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--Group 7Gaurav GuptaVivek Sharan

Amrita Pattnaik

Anand WardhanSrikant Sharma

LBSIM, New Delhi

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` CREDIT RISK

It is the risk that a counterparty in financialtransaction will fail to fulfill their obligation.

` CREDIT DERIVATIVES:

Credit derivatives are derivative instruments

that seek to trade in credit risks.

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Credit default swap

Credit spread option

Credit linked note

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` A huge market with over $40 trillion of notional principal

` Buyer of the instrument acquires protection from the selleragainst a default by a particular company or country (the

reference entity)` Example: Buyer pays a premium of 90 bps per year for $100

million of 5-year protection against company X

` Premium is known as the credit default spread. It is paid forlife of contract or until default

`

If there is a default, the buyer has the right to sell bonds witha face value of $100 million issued by company X for $100million (Several bonds are typically deliverable)

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DefaultProtectionBuyer, A

DefaultProtectionSeller, B

90 bps per year

Payoff if t ere is a efault byreference entity= 00( -R)

Recovery rate,R, is the ratio of the value of the bond issuedby reference entity immediately after default to the face valueof the bond

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` Payments are usually made quarterly in arrears` In the event of default there is a final accrual

payment by the buyer` Settlement can be specified as delivery of the

bonds or in cash

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` Allows credit risks to be traded in the sameway as market risks

` Can be used to transfer credit risks to athird party

` Can be used to diversify credit risks

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Portfolio consisting of a 5-year par yield corporatebond that provides a yield of 6% and a longposition in a 5-yearCDS costing 100 basis points

per year is (approximately) a long position in ariskless instrument paying 5% per year

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` Conditional on no earlier default a reference entityhas a (risk-neutral) probability of default of 2% ineach of the next 5 years. (This is a defaultintensity)

` Assume payments are made annually in arrears,that defaults always happen half way through ayear, and that the expected recovery rate is 40%

` Suppose that the breakeven CDS rate iss per

dollar of notional principal

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Time(years)

DefaultProbability

Survival

Probability1 0.0200 0.9800

2 0.0196 0.9604

3 0.0192 0.94124 0.0188 0.9224

5 0.0184 0.9039

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Time

(yrs)

Survival

Prob

Expected

Paymt

Discount

Factor

PV ofEx

p Pmt1 0.9800 0.9800s 0.9512 0.9322s

2 0.9604 0.9604s 0.9048 0.8690s

3 0.9412 0.9412s 0.860 0.8101s

4 0.9224 0.9224s 0.818 0. 552s5 0.9039 0.9039s 0. 88 0. 040s

Total 4.0 04s

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Time(yrs)

DefaultProbab.

Rec.Rate

ExpectedPayoff

DiscountFactor

PV ofExp.Payoff

0.5 0.0200 0.4 0.0120 0.9753 0.0117

1.5 0.0196 0.4 0.0118 0.9277 0.0109

2.5 0.0192 0.4 0.0115 0.8825 0.0102

3.5 0.0188 0.4 0.0113 0.8395 0.0095

4.5 0.0184 0.4 0.0111 0.7985 0.0088

Total 0.0511

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Time DefaultProb

ExpectedAccr Pmt

DiscFactor

PV of Pmt

0.5 0.0200 0.0100s 0.9753 0.0097s

1.5 0.019 0.009 s 0.9277 0.0091s

2.5 0.0192 0.009 s 0. 25 0.00 5s

3.5 0.01 0.0094s 0. 395 0.0079s

4.5 0.01 4 0.0092s 0.79 5 0.0074s

Total 0.042 s

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` PV of expected payments is 4.0704s+0.0426s4.1130s

`

The breakevenC

DS spread is given by4.1130s = 0.0511 ors = 0.0124 (124 bps)` The value of a swap negotiated some time

ago with a CDS spread of 150bps would be4.11300.01500.0511 or 0.0106 times theprincipal.

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` Suppose that the mid market spread for a 5year newly issued CDS is 100bps per year

` We can reverse engineer our calculations toconclude that the default intensity is 1.61% peryear.

` If probabilities are implied from CDS spreads

and then used to value anotherC

DS the resultis not sensitive to the recovery rate providingthe same recovery rate is used throughout

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` CREDIT SPREAD:

The difference between the yield on theborrowers debt (loan or bond) and the yield on

the referenced benchmark such as U. S. Treasurydebt of the same maturity.

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` CREDIT SPREAD OPTION

A credit spread option grants the buyer the right,but not the obligation, to purchase a bond during a

specified futureexercise

period at thecontemporaneous market price and to receive an

amount equal to the price implied by a strikespread stated in the contract

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An investor may purchase from an insurer anoption to sell a bond at a particular spread aboveLIBOR credit spread.

If the spread is higher on the exercise date, thenthe option will be exercised. Otherwise it willlapse

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A credit-linked note (CLN) is essentially a funded CDS,which transfers credit risk from the

note issuer to the investor.

The issuer receives the issue price for each CLNfrom the investor and invests this in low-risk collateral.

If a credit event is declared, the issuer sells the

collateral and keeps the difference between the facevalue and market value of the reference entitys debt

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Refer to the Steel company case again.

Bank A would extend a $1 million loan to the SteelCompany.

At same time Bank A issues to institutional investorsan equal principal amount of a credit-linked note,whose value is tied to the value of the loan.

If a credit event occurs, Bank As repaymentobligation on the note will decrease by just enough to

offset its loss on the loan.

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Bank A Institutional investors

I n s t i t u t i

o n a l

i n v e s t o r

s

$1 Million

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` Binary CDS

` First-to-default Basket CDS

` Total return swap

` Credit default option` Collateralized debt obligation

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` The payoff in the event of default is a fixed cashamount

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` Example: European option to buy 5 yearprotection on Ford for 280 bps starting in one year.If Ford defaults during the one-year life of theoption, the option is knocked out

` Depends on the volatility ofCDS spreads

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` Similar to a regularCDS except that severalreference entities are specified

` In a first to default swap there is a payoff when the

first entity defaults` Second, third, and nth to default deals are defined

similarly

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` Security created from a portfolio of loans, bonds, creditcard receivables, mortgages, auto loans, aircraft leases,music royalties, etc

` Usually the income from the assets is tranched

` A waterfall defines how income is first used to pay thepromised return to the senior tranche, then to the nextmost senior tranche, and so on.

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Asset 1

Asset 2

Asset 3

Asset n

Principal=$100

million

SPV

Tranche 1

(equity)

Principal=$5 million

Yield= 30%

Tranche 2

(mezzanine)


Yield= 10%

Tranche 3

(super senior)


Yield= 6%

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Subprime Mortgage

Portfolio Equity Tranche (5%)

Not Rated

Mezzanine Tranche (20%)

BBB

Super Senior Tranche (75%)

AAA

Equity Tranche (5%)

Mezzanine

Tranche (15%) BBB

Super Senior Tranche (80%)AAA

The mezzanine tranche

is repackaged with

other similar mezzanine

tranches

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` Between 2000 and 2006 mortgage lenders in the U.S.relaxed standards (liar loans, NINJAs, ARMs)

` Interest rates were low

` Demand for mortgages increased fast

` Mortgages were securitized using ABSs and ABS CDOs

` In 2007 the bubble burst

` House prices started decreasing. Defaults andforeclosures, increased fast.

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` A cash CDO is an ABS where the underlying assetsare corporate debt issues

` A synthetic CDO involves forming a similar structurewith short CDS contracts on the companies

` In a synthetic CDO most junior tranche bears lossesfirst. After it has been wiped out, the second most

junior tranche bears losses, and so on

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CDS 1

CDS 2

CDS 3

CDS n

Average Yield

8.5%

Trust

Tranche 1: 5% ofprincipal

esponsible forlosses

between 0% and5%

Earns 1500 bps

Tranche 2: 10% ofprincipalesponsible forlosses

between 5% and 15%

Earns 200 bps



between 15% and 25%

Earns 40 bps



between 25% and75%

Earns 10bps

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` The bps of income is paid on the remainingtranche principal.

` Example: when losses have reached 7% of the

principal underlying theC

DSs, tranche 1 has beenwiped out, tranche 2 earns the promised spread(200 basis points) on 80% of its principal

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