derivatives. or example, letters of credituarantee payment in case of a default. /ut credit derivatives, as we know them today,differ sinificantly from these traditional instruments. 9et us understand some of the keyfeatures of credit derivatives. !n eneral, credit derivatives can be classified on the basis

of'

(nderlying credit sinle entity or a roup of entities

"onditions of exercise default, ratin downrade, increase in credit spread.

%ay off function fixed amount, linear pay off, non linear pay off.

!n a single name "4$ , the contract is between a protection buyer and a protection seller.!n a basket "4$ , there is a portfolio of assets. !n a first to default "4$ , compensation is payable after the first default. The structure is terminated after the first event. !n an nth to

default "4$ , the pay off occurs only when the n th default happens. !n a standard basket"4$ , compensation is payable for each and every default.

The key factor in determinin the spread for a basket CD( is the default correlation of thereference entitles in the basket. !f the default correlation between the reference entities is%ero, the probability of multiple defaults will be very low. !n other words, the value of afirst-to-default CD( will be sinificantly hiher than that of say a )1 th-to-default CD(.>n the other hand, if the default correlation amon the reference entities is perfect, eitherall the reference entities will default or none will default. !n such a case, a first-to-defaultand an )1th-to-default CD( will have the same value.

The conditions of exercise depend on how the credit events are defined. Credit eventscan be default, bankruptcy, failure to pay, restructurin, widenin of credit spread, etc.

The pay off is usually linked to the amount that cannot be recovered. This is oftenmeasured by par value " price of the bond after the credit event. &lternatively the protection buyer can hand over the reference asset to the protection seller and receive acash payment e$ual to the par value. inally, a credit derivative may also be structuredwith a binary payout. This means in case of a credit event, the payment is fixed andindependent of the actual impairment.

Credit (efault S<a%s#e have already been referrin to Credit Default (waps 6CD(: in this Chapter. Pow, itis time to understand CD( in more detail. !n many ways, the CD( is the simplest form of

credit derivative. !t is also by far the most popular credit derivative. !n a CD(, one partysells protection aainst default on an underlyin instrument to another party. Unlikeinsurance contracts, the two parties involved in a CD( may have nothin to do with thereference entity. !n other words, the parties may be bettin on the probability of defaultof an instrument issued by a third party. !t is precisely because of this element ofspeculation, that the CD( market hit 34 trillion in notional value at its peak. 6!n the past)5 months, however, the market has shrunk sinificantly due to offsettin of contracts.:

4<

4<



The protection buyer pays a premium while the protection seller stands ready tocompensate the buyer in case of a credit event. &s mentioned earlier, the compensationmay be fixed or variable. Qariable compensation may be either in cash or payment offace value aainst the receipt of the underlyin bond. Cash settlement is preferred whentransfer of the ownership of the obliation is difficult. >n the other hand, the protection

seller may prefer physical settlement if this enables direct interaction with the bankruptentity durin post default neotiations. The protection buyer too may prefer thisarranement as the payment is transparent and not subLect to any uncertainty or disputeabout the exact recovery value of the underlyin asset.

CD( is certainly a form of credit insurance. /ut it does not eliminate credit risk. &ll thathappens is that exposure to the underlyin credit is replaced by that to the protectionseller. The effectiveness of CD( as a credit insurance mechanism implicitly assumes alow correlation between the default risk of the underlyin credit and the protection seller.

9et us briefly understand the important terms used in the context of CD('

The premium amount paid by the protection buyer, as a percentae of the notional principal is called the "4$ spread . The premium is often expressed as basis points.The premium can also be a lumpsum amount.

The reference entity is defined as the entity on which the protection is bouht andsold.

& credit event is defined as the situation that will trier the payment ofcompensation by the protection seller to the protection buyer.

The three most important credit events are bankruptcy, failure to pay andrestructuring .

!n case of a credit event, the purchaser of the CD( can sell a bond issued by the

reference entity to the seller of the CD( and receive the par value. This bond is calledthe reference obligation.

The par value of the reference obliation is termed as the swap;s notional principal .

&lternatively, cash compensation is possible. The protection seller can pay thedifference between the reference obliation;s par and market value.

& CD( can be unwound in three ways.

The counterparties can exchane the current market-to-market value. &ll the futurecash flow streams are cancelled. The onoin leal risk is eliminated.

The second way to unwind a CD( is to replace the current investor by a new

counterparty. &ssinment will be subLect to the protection buyer areein to take onthe counterparty risk of the protection seller.

The third way to unwind a CD( is throuh an offsettin transaction. &n offsettinlon or short protection can be entered into with another counterparty. /ut such anunwindin involves sinin of further documentation and adds to leal risk. #herethe position is illi$uid and assinment is not possible, this kind of unwindin may

43

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make sense. !ntuitively, the mark-to-market value of a CD( is e$ual to the cost ofenterin into an offsettin transaction.

=ther 'ariations of C(S&n asset default swap is essentially a sinle name CD( where the underlyin reference is

an asset backed security.

!n an e2uity default, swap, compensation is payable if the stock value falls below a prespecified level.

& callable default swap is a CD( that can be terminated by the protection buyer at somestrike spread at a future date. Thus it is nothin but a CD( with an embedded shortreceiver option. +ffectively, this means the protection buyer has the riht to *sell backto the protection seller. The protection buyer will be motivated to do so if there issufficient spread tihtenin. This way, the protection buyer can avoid payin what lookslike a hih premium, oin by the current market scenario. !n return for this facility, the

callable default swap spread tends to be hiher.

& total rate of return swap 6T?>?(: is another way of transferrin credit risk. >ne party passes on the total return on a security, in exchane for a fixed return calculated as9!/>? plus some spread. The cash flows are exchaned on specific payment dates. &tthe end of the swap, the accumulated ain or loss in the value of the security isexchaned. The different elements of a T?>?( are reference asset , total return payer

and total return receiver . !f the underlyin asset is a portfolio of bonds owned by thetotal return payer, the payer transfers the credit risk of the portfolio to the total returnreceiver. !f the credit $uality of the portfolio deteriorates, and there are capital losses, thereceiver will bear the loss.

The reference asset may be a bond, index or basket of assets. Usually, it is a widely$uoted and traded bond. The total return payer is the leal owner of the reference asset.The payer pays the total income from the reference asset in return for a floatin rate ofinterest. The total return receiver derives the economic benefit of ownin the referenceasset without actually holdin the asset on the balance sheet. The total return includesinterest@dividends, ains@losses due to market movements and credit losses. There is noexchane of the notional principal of the swap. /ut if the reference asset is amortisedover the life of the swap, the notional principal is reduced accordinly. T?>?( aresometimes collaterali%ed and marked-to-market daily. The cash flows may be exchaned periodically or at maturity.

&ny increase or decrease in the value of the asset leads to cash flows. !f the asset hasincreased in value, the total return payer must pass on the increase in value to the totalreturn receiver. !f the asset has decreased in value, the total return receiver mustcompensate the total return payer. !n case of a default, the T?>?( terminates and thetotal return receiver must pay compensation.

S%ecial %ur%ose 'ehicles and C(=s

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Collateralised Debt >bliation 6CD>: is the eneral term for an asset backed securitythat issues securities and pays principal and interest from an underlyin pool of debtinstruments. !f the underlyin pool consists entirely of bonds, it called a Collateralised/ond >bliation 6C/>:. !f it consists only of loans, it is called Collaterali%ed 9oan>bliation 6C9>:.

CD>s are used to repackae securities to create structured products with a completelydifferent risk complexion, compared to the underlyin debt instruments. CD>s aredivided into tranches with different derees of certainty reardin payments andconse$uently different credit ratins. The tranche with the lowest credit ratin is calledthe e2uity tranche. The hihest credit rated tranche is referred to as senior or super

senior . !n between there are me::anine tranches. Usually, the oriinator of the CD>retains the e$uity tranche.

!n a balance sheet "4;, the main motivation is to remove selected assets from the balance sheet to manae credit risk, improve li$uidity, etc. Arbitrage "4;s focus on

creatin structured products that take advantae of the spread between assets in the pooland the promised payments to security holders. #hereas balance sheet CD>s tend to be*static, arbitrae CD>s are manaed actively. "ash flow arbitrage "4;s depend primarily on cash flows from the underlyin pool of assets to dischare the obliationstowards investors. 'arket value arbitrage "4;s sell securities in the pool from time totime to meet the obliations towards investors. The deree of active manaement has animpact on the leal and accountin aspects of the CD>.

Many structured credit products can be created throuh securiti%ation. & special purposevehicle 6(0Q: often substitutes the investment bank. The (0Q is a leal trust that purchases and holds the notes as collateral and simultaneously enters into a CD( as a protection seller. The (0Q issues securities to investors.

!n a synthetic CD>, the money collected is invested in risk free instruments. &t the sametime, a portfolio of CD( is sold to third parties. !n the absence of a credit event, the (0Qmakes the coupon payment as well as the premium on CD( to investors. &fter a creditevent is triered, the (0Q li$uidates the notes. irst the CD( protection buyers aretaken care of. Then the remainder is distributed to the shareholders.

!n a synthetic CD>, unlike cash CD>, assets are retained by the sponsorin orani%ation.They are not transferred to the (0Q. The performance of a synthetic CD> is not linkedto an underlyin revenue stream but to a reference portfolio of assets. ?eferencin a portfolio can be done throuh a CD(, total return of rate swap or credit linked note.Unless stated specifically, a synthetic CD> normally uses CD( to transfer risk.

+ssentially, in a synthetic CD>, CD( and overnment bonds are combined to substitutecorporate loans as the assets in the (0Q. The premium from the CD( and the interestearned on risk free securities are paid to investors in a way that reflects the risk they are bearin. #hen the CD( is triered, the asset value is reduced. The pay off for the

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lower tranches depends on the amorti%in rate of the assets, which is determined by thenumber of CD(s triered.

The market has standard definitions of CD> tranches. (o individual tranche tradin isalso possible. & (inle Tranche CD>, 6(TCD>: is a contract between two parties on a

particular tranche of a synthetic CD> on a standalone basis. !n a sinle tranche, one sidesells protection aainst losses on a tranche and the other side arees to buy the protection.!f the correlation between the CD> assets is low, the e$uity tranche will be very risky./ut the senior tranches will be relatively safe. >n the other hand when the correlation is perfect, all the tranches will be e$ually risky. !t is clear that durin the sub prime crisis,correlations turned out to be hiher than expected. /anks such as U/( ot into bitrouble with their super senior tranches.

#e need to differentiate between corporate CD( and &/( 6&sset /acked (ecurities:CD(. !n the corporate market, the focus is on the corporate entity. 9ess emphasis is placed on the credit;s individual obliations. !n the &/( market, the focus is on a

specific instrument typically a particular tranche from a particular securiti%ation of a particular oriinator.

!n case of corporate CD(, the usual practice is for all obliations of a seniority to bereference obliations. !n the corporate CD( market, it does not much matter whichsenior unsecured obliation is tendered for physical settlement or marked to market forcash settlement. !n the case of &/( CD>, each tranche has a distinct credit $uality and adistinct credit ratin. &/( CD( focus on the specific tranche.

The credit problem in case of a corporate CD( is clearly defined. Credit events are easilydiscernable. >n the other hand, credit problems in &/( securiti%ation are not that clearlydefined. The flexibility of an &/( tranche;s cash flows means that the existence orextent of a credit problem is ambiuous. 0roblems may resolve themselves. They willusually not rise to the same level of distress as a defined credit event in a corporate CD(.Many &/( tranches stipulate deferment of interest payments if collateral cash flow isinsufficient due to delin$uencies and defaults. 9ater, if cash flow recovers, deferredinterest can be made up.

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Exhibit !

Im%act of &inancial Sector Stabili>ation Measures on

Credit (efault S<a% C(S/ S%reads

+ef ' !M Klobal inancial (tability ?eport, >ctober 4112, www.imf.or

Credit s%read &or<ardThe protection buyer and protection seller aree to a credit spread. The buyer receives thedifference between the credit spread at maturity and an areed " upon spread, if positive.>n the other hand, if the difference is neative, a payment is made. !f i is the prevailinspread and r is the areed upon spread and the modified duration is 4, then thecompensation payable to the buyer is iven by'

Compensation E 6i - r: 6D: 6Potional amount:.

Credit s%read o%tions

Credit-spread options are options on asset swaps. They are used to hede aainst the riskof chanes in credit spreads. & reference asset is selected and a strike spread and maturityare set. The pay off depends on whether the actual spot spread on the exercise date isabove or below the spread on the reference security. The credit spread can be relative toa risk free instrument or any other bond. Credit spread options may be of the +uropeanor &merican type.

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http://www.imf.org/

http://www.imf.org/



The buyer of a call option has the riht to buy the spread at a pre specified strike price.(uch an option has value if the spread at exercise is reater than the specified strikespread. The buyer of a credit spread put option has the riht to sell the spread at a prespecified strike price on the exercise date. The option has value if the spread at exerciseis less than the strike spread.

Credit S<a%tions& credit swaption involves payment streams that are continent on the occurrence of acredit event. & swaption is nothin but an option on a swap. The holder of a swaptioncan enter into a swap with a pre specified fixed payment stream over a specified period oftime.

& credit swaption can be an option to buy or sell credit protection at a pre specified CD(strike spread. The underlyin is the forward CD( spread from the option expiry date tothe maturity date of the CD(. & swaption can be +uropean, &merican or /ermudan. !n a payer default swaption, there is a riht to buy the protection. The option holder benefits

if the spread widens sufficiently enouh by the maturity date. The receiver default swaption confers the riht to sell protection. The option holder benefits if the spreadtihtens sufficiently enouh by the maturity date. & credit default swaption can also bestructured with a provision for a knockout. !f there is a credit event between the tradedate and the expiry date, the knock out provision cancels the default swaption withimmediate effect. The payer default swaption buyer will have the riht to buy the protection at the strike spread. !n case of a receiver default swaption, the referencespread would widen and the option would not be exercised after a credit event. (o aknock out provision is not needed.

Credit default swaptions may be structured such that the underlyin asset is a credit

index. This may be preferred if the investor wants to take a macro view as opposed to aview on a specific credit. 0ortfolio volatility also tends to be lower.

Credit linked note& credit linked note 6C9P: is a funded credit derivative. eatures of the derivative areembedded in a eneric cash instrument. Typically, a C9P combines a credit derivativewith a reular bond. The credit risk is transferred throuh the issue of bonds eitherdirectly by the protection buyer or by a (pecial 0urpose Qehicle 6(0Q:.The investor isthe credit protection seller while the issuer of the note is the protection buyer. Theinvestor@protection seller pays up front the par value of the bond and receives interest payments at 9!/>? plus a spread. !n case of a credit event, the investor will receive the

recovery value of the underlyin asset in the CD( and lose claim over the principal. >rto put it differently, the investor will receive the principal less the amount that cannot berecovered.

& true credit derivative C9P has a third party as reference name. The settlement processis similar to that of CD(. The protection buyer, in case of a cash settlement, will pay therecovery value to the protection seller. !n case of physical settlement, the note isterminated. The reference security is handed over to the protection seller.

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(ome C9Ps may be issued by a party which is also the reference name. The occurrenceof a credit event implies immediate termination of the bond. Po settlement process isneeded because the protection seller is already holdin the bond.

& standard C9P is issued with reference to a specific bond. & C9P that is referenced tomore than one credit is called basket credit linked note. & variant of the basket C9P isthe first-to-default "36 , in which the investor is sellin protection on the first credit-to-default. The return on the C9P is a multiple of the averae spread of the basket. !n a physical settlement, the defaulted asset is delivered to the bond holder. !n cashsettlement, the C9P issuer pays redemption proceeds to the bond holder. This is nothin but the difference between the principal and recovery value.

(ynthetic C9P can be issued by a (0Q that holds collateral securities financed by theissue. The (0Q uses the issue proceeds to purchase the collateral and then sells credit protection to a counterparty. The (0Q also provides interest on the collateral aainst the

(0Q;s future performance under the CD(. The (0Q may also enter into an interest rateswap to modify cash flows suitably. or example, the cash flows on the collateral may befixed rate but the C9P cash flows may be re$uired in floatin rate form.

The C9P coupon is the sum of the returns on the collateral and the CD( premium.!nvestors in the C9P receive their coupon and principal at the time of redemption in theabsence of any credit event. !f a credit event happens durin the life of the C9P, thecollateral is sold to form the par payment made by the (0Q to the CD( counterparty. TheC9P is redeemed by the issuer at %ero percent. &ccrued interest payments from thecollateral@CD( premium form an accrued C9P coupon which the investor receives.

The CD( counterparty is only eliible for )118 of the notional amount. +xcess value ofthe collateral belons to the investors. !f the collateral has lower than market value, theCD( counterparty receives the compensation. The counterparty reduces the amount ofdefaultable obliations it delivers. #hen the market value of the collateral falls sharply,the investor loses the entire notional value of the C9P. The CD( counterparty will alsosuffer a loss.

The collateral provides a base return to the investors and acts as a collateral for the CD(counterparty. (o the collateral must be acceptable to both the parties. The collateralshould be chosen such that the probability of thins oin wron with the reference entityand collateral, simultaneously is minimi%ed.

!n eneral, the C9P investors are exposed to three kinds of risk'

Credit risk of the reference entity

Credit risk associated with the securities makin up the collateral

Counterparty risk associated with the protection buyer.

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!f the collateral is hihly rated and the CD( counterparty is hihly rated, the focus shiftsto the credit risk of the reference entity. #hen the (0Q uses interest rate swaps to modifythe cash flows, there is an additional source of risk.

+ffectively, C9Ps ive investors an opportunity to exploit anomalies in pricin between

the cash and credit protection markets. C9Ps enable investors to customi%e theirexposure with respect to currencies, maturities and coupon structures. C9Ps can betraded in the same way as bonds. /ut C9Ps lack li$uidity, when compared to bonds.Moreover, there are fixed costs associated with the creation of the (0Q and the variousaspects of the C9P. (o C9Ps may make more sense for medium term rather than shortterm investors.

& ood example of C9P use is Citiroup which had considerable exposure to +nron in4111. Thouh +nron at that time was flyin hih, Citiroup decided to hede theexposure usin securities which resembled credit linked notes. Citi created a trust whichissued the securities in the form of five year notes with interest payments. The proceeds

were invested in hih $uality debt. !f +nron did not o bankrupt, investors would receivethe principal after < years. !n the event of bankruptcy, Citi could swap the loan it hadmade to +nron, for the securities in the trust.

ConclusionCredit risk manaement is more complex compared to market risk manaement withreard to data availability and modelin. Credit risk is also firm specific unlike marketrisk. !s this chapter, we have tried to understand the basic principles of measurin creditrisk. #e have also seen how credit risk can be manaed usin credit derivatives. &sfinancial instruments become more and more complex and speciali%ed, the distinction between market and credit risk is becomin increasinly blurred. #e shall examine this

theme in more detail in a later chapter.

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References'

+.! &ltman, *inancial ?atios, Discriminant &nalysis and the 0rediction of Corporate/ankruptcy, !ournal of inance, (eptember )235, pp. <52-312

?obert C Merton, *>n the 0ricin of Corporate Debt' The ?isk (tructure of !nterest ?ates,Nournal of inance, 42, )27F, pp. FF2-F71.

+dward. !. &ltman, *Credit risk measurement and manaement' The ironic challene in thenext decade, Pew Zork University (tern (chool of /usiness, #orkin 0aper, ebruary)225, !P-25-11=.

?anaraLan A (undaram, *The Merton@AMQ &pproach to 0ricin Credit ?isk, #orkin0aper, (tern (chool of /usiness, Nanuary 4, 411).

Nohn C ull, *>ptions, utures and >ther Derivatives, 0rentice all, 4113

Nohn C ull, *?isk Manaement and inancial !nstitutions, 0earson +ducation, 4117.

0hilippe Norion, *inancial ?isk Manaer andbook, Nohn #iley O (ons, 4117.

Nohn / Caouette, +dward ! &ltman, 0aul Parayanan and ?obert # N Pimmo, *ManainCredit ?isk " The reat challene for lobal financial markets, Nohn #iley O (ons, 4115.

U/( &nnual ?eports, 4117 O 4115.

rank 0artnoy, David & (keel, *The promise and perils of credit derivatives, #orkin0aper, University of (an Dieo (chool of 9aw.

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