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October 7/14, 2004
Danilo ZanettiDanilo ZanettiIHMIHM
IntroductionIntroduction to to Credit Credit DerivativesDerivatives
October 7/14, 20042
Single-name Credit Default Swaps (CDS), Preamble- Basic Terminology and Mechanics
Market OverviewCredit Risk FrameworkSingle-name Credit Default Swaps (CDS), Part 1
- Static Replication and Pricing- Unwind Valuation- Legal Issues
Measures of Spreads for BondsBond Pricing, Probability, Bond-Equivalent CDS SpreadSingle-name Credit Default Swaps (CDS), Part 2
- Default Swap Basis Single-name Credit Linked Notes (CLN)
ContentContent
October 7/14, 20043
CDS and CLN on Credit Indices- with emphasis on DJ iTraxx Europe Index Family
Credit Options- Credit-Spread Options/Warrants- Credit Default Swaptions
Correlation Products- First-to-Default (FtD) CDS- Tranched Credit-Index Products (Tranched DJ iTraxx)
OutlookReferences
ContentContent((cont'dcont'd))
October 7/14, 20044
SingleSingle--name name Credit Default Credit Default SwapsSwaps
(CDS)(CDS)
PreamblePreamble
Single-name CDS, Part 1Single-name CDS, Preamble
October 7/14, 20045
Basic Basic Terminology Terminology and and MechanicsMechanics
... Basics
October 7/14, 20046
SingleSingle--name name CDSCDSDescriptionDescription
The single-name CDS is the standard credit derivativeand the basic building block of the credit derivatives market
A CDS is a
- bilateral contract- enables an investor to buy protection against default of an asset issued by a specified reference entity- reference entity typically a corporate, bank or sovereign issuer - upon a legally defined credit event, the buyer of protection receives a compensation payment for the loss on the investment- common to define triggering of credit event using a reference asset/reference obligation such that capital structure seniority of covered debt
is specified exactly- the loss protection is acheived through payment of a periodic fee to the protection seller- the protection fee can also be paid upfront (although not usual)- typically specified using confirmation document and definitions of the International Swap and Derivatives Association (ISDA)
October 7/14, 20047
SingleSingle--name name CDSCDSMechanicsMechanics
Between trade initiation and default or maturity (whichever first), the protection buyer makes regular payments to the protection seller:
Protection buyer sells credit risk to protection sellerProtection seller buys credit risk from protection buyer
Terminology: CDS spread, CDS premium, default swap spread
Protection sellerProtection seller
Reference EntityReference Entity
Protection buyerProtection buyer
Credit risk
CDS spread
October 7/14, 20048
Protection buyerProtection buyer Protection sellerProtection seller100 - Recovery
Cash settlement : Price of defaultet asset determined via dealer poll typically within less than 30 days after credit event such that the recovery value of the reference obligation is stabilized
Physical settlement : Delivery of cheapest to deliver obligation out of a basket of deliverables assets ranked pari passu to reference obligation
Protection buyerProtection buyer Protection sellerProtection seller100
BondBondConvertibleConvertible
CTD BondCTD Bond
SingleSingle--name name CDSCDSMechanics Mechanics ((cont'dcont'd))
October 7/14, 20049
SingleSingle--name name CDSCDSCashflow Cashflow representationrepresentation
Non default case:
CDS
CDS
T
0
CDS
Recovery100 −
CDST
τ0
Default case:
October 7/14, 200410
Market Market OverviewOverview
Market Overview
October 7/14, 200411
Market Market OverviewOverviewExplosive growth of Credit Explosive growth of Credit DerivativesDerivatives
Credit Derivatives Volumes Trades (US$ billions)
October 7/14, 200412
Market Market OverviewOverviewFactors contributing increased activityFactors contributing increased activity
Standardized documentation
Current documentation framework are the 2003 ISDA credit derivatives definitions
Further details in section on Legal Issues
Liquidity provider to cash market during market stress
"September 11" had a 3-fold increase in trading volumes but still consistent two-ways flows (stable share of protection bought vs protection sold)
Positioning of credit derivatives desk being typically long protection (short risk) is favourable for increased request for protection (desks sell their protection inventory)
October 7/14, 200413
Market Market OverviewOverviewFactors contributing increased activity Factors contributing increased activity ((cont'dcont'd))
"Enron's decline" After disclosure of Enron's off balance sheet liabilities spreads widened and
credit derivatives activity increased After downgrade of Enron's debt to junk liquidity in the cash market decreased
and credit derivatives desks sold their inventory of protection and/or unwinded existing contracts
Confidentiality vs credit referenceCustomization of transaction terms according to needs of protection
buyer/seller (tenor, seniority, currency,...)
Provider of increased liquidity to individual names under stress
Confidential isolation/transfer of credit risk
October 7/14, 200414
Market Market OverviewOverviewFactors contributing increased activity Factors contributing increased activity ((cont'dcont'd))
Long term repo for corporate bonds nearly impossible, same for short-selling of bank loans
Long protection in credit derivatives corresponds to synthetical creation of an (unfunded) short position in cash instrument
No funding costs, low administration costsStructured notes have funding costs
Efficient vehicle for shorting credit
Off-balance sheet instruments with leverage advantage wrt to cash instruments
Regulatory capital relief/economic risk reduction/portfolio diversification
October 7/14, 200415
Market Market OverviewOverviewFactors contributing increased activityFactors contributing increased activity ((cont'dcont'd))
Transition from lending to intermediationTransition among banks from traditional lending role to intermediator in
issuance and sale of bonds over the last decadeShift from loans to bonds
Increased amount of corporate credit risk in the market
Increased credit spread volatility
Loans not widely traded in the secondary market, accounted on an accrual basis and possibility of quiet negotiation with banks syndicate in case of credit problems
Bonds widely traded in the secondary market, accounted on a mark-to-market basis and traded on basis of publicly available information
October 7/14, 200416
Market Market OverviewOverviewEvolution of Market Evolution of Market ParticipantsParticipants
Evolution of Credit Derivatives Market
Bank Portfolio Managers Asset Managers
Life Insurance/P&C Insurers/Reinsurers/Monoliners Hedge Funds
October 7/14, 200417
Market Market OverviewOverviewDiversity Diversity of Market of Market ParticipantsParticipants
October 7/14, 200418
Market Market OverviewOverviewFuture Future ParticipantsParticipants: : CorporatesCorporates
Sources and traditional hedges of corporate credit risk
- Common sources of credit risk for a company are trade receivables, vendor financings, long-term contracts, outright loans, joint ventures, partnerships,...
- Hedge of credit risk is traditionally achieved via credit insurance, lettersof credit
- Insurers often retain the right to revoke coverage in the event of a rating downgrade and the coverage period is typically no longer than one year
- Securitisation programs remove most of credit risk from balance sheet but can be quite costly and are public
October 7/14, 200419
Obstacles for corporate to embrace credit derivatives
- Credit spreads peak in 2001 and 2002 not paralleled by a peak in premium charges by credit insurers
- Timing mismatches between credit event unter CDS contract and a default by the corporate's counterparty (different triggering mechanism)
- Fair value accounting (marking-to-market) produces potential earnings volatility
- Corporates may have exposure to credits not actively traded in the CDS market
Market Market OverviewOverviewFuture Future ParticipantsParticipants: : Corporates Corporates ((cont'dcont'd))
October 7/14, 200420
Market Market OverviewOverviewFuture Future ParticipantsParticipants: : Corporates Corporates ((cont'dcont'd))
October 7/14, 200421
Market Market OverviewOverviewConduit Conduit of Informationof Information
Bond market
Convertible market
Loan market
CDS market
Equity market
Credit Derivatives
Desk
In sourcing and selling generic credit risk the credit derivatives desk serves as a link between many different markets:
Example: - A corporation issues a convertible bond (CB)- CB funds look for cheap call options on the underlying equity- CB funds buy the bond + buy protection via CDS stripping out credit risk- CDS spreads will widen due to increase demand for
protection
October 7/14, 200422
Market Market OverviewOverviewGlobal Global Positions by Sector Positions by Sector
Banks and broker dealers are overall net buyers of protection, biggest provider of liquidity and most important intermediaries
Insurance industry and, in particular, financial guarantors are net protection sellers
Smaller regional banks where net sellers of protection as an additional channelfor originating credit
October 7/14, 200423
Market Market OverviewOverviewMarket Share Market Share by Productby Product
Market share figures recently skewed towards credit-index products due to introduction of iTraxx credit-index and sub-indices (portfolio products)
October 7/14, 200424
Market Market OverviewOverviewReference Entities Reference Entities
October 7/14, 200425
Market Market OverviewOverviewTop Top Counterparties Counterparties and Credit and Credit EventsEvents
Counterparty risk is heavily concentrated among the top 10 global banks and broker dealers.
Credit events are concentrated within a limited universe of actively traded, fallen angel credits
The hedge fund industry is excluded from the survey
October 7/14, 200426
Market Market OverviewOverviewConcerns Concerns
Ultimate protection sellers may be less informed and knowledgeable about the credit than the originator (especially under physical settlement)
Informational asymmetries
Counterparty concentration
The market is concentrated among the top 10 global banks and broker dealers Withdrawal of such institutions from the market may produce negative effects
Moral hazard
Separation of loan underwriting/origination from credit ownership creates the potential for moral hazard
Source: Fitch 09/2003
October 7/14, 200427
Credit Risk FrameworkCredit Risk Framework
Credit Risk Framework
October 7/14, 200428
Credit Risk FrameworkCredit Risk FrameworkEmpirical Studies Empirical Studies of Recovery Ratesof Recovery Rates
Market standard source for recovery rates is Moody's historical default rate study (www.moodysqra.com)Recovery rates depend on subordination levelWide variation in recovery rate even for same subordination level
October 7/14, 200429
Credit Risk FrameworkCredit Risk FrameworkEmpirical Studies Empirical Studies of Default of Default ProbabilitiesProbabilities
Table shows average default probability of a bond starting with an initial rating and defaulting within the given time horizonHighly rated bonds have a lower cumulative default probability
October 7/14, 200430
Credit Risk FrameworkCredit Risk FrameworkCredit Credit CurvesCurves/Credit /Credit SpreadsSpreads
Credit Curve:
- Investors have different views about how the credit risk of a company can be measured
- It is customary to express credit risk in form of an excess yield over some benchmark interest rates as a function of the maturity of a credit exposure,
a so-called credit curve
Credit Spreads*:
- The excess yield is known as credit spread- There are various credit spread measures (CDS-Spread, Z-Spread, I-Spread, ASW-Spread, BE CDS-Spread)
* See sections Measures of Spreads for Bonds and Bond Pricing, Probability, BE CDS-Spread
October 7/14, 200431
Credit Risk FrameworkCredit Risk FrameworkCredit Credit CurvesCurves/Credit /Credit Spreads Spreads ((cont'dcont'd))
Maturity
Credit Spread
Upward sloping credit curve
Maturity
Credit Spread
Inverted credit curve
Maturity
Credit Spread
Humped credit curve
Upward sloping credit curve:- Common shape- Constant expected credit quality- Increased uncertainty with increasing maturity increases credit spread
Humped credit curve:- Observed for credits likely to worsen in the medium term with small change of defaulting in the short term- Survival over the medium term increases likelihood of survival in the long term thus lowering credit spreads
Inverted credit curve:- Significant deterioration of credit quality- High probability of a default
October 7/14, 200432
Credit Risk FrameworkCredit Risk FrameworkCredit Credit CurvesCurves/Credit /Credit Spreads Spreads ((cont'dcont'd))
Source: JPMorgan ORBIT
CDS-Spreads credit curve dynamics for ABB International Finance Ltd:
October 7/14, 200433
Source: JPMorgan ORBIT
CDS-Spreads credit curve dynamics for FIAT Spa:
Credit Risk FrameworkCredit Risk FrameworkCredit Credit CurvesCurves/Credit /Credit Spreads Spreads ((cont'dcont'd))
October 7/14, 200434
SingleSingle--name name Credit Default Credit Default SwapsSwaps
(CDS)(CDS)
Part 1Part 1
Single-name CDS, Part 1
October 7/14, 200435
Static Replication Static Replication and Pricingand Pricing
... Static Replication and Pricing
October 7/14, 200436
SingleSingle--name name CDSCDSFloatingFloating--rate rate note note (FRN)(FRN)
Description: - A FRN is a Bond that pays a coupon linked to a variable interest-rate index, usually Libor, Euribor,...- FRN have a very low interest-rate sensitivity, since in a rising interest-
rate environment, the rise in the Libor rates is compensated by a stronger discounting of the Libor payments. Similarly for a decreasing interest-
rate environment.Default-free FRN:
- Senior par floaters of AA rated issuers pay a coupon of Libor flat- We assume in the sequel Libor flat par FRN's to be default-free
default-free par FRN
T
0
100Libor
100
October 7/14, 200437
SingleSingle--name name CDSCDSFRN FRN cont'dcont'd
Defaultable FRN:- Subordinated par floaters of AA rated issuers pay a coupon higher
than Libor to compensate investors for the increased credit-risk- Par floaters of issuers rated lower than AA require also coupon payments higher than Libor for the increased credit-risk
defaultable par FRN
100
SpreadLibor +
T
0
100
Credit-risk: Coupons and face value are at risk
October 7/14, 200438
Idea: Set up a static hedge/replication, ie,
- find a portfolio of instruments that exactly offsets the cashflows of the CDS in every possible scenario- in particular, this must hold before and after default
Construction of a statically hedged portfolio for the protection buyer:
- buy protection for a notional of 100
SingleSingle--name name CDSCDSStatic hedgeStatic hedge//replicationreplication: Construction: Construction
Recovery100 −
Tτ
0
long CDS
CDS
T
0
October 7/14, 200439
- fund 100 cash at LIBOR flat (or equivalently short a default-free parFRN for initial cash of 100)
- invest the 100 cash into a defaultable par FRN
SingleSingle--name name CDSCDSStatic hedgeStatic hedge//replicationreplication: Construction (: Construction (cont'dcont'd))
long defaultable FRN
100
SpreadLibor +
T
0
100
Libor
short default-free FRN
T
0100
100
October 7/14, 200440
- hold the portfolio to maturity or default – depending on whichever comes first- if no default, unwind the hedge at maturity at no cost
SingleSingle--name name CDSCDSStatic hedgeStatic hedge//replicationreplication: Non : Non default scenariodefault scenario
Libor
short default-free FRN
T
0100
100
long defaultable FRN
100
SpreadLibor +
T
0
100
long CDS
CDS
T
0
+ + = 0
Reference EntityReference Entity
October 7/14, 200441
- if default, deliver the defaulted FRN to the protection seller in return for 100 and use the proceeds to repay the funding loan (or default-free par FRN). The net cost is also zero.
SingleSingle--name name CDSCDSStatic hedgeStatic hedge//replicationreplication: Default : Default scenarioscenario
= 0+ +Libor
short default-free FRN
T
0100
100 τ
long defaultable FRN
Recovery
SpreadLibor +
T
0
100τ
Reference EntityReference Entity
Recovery100 −
Tτ
0
long CDS
CDS
October 7/14, 200442
Pricing problem:
The static hedge portfolio has no initial costs and no close-out costs
Therefore pricing the default swap is equivalent to set the default swap spread equal to the par FRN spread:
SingleSingle--name name CDSCDSStatic hedgeStatic hedge//replicationreplication: Pricing: Pricing problem problem and Par CDS and Par CDS SpreadSpread
What default swap spread makes the net present value of the CDS equal to zero
?
Par CDS Par CDS SpreadSpread = Par FRN = Par FRN SpreadSpread
October 7/14, 200443
Construction of static hedge for protection seller:
- borrow a defaultable par FRN in the Repo market and short it for initial cash of 100- invest the 100 cash into a default-free par FRN- hold the portfolio to maturity or default – depending on whichever comes first- on default, sell the default-free par FRN, pay 100 to the protection
buyer in return for the defaulted FRN and cover the short FRN position
- at maturity, the 100 cash from the default-free par FRN are returned and used for the completion of the Repo contract
Difficult the borrow the reference asset on RepoStatic hedge usually not feasible
SingleSingle--name name CDSCDSStatic hedgeStatic hedge//replicationreplication forfor protection sellerprotection seller
October 7/14, 200444
Defaultable par FRN can be replaced by fixed-rate Bond of the same issuer provided it is of same seniority as the FRN (same recovery value upon default)
Repo specials: Costs for maintaining short FRN position until maturity of CDSincrease the level of the CDS spread when selling protection
Transaction costs increase bid-ask spreads for CDS
Accrued interest: buyer of protection must usually pay at default the CDS spread accrued since the last coupon date
Delivery option for protection buyer is usually not modelled: After default not all pari passu assets have the same recovery value and the protection buyer can choose to deliver the cheapest asset
Usual to assume constant recovery value of the reference asset
Customary to assume that counterparties are default-free
SingleSingle--name name CDSCDSMiscellaneous aspects Miscellaneous aspects
October 7/14, 200445
CDS is a par product: The default payment corresponds to difference between defaulted bond and face-value of the bond
Premium bond: Hedging credit risk of a premium bond with a CDS of same face-value underhedges the credit risk
Discount bond: Hedging credit risk of a discount bond with a CDS of same face-value overhedges the credit risk
SingleSingle--name name CDSCDSMiscellaneous aspects Miscellaneous aspects ((cont'dcont'd))
October 7/14, 200446
Unwind Unwind valuation valuation MarkingMarking--toto--MarketMarket
... Unwind Valuation
October 7/14, 200447
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: Motivation : Motivation
The trigger of a default swap to pay out is defined in terms of a credit event
On a mark-to-market basis the value of a default swap is changing in line with changes in the credit quality of the reference entity
Changes in the credit quality of the reference entity are reflected in changes in the market quotes of par CDS spreads
We will show that a default swap is sensitive to CDS spreads changes and thus is very much a credit spread product
October 7/14, 200448
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: Simple: Simple Example Example
The market par CDS spread for a reference entity is currently 100bpConsider entering the following 1-period short protection CDS position:
Short CDS
0
TCDS
100-Recovery
CDS spread payment
0
100 bp
60
Actual PV
100-Recovery
non default
default
( Interest rates flat @ 2.00%, Recovery @ 40% )
October 7/14, 200449
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: Simple : Simple Example Example ((cont'dcont'd) )
Payoff structure at maturity:- If there is no default, after 1-period a premium of 100bp will be realized- If there is a credit event a loss of 40=100-Recovery will be incurred
Credit deterioration:- Assume there is a simultaneous downgrade of the reference entity- Due to the credit deterioration of the reference entity the par CDS spread quoted on the market jumps from 100bp to 300bp
What is the current value of the short CDS position after credit deterioration assuming that expected recovery and interest rates remain unchanged
?
October 7/14, 200450
Assume to enter an offsetting long CDS position @ 300 bp to the existing short CDS position @ 100 bp - with maturity and reference entity being exactly the same
If a credit event occurs, the settlement received from the long CDS and short CDS position will exactly offset each other
Only the CDS spreads of the long CDS and short CDS differ
The unwind value (mark-to-market value) of the short CDS position can be computed as follows:
In numbers:
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: : Discounted Spreads Discounted Spreads ModelModel
( ) ( )444444 3444444 21
4434421
factordiscountrisky
newnewold
valueMtMspreadCDSrateInterest
spreadCDSspreadCDSvalueUnwind++
×−=1
1
( ) ( ) { 90.1100300%00.21
1300100 −=×++
×−=nominalvalueMtM
bpbpbpvalueUnwind
4434421
October 7/14, 200451
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: : JPMorgan JPMorgan Model (Model ( industry standardindustry standard))
The expected cash inflow for to the protection seller is
The expected cash outflow is
The default probability can be stripped out of the offsetting par CDS position quoted @ 300bp, since by definition of the par CDS spread the following musthold:
( )rateInterest
probDefaultRecoveryPV outcash +××−=
11100
( )RecoveryspreadCDSspreadCDSprobDefault
new
new
−+=
100
( ) incashPVrateInterest
probDefaultRecovery =+
××−1
1100
[ ] newoutcash spreadCDSrateInterest
probDefaultPV ×+
×−×=1
11100
=[ ] old
factor discountprob survival
incash spreadCDSrateInterest
probDefaultPV ×+
×−×=44 344 21
444 3444 21 111100
October 7/14, 200452
CDS spread payment
?
100 bp
60
Unwind value
100-Recovery
( Interest rates flat @ 2.00%, Recovery @ 40% )
( ) %76.4%40%100300
300=
−+=
bpbpprobDefault
( ) %24.951 =−= probDefaultprobSurvival
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: : JPMorgan JPMorgan Model (Model (cont'dcont'd))
The probabilities stripped out of the offsetting par CDS can be used to find out the unwind value of the original CDS position:
October 7/14, 200453
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: : JPMorgan JPMorgan Model (Model (cont'dcont'd))
The unwind value (mark-to-market value) of the short CDS position can be computed as follows:
93.0100%00.21
1%24.95100 =×+
××= bp PV incash
( ) 8.2%00.21
1%76.440100 =+
××−=outcashPV
- 87.18.293.0 −=−=4434421
valueMtM
valueUnwind
October 7/14, 200454
SingleSingle--name name CDSCDSUnwind Unwind valuationvaluation: : ExerciseExercise
Credit improvement:
- Assume there is a simultaneous upgrade of the reference entity
- Due to the credit improvement of the reference entity the par CDSspread quoted on the market tightens from 100bp to 50bp
Show that the unwind value with the cash differential method corresponds to:
Show that for the JPMorgan model the following holds:
49.0=4434421
valueMtM
valueUnwind
%83.0=probDefault
48.049.097.0 =−=4434421
valueMtM
valueUnwind
October 7/14, 200455
SingleSingle--name name CDSCDSUnwind Unwind valuation valuation in in BLOOMBERG'sBLOOMBERG's CDSW: CDSW: Discounted Spreads Discounted Spreads ModelModel
Input in the section Deal Information
- notional amount
- maturity
- deal spread of the CDS
- ...
Input into the Spreads section
- Recovery Rate
- Par CDS spreads (the current spread as a flat spread curve)
Select the model 'Disctd Spreads' in the Calculator section
In the Calculator section the Market Value (to the negative) corresponds to the unwind value of the short CDS position
October 7/14, 200456
SingleSingle--name name CDSCDSUnwind Unwind valuation valuation in in BLOOMBERG'sBLOOMBERG's CDSW: CDSW: Discounted Spreads Discounted Spreads Model Model ((cont'dcont'd))
newspreadCDS
Recovery
probDefault
notional of%90.1−
oldspreadCDS
CDSW for our example CDS:
October 7/14, 200457
SingleSingle--name name CDSCDSUnwind Unwind valuation valuation in in BLOOMBERG'sBLOOMBERG's CDSW: CDSW: JPMorgan JPMorgan ModelModel
Select the model 'JPMorgan' in the Calculator section – all the rest is analogous to the 'Disctd Spreads' model
newspreadCDS
Recovery
probDefault
notional of%90.1−
oldspreadCDS
October 7/14, 200458
SingleSingle--name name CDSCDSCDSW Default CDSW Default SettingsSettings......
October 7/14, 200459
SingleSingle--name name CDSCDSUnwind alternatives/Unwind alternatives/SummarySummary
The owner of a default swap position can monetize a change in the CDS spread by:
- terminating the transaction
- reassigning the default swap to another counterparty (novation)
- enter into an offsetting position with another counterparty
In all cases the unwind value or mark-to-market has to be negotiated between the counterparties
The industry standard for negotiation is the JPMorgan Model – and it is sufficient for the counterparties to agree upon
- the par CDS spread curve
- the recovery rate
(Notice that the unwind value is quite robust to various recovery assumptions)
October 7/14, 200460
Legal Legal Issues Issues
... Legal Issues
October 7/14, 200461
SingleSingle--name name CDSCDSStandardization Standardization of CDSof CDS ConfirmationConfirmation
Current documentation framework are the 2003 ISDA credit derivatives definitions
History to date...
- 1998 standard form of confirmation
- 1999 credit derivatives definitions
- Supplements (restructuring, successor* and credit events, convertibles)
- 2003 ISDA credit derivatives definitions
Standardized documentation led to dramatic growth of credit derivatives market
Investment Grade and High Yield North American confirmation based on the2003 ISDA credit derivatives definitions
Standard 2003 contracts began trading June 20, 2003
Contracts proved effective by Enron, Worldcom, ... defaults
Worldcom: close to 600 contracts outstanding, estimated over 7 billion in notional, no disputes or litigation and no mechanical settlement problems*For instance in case of a Reference Entity merger
October 7/14, 200462
SingleSingle--name name CDSCDSStandard Non Standard Non Emerging Emerging Market Corporate CDSMarket Corporate CDS
October 7/14, 200463
SingleSingle--name name CDSCDSTriggering Mechanism Triggering Mechanism of CDSof CDS
Watch : A predefined group of Obligations of the Reference Entity
Check: Has a Credit Event occured ?
Deliver: A predefined group of Deliverable Obligations in return for par
ObligationsObligations Credit Credit EventsEventsDeliverable Deliverable ObligationsObligations
Watch Check Deliver/Settle
October 7/14, 200464
SingleSingle--name name CDSCDSWatch ObligationsWatch Obligations
ObligationsObligations
Watch
Credit Credit EventsEventsDeliverable Deliverable ObligationsObligations
Check Deliver/Settle
Derivative Contracts General Creditors
Bonds Loans
"Payment"
"Borrowed Money"
Borrowed Money: bond, note, loan, commercial paper,money market accounts, savings accounts and reimbursements from letters of credit
October 7/14, 200465
ObligationsObligations
Watch
Credit Credit EventsEventsDeliverable Deliverable ObligationsObligations
Check
SingleSingle--name name CDSCDSCheck Credit Check Credit EventsEvents
Standard Credit Events unter ISDA
- Failure to Pay
- Bankruptcy
- Restructuring (soft credit event)
Emerging market and sovereign Reference Entities generally include Repudiation/Moratorium
High Yield CDS trade without Restructuring as a Credit Event
Bankruptcy deemed to have occurred only if the default occurs with respect to the Reference Entity, all other Credit Events are deemed to have occurred if default occurs on any obligation
Deliver/Settle
October 7/14, 200466
ObligationsObligations
Watch
Credit Credit EventsEventsDeliverable Deliverable ObligationsObligations
Check
SingleSingle--name name CDSCDSDeliverDeliver//Settle Deliverable ObligationsSettle Deliverable Obligations
Deliverable Obligations means any Bond, Loan, Convertible, Exchangeable,... satisfying the Deliverable Obligation Characteristics, ie, ranked senior or better in the capital structure (eg, senior unsecured)
Deliver/Settle
Protection buyerProtection buyer Protection sellerProtection seller100
ConvertibleConvertibleLoanLoan
BondBondCTD BondCTD Bond
October 7/14, 200467
SingleSingle--name name CDSCDSPhysical Settlement TimelinePhysical Settlement Timeline
October 7/14, 200468
SingleSingle--name name CDSCDSFirst First two two "major "major defaultsdefaults" in " in the the European CDS Market European CDS Market
On 30 September, 2001, Railtrack plc, the owner of UK railway infrastructure, was placed under administration
On 4 October, 2001, SAirGroup applied for a moratorium of debt enforcement
The credit events of Railtrack plc and SAirGroup clearly constitued a Bankruptcycredit event, given that both companies were either insolvent or in severe financial difficulty
A significant number of CDS have been "triggered"
The credit derivative market has worked well...
October 7/14, 200469
Measures Measures of of Spreads for Spreads for BondsBonds
Measures of Spreads for Bonds
October 7/14, 200470
Investors have different views about how the credit risk of a company can be measuredIt is customary to express credit risk in form of an excess yield over some benchmark interest rates, a so-called credit spread
Several ways for looking at credit spreads implied by bond prices:
- Z-Spread- I-Spread- Par ASW-Spread
Z-Spread, I-Spread and par ASW-Spread are all available on BLOOMBERG
Goal:
- introduce credit spreads concepts by examples- explain their relationship by examples
Measures Measures of of Spreads for Spreads for BondsBondsMotivation/Motivation/GoalGoal
October 7/14, 200471
Measures Measures of of Spreads for Spreads for BondsBondsYieldYield--toto--Maturity Maturity (YTM)(YTM)
Premium Bond:
Discount Bond:
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-105 10 11010
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-92.13 5 1055
%06.8)1(
105)1(
5)1(
513.92 32 =⇒+
++
++
= YTMYTMYTMYTM
%06.8)1(
110)1(
10)1(
10105 32 =⇒+
++
++
= YTMYTMYTMYTM
October 7/14, 200472
Measures Measures of of Spreads for Spreads for BondsBondsZZ--Spread Spread
Premium Bond:
Discount Bond:
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-105 10 11010
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-92.13 5 1055
%17.6)%00.21(
110)%00.11(
10)%50.01(
10105 32 =⇒++
+++
+++
= ZZZZ
%12.6)%00.21(
105)%00.11(
5)%50.01(
513.92 32 =⇒++
+++
+++
= ZZZZ
October 7/14, 200473
Measures Measures of of Spreads for Spreads for BondsBondsII--Spread Spread
Premium Bond:
Discount Bond:
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-105 10 11010
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-92.13 5 1055
%06.6%00.2%06.83 =−=−= YearSwap RateYTMSpreadI
%06.6%00.2%06.83 =−=−= YearSwap RateYTMSpreadI
October 7/14, 200474
Measures Measures of of Spreads for Spreads for BondsBondsAsset Asset SwapSwap: Definition : Definition
Definition:
Package consisting of fixed cashflows of a bond, and an agreement to swap these fixed cashflows for a series of floating payments. These payments "float" with an index rate, normally LIBOR.
Construction: - buy the bond to be asset swapped- pay a swap, arranged so that the fixed leg of the swap exactly offsets the coupon payments of the bond- adjust the floating leg of the swap so that the net present value of the package is par
Main purpose: - enable a credit investor to take exposure to credit quality of a fixed-rate bond - without taking interest rate risk
October 7/14, 200475
=
Bond
Swap
+
Asset Swap
= FRN with Price of Par
Measures Measures of of Spreads for Spreads for BondsBondsAsset Asset SwapSwap: : Package Package
October 7/14, 200476
Measures Measures of of Spreads for Spreads for BondsBondsAsset Asset SwapSwap: Par Asset : Par Asset Swap Spread Swap Spread (Par ASW)(Par ASW)
Par ASW)()( receivedPVpaidPV =
)(100)( BondValueFairpaidPV +=
)()(
AnnuityPVpriceDirtyBondValueFairASWPar −
=
)(),()(100
AnnuityPVASWParParLiborPVpriceDirtyreceivedPV ×++=44 344 21
Swap +
-
October 7/14, 200477
Measures Measures of of Spreads for Spreads for BondsBondsAsset Asset SwapSwap: : ObservationsObservations
Interpretation: par ASW spread is an annuity that compensates the bond holder for the difference between the riskless price of the bond and its market price
Credit risk: the buyer of the asset swap still owns the bond with the associated credit risk
Interest rate risk: the buyer does not retain the bond's coupons (hence does not take the associated interest rate risk )
Counterparty default risk: when the bond is trading at a discount, the assets swap buyer has immediate credit risk vs the seller equal to par minus the bond price. For premium bonds the opposite holds.
Default contingent exposure to mark-to-market value of swap: the bond is credit-linked, but the swap is usually not and does not terminate upon default, but can be at its market value.
Clean asset swap: an asset swap package with a credit-linked swap. The par ASW spread will be different than for a normal asset swap package.
October 7/14, 200478
Measures Measures of of Spreads for Spreads for BondsBondsAsset Asset SwapSwap: Par ASW : Par ASW Example Example
Premium Bond:
Discount Bond:
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-105 10 11010
Bond CashFlows
Swap ratesYear 0 Year 1 Year 2 Year 3
0.50% 1.00% 2.00%
-92.13 5 1055
( ) ( ) ( ) ( )( ) ( ) ( ) ( )
%31.692.2
10541.123
%00.211
%00.111
%50.01192.2
%00.21110
%00.1110
%50.011041.123
32
32
=−
=⇒
++
++
+==
++
++
+==
ASWParAnnuityPV
BondValueFair
( ) ( ) ( ) ( )( ) ( ) ( ) ( )
%72.592.2
13.9282.108
%00.211
%00.111
%50.01192.2
%00.21105
%00.115
%50.01582.108
32
32
=−
=⇒
++
++
+==
++
++
+==
ASWParAnnuityPV
BondValueFair
October 7/14, 200479
Measures Measures of of Spreads for Spreads for BondsBondsAsset Asset SwapSwap: : ExerciseExercise
What is the default contingent risk assumed by the asset swap buyer
- if the bond defaults immediately
- in case of the premium and in case of the discount bond
- assuming a bond recovery price of 40% ?
What is the immediate counterparty credit risk
- before and after bond default ?
Premium bond default (buyer's view):
Value at inception
Value after default
Loss
+105
+ 40
- 65
- 5
- 5
0
+100
+35
- 65
Bond Swap Total
does not terminate upon
default
immediate counterparty credit risk of asset swap
seller
October 7/14, 200480
Discount bond default (buyer's view):
Value at inception
Value after default
Loss
+ 95
+ 40
- 55
+ 5
+ 5
0
+100
+45
- 55
Bond Swap Total
does not terminate upon
default
Measures Measures of of Spreads for Spreads for BondsBondsAsset Asset SwapSwap: : Exercise Exercise ((cont'dcont'd))
immediate counterparty credit risk of asset swap
buyer
October 7/14, 200481
Measures Measures of of Spreads for Spreads for BondsBondsSummary Summary of of examplesexamples
Premium Bond
Discount Bond Description
YTM 8.06% 8.06%
Z-Spread 6.17% 6.12% Best measure of comparable bond value as adjusts for shape of Swap curve
I-Spread 6.06% 6.06% Not as good as Z-Spread (ignores shape of Swap curve)
Good approximation for high grade bonds
Par ASW 6.31% 5.72% A tradable value
Not a good value measure for bonds far from par
October 7/14, 200482
Measures Measures of of Spreads for Spreads for BondsBondsGeneral General relationships relationships
Z-Spread vs I-Spread:
- For upward-sloping yieldcurve the Z-Spread is higher than the I-Spread
- For a flat yieldcurve Z-Spread and I-Spread are equal
The relations hold for par, premium and discount bonds.
SpreadZSpreadI <
SpreadZSpreadI =
October 7/14, 200483
Measures Measures of of Spreads for Spreads for BondsBondsGeneral General relationships relationships ((cont'dcont'd) )
Z-Spread, I-Spread vs par ASW for premium bond:
- For upward-sloping yieldcurve Z-Spread and I-Spread will be lowerthan the ASW spread
- For a flat yieldcurve similarly
ASWParSpreadZSpreadI <<
ASWParSpreadZSpreadI <=
Z-Spread, I-Spread vs par ASW for discount bond:
- For upward-sloping yieldcurve Z-Spread and I-Spread will be higher than the ASW spread
- For a flat yieldcurve similarly
ASWParSpreadISpreadZ >>
ASWParSpreadISpreadZ >=
October 7/14, 200484
Measures Measures of of Spreads for Spreads for BondsBondsGeneral General relationships relationships ((cont'dcont'd) )
Why is the par ASW spread higher than the Z-Spread for a premium bond ?
- For a premium bond and a flat yield curve the Coupon is by definition higher than Libor + Z-Spread- In an asset swap package with a swap paying the Coupon and receiving Libor + Z-Spread, the swap value will be negative after a default- To compensate for the additional risk of having a swap not terminating on default, the swap must pay a higher spread than the Z-Spread- ... and therefore
ASWParSpreadZSpreadI <=
- In a so-called clean asset swap package the swap terminated upon default and therefore the clean par ASW spread would correspond to
the Z-Spread
October 7/14, 200485
Bond Bond PricingPricing, , ProbabilityProbability, , BondBond--Equivalent Equivalent CDSCDS--SpreadSpread
(BE CDS(BE CDS--SpreadSpread))
Bond Pricing, Probability, BE CDS-Spread
October 7/14, 200486
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadFrameworkFramework
100
106
40
Actual Price
Cash at maturity
Expected Recovery if default
Survival probability
Default probability
( Interest rates flat @ 2.00% )
October 7/14, 200487
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadBootstrapping ProbabilitiesBootstrapping Probabilities
( )eryRecovprobDefaultCashprobSurvivalfactorDiscountpriceMarket ×+××=
Bond pricing equation:
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛×−+××
+=
=
401106%00.21
1100444 3444 21
probDefault
probSurvivalprobSurvival
Bootstrapping probabilities:
%94.93=probSurvival
%06.6=probDefault
October 7/14, 200488
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadFilling Filling in in ProbabilitiesProbabilities
100
106
40
Actual Price
Cash at maturity
Expected Recovery if default
93.94%
6.06%
( Interest rates flat @ 2.00% )
October 7/14, 200489
100
106
40
93.94%
6.06%
?
101
40
93.94%
6.06%
Bond A Bond B
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadComputing the Computing the Fair Value of Fair Value of another bondanother bond
Bond pricing equation:
( )40%06.6101%94.93%00.21
140.95 ×+××+
=
Idea: Compute the Fair Value of another bond with different coupon, but of same seniority, based on the probabilities determined for the first bond
95.40
October 7/14, 200490
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadInvestment Investment strategies strategies Contingent PayoffsContingent Payoffs
Invest 1000 CHF into Bond A or Bond B:
Bond A Bond B
Price 100% 95.40%
# purchased 10 10.482
Cash at maturity 106 CHF 101 CHF
Expected Recovery 40% 40%
Payoff if no default 1060 CHF 1058.68 CHF
Payoff if default 400 CHF 419.28 CHF CHF
Compute contingent payoffs:
October 7/14, 200491
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadInvestment Investment strategies strategies Expected valuesExpected values
Weighted payoff if no default 1060 CHF x 93.94% 1058.68 CHF x 93.94%
Weighted payoff if default 400 CHF x 6.06% 419.28 CHF x 6.06%
Compute expected values:
Expected value 1020 CHF 1020 CHF
+ +
= =
Bond A Bond B
October 7/14, 200492
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadYTM, ZYTM, Z--SpreadSpread, Par ASW, Par ASW
First compute spread measures for Bonds A and B:
Bond A Bond B Formula
YTM 600 bp 587 bp ( )YTMmaturity at CashPrice
+=
1
Z-Spread/I-Spread 400 bp 387 bp ( )ZLibormaturity at CashPrice
++=
1
Par ASW 400 bp 370 bp ( )
( )Libor1
PriceLibor1maturity at Cash
ASWarP
+
−+= 1
( Libor @ 2.00% )
October 7/14, 200493
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadBE CDSBE CDS--SpreadSpread
Bonds A and B have equal issuer and same seniorityBonds A and B are w.r.t credit risk of equal value (same expected recovery,
same default probability)Goal: Introduce a metric telling that A and B are of equal value w.r.t credit risk
Idea: - Sell protection against default of Bonds A and B via a Credit Default Swap contract- Use the default probability/survival probability derived from the Bonds prices to value the Credit Default Swap contract- Determine the CDS Spread such that the Credit Default Swap
contracts has a value of zero Bond Equivalent (BE) CDS Spread
Interpretation of BE CDS Spread: Answers the question
If Bond A or Bond B were a CDS contract, what would the CDS spread be ?
October 7/14, 200494
BE CDS)()( receivedPVpaidPV =
Credit Default Swap
0 T
CDS
100-Recovery
+
-
( ) CDSprobSurvivalfactorDiscountreceivedPV ××=
( ) ( ) ( )RecoveryprobSurvivalfactorDiscountpaidPV −×−×= 1001
( ) ( )probSurvival
RecoveryprobSurvivalCDSBE −×−=
1001
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadBE CDSBE CDS--Spread Spread ((cont'dcont'd))
BE CDS for the 1-period situation:
October 7/14, 200495
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadBE CDSBE CDS--Spread Spread ((cont'dcont'd))
Bond A Bond B Formula
YTM 600 bp 587 bp ( )YTMmaturity at CashPrice
+=
1
Z-Spread/I-Spread 400 bp 387 bp ( )ZLibormaturity at CashPrice
++=
1
Par ASW 400 bp 370 bp ( )
( )Libor1
PriceLibor1maturity at Cash
ASWarP
+
−+= 1
( Libor @ 2.00% )
BE CDS 387 bp 387 bp( ) ( )
probSurvivalRecoveryprobSurvivalCDSBE −×−
=1001
BE CDS is robust to the price of the bond (same for premium, par or discount bond) and also to the shape of the interest-rate curve
October 7/14, 200496
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadGeneral General relationshipsrelationships
Z-Spread, I-Spread vs par ASW and BE CDS for premium bond:
ASWParSpreadZSpreadICDSBE <≤<
ASWParSpreadISpreadZCDSBE >≥>
Z-Spread, I-Spread, par ASW and BE CDS for discount bond:
The best overall proxy for the BE CDS spread is the Z-Spread !
October 7/14, 200497
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadExerciseExercise
Compute all the credit spread measures for the following deep discount bond:
October 7/14, 200498
Bond Bond PricingPricing, , ProbabilityProbability, BE CDS, BE CDS--SpreadSpreadExerciseExercise ((cont'dcont'd))
Deep Discount bond Formula
( Libor @ 2.00%, Survival prob = 78.50% )
YTM 17.78 % ( )YTMmaturity at CashPrice
+=
1
Z-Spread/I-Spread 15.78 % ( )ZLibormaturity at CashPrice
++=
1
Par ASW 14.20 % ( )
( )Libor1
PriceLibor1maturity at Cash
ASWarP
+
−+= 1
BE CDS 16.43 % ( ) ( )probSurvival
RecoveryprobSurvivalCDSBE −×−=
1001
October 7/14, 200499
SingleSingle--name name Credit Default Credit Default SwapsSwaps
(CDS)(CDS)
Part 2Part 2
Single-name CDS, Part 2
October 7/14, 2004100
SingleSingle--name name CDSCDSThe The Default Default SwapSwap Basis: Definition / Basis: Definition / CalculationCalculation
Definition: The basis in credit markets is the difference between the pricing of an individual (or a group of) bonds in the cash market and the pricing of the same issuer (or same group of issuers) using the CDS market
Terminology: Commonly referred to as default swap basis
Calculation (sophisticated):
Calculations (practical):
SpreadCDSBESpreadCDSBasisSwapDefault −=
SpreadASWSpreadCDSBasisSwapDefault −=
SpreadZSpreadCDSBasisSwapDefault −=
October 7/14, 2004101
Source: JPMorgan Credit Navigator
SingleSingle--name name CDSCDSThe The Default Default SwapSwap Basis: Basis: ExampleExample
Default Swap Basis for ABB International Finance Ltd:
October 7/14, 2004102
SingleSingle--name name CDSCDSThe The Default Default SwapSwap Basis: Basis: Example Example ((cont'dcont'd))
ABB Intl Finance 11.5£ May 2009 has currently negative basis (coupon stepsdown if ABB investment grade)
- Par 5Y CDS is currently trading at mid 140 bp- Z-Spread is 250 bp, Par ASW-Spread is 271 bp- Z-Basis is –110 bp, ASW-Basis is –131 bp
SpreadZ
SpreadASWPar
October 7/14, 2004103
SingleSingle--name name CDSCDSDrivers behind Drivers behind Default Default Swap Swap BasisBasis
Fundamental factors:
Technical factors:
(CDOs issuance)
October 7/14, 2004104
SingleSingle--name name CDSCDSTrade Trade strategiesstrategies
Positive basis:
- CDS is cheaper than Bond- Short Bond and sell protection (buy credit risk) via CDS- Position is credit-risk neutral- Investigate why cash and derivatives market price same risk differently
Negative basis:
- Bond is cheaper than CDS- Buy Bond and buy protection (sell credit risk) via CDS- Position is credit-risk neutral- Investigate why cash and derivatives market price same risk differently
October 7/14, 2004105
SingleSingle--name name CreditCredit--Linked Linked NotesNotes(CLN)(CLN)
Single-name CLN
October 7/14, 2004106
SingleSingle--name name CLNCLNDescriptionDescription
Motivation: - Investor wishes to take exposure to the credit derivatives market but requires a cash instrument (plan restrictions, regulatory constraints)- Investor does not have an ISDA master agreement in place- Investor wants to capture the relative value offered by the credit
derivatives market (eg, positive basis)
A funded Credit Linked Note (CLN) is - a security - paying a fixed or floating-rate coupon - having an embedded credit derivative (coupons and principal repayment are dependent upon the financial well being of a reference entity)- sometimes having principal protection
Two forms are common- CLN issued by corporate entity (bank or otherwise), unrated, unlisted- CLN issued by Special Purpose Vehicles (SPV), rated/unrated, listed
October 7/14, 2004107
SingleSingle--name name CLNCLNCLN CLN issued by corporate entityissued by corporate entity: : MechanicsMechanics
Investor pays par to buy the noteIssuer invests the proceeds receiving Libor+CDS spread+funding spreadIssuer pays Libor+CDS spread+funding spread less administrative fees and correction for possibility of early termination in case of a credit event
InvestorInvestor
Reference EntityReference Entity
IssuerIssuer
Credit risk
Credit Credit Derivatives DeskDerivatives Desk
ParPar
Credit Linked Coupons
Credit Linked Coupons
October 7/14, 2004108
Cash settlement : Price of defaultet asset determined via dealer poll
Physical settlement : Delivery of cheapest to deliver obligation out of a basket of deliverables assets ranked pari passu to reference obligation
SingleSingle--name name CLNCLNCLNCLN issued by corporate entityissued by corporate entity:: MechanicsMechanics ((cont'dcont'd))
InvestorInvestorIssuerIssuerCredit Credit
Derivatives DeskDerivatives Desk100-Recovery
Credit Linked Coupons
Credit Linked Coupons
100-Recovery
BondBondConvertibleConvertible
CTD BondCTD Bond
InvestorInvestorIssuerIssuerCredit Credit
Derivatives DeskDerivatives Desk
Credit Linked Coupons
Credit Linked Coupons
BondBondConvertibleConvertible
CTD BondCTD Bond
October 7/14, 2004109
SingleSingle--name name CLNCLNCLN CLN issued by issued by SPV: SPV: MechanicsMechanics
Investor pays par to buy the noteIssuer invests the proceeds into AAA collateral and enters into a swap transaction receving Libor+CDS spread in exchange for the fixed couponsIssuer pays Libor+CDS spread less administrative fees and correction for possibility of early termination in case of a credit event
InvestorInvestor
Reference EntityReference Entity
Credit risk
Credit Credit Derivatives DeskDerivatives Desk
ParFixed Rate
LIBOR + CDS spread LIBOR+CDS spread
Fixed Fixed Rate AssetRate Asset((CollateralCollateral))
Fixed Rate Par
IssuerIssuer
Securitization of credit-linked asset swap
October 7/14, 2004110
Cash settlement : Liquidation of collateral, price of defaultet asset determined via dealer poll
SingleSingle--name name CLNCLNCLNCLN issued byissued by SPV: SPV: MechanicsMechanics ((cont'dcont'd))
InvestorInvestorIssuerIssuerCredit Credit
Derivatives DeskDerivatives Desk100-Recovery
LIBOR+CDS spread LIBOR + CDS spread
Recovery
Fixed Fixed Rate AssetRate Asset((CollateralCollateral))
Fixed Rate 100
(Market value of Collateral assumed to be 100)
Physical settlement : see above...
October 7/14, 2004111
CDS and CLN on CreditCDS and CLN on Credit--IndicesIndices((withwith emphasisemphasis on DJ on DJ iTraxxiTraxx Europe Index Europe Index FamilyFamily))
CDS and CLN on Credit-Indices (DJ iTraxx Europe)
October 7/14, 2004112
June 21, 2004: iBoxx Ltd and TRAC-X LCC are merging their European tradable CDS indices thereby creating Dow Jones iTraxx Europe (DJ iTraxx Europe)
The DJ iTraxx platform will offer one benchmark for all credit investorsPredecessors: JECI1, JECI2, DJ TRAC-X Europe 1, DJ TRAC-X Europe 2,...
Infos under www.iboxx.com. Most material is drawn from there...
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesBrief Brief historyhistory
October 7/14, 2004113
Liquidity and Standardisation:- 20 market makers brought together into DJ iTraxx Europe platform
- Portfolio composition rules bring together most liquid reference entities- Standardised documentation for all DJ iTraxx notes (CLN) and swaps (CDS)
Transparency:- One benchmark credit index- Portfolio inclusion rules
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesOverviewOverview
October 7/14, 2004114
Diversification:- Cost efficient and timely access to the credit markets via CDS and
CLN on DJ iTraxx Europe
Independency, Track History:- International Index Company (IIC) as independent index supplier and administrator- IIC manages the indices and carries out the rebalancing process on behalf of Dow Jones Indices - IIC includes the former management team from iBoxx Ltd
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesOverview Overview ((cont'dcont'd))
October 7/14, 2004115
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Index Europe Index FamilyFamily
October 7/14, 2004116
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Product DescriptionsProduct Descriptions
October 7/14, 2004117
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Product Descriptions Product Descriptions ((cont'dcont'd))
October 7/14, 2004118
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Product Descriptions Product Descriptions ((cont'dcont'd))
October 7/14, 2004119
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Product Descriptions Product Descriptions ((cont'dcont'd))
October 7/14, 2004120
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Inclusion RulesInclusion Rules
October 7/14, 2004121
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Inclusion Rules Inclusion Rules ((cont'dcont'd))
October 7/14, 2004122
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Inclusion Rules Inclusion Rules ((cont'dcont'd))
October 7/14, 2004123
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Reference Reference Portfolio Portfolio ExampleExample
October 7/14, 2004124
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Mechanics Mechanics and Credit and Credit EventsEvents: : Unfunded Unfunded CDS FormCDS Form
Consider buying protection of €10 MM on the DJ iTraxx Europe main index in unfunded CDS form with maturity 09/2009
The running CDS premium is 45bp p.a.The current market quote is a par CDS premium of 42.50bp/43bp (JPMorgan
quote under BLOOMBERGs JITX:
The CDS is executed at 45bp p.a.The present value difference between 45bp and the bid of 42.5bp inclusive the
accrued interest is paid by the protection seller to the protection buyer
October 7/14, 2004125
The upfront payment of €17,861 is settled on T+3 days and calculated via BLOOMBERGs CDSW*:
*The current market standard is to model the CDS Index as a single-name CDS contract with a hypothetical reference entity. For more details see section on unwind valuation of single-name CDS.
curveCDSparflat
recovery assumed
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Mechanics Mechanics and Credit and Credit EventsEvents: : Unfunded Unfunded CDS Form (CDS Form (cont'dcont'd))
model JPMorgan
October 7/14, 2004126
Protection sellerProtection seller
DJ DJ iTraxx iTraxx EuropeEurope
Protection buyerProtection buyer
Credit risk
45 bp p.a = €45,000
€17,861
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Mechanics Mechanics and Credit and Credit EventsEvents: : Unfunded Unfunded CDS Form (CDS Form (cont'dcont'd))
The protection buyer receives the upfront premium and pays to protection seller 45bp p.a. quarterly on €10 MM until maturity
No Credit Event
October 7/14, 2004127
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Mechanics Mechanics and Credit and Credit EventsEvents: : Unfunded Unfunded CDS Form (CDS Form (cont'dcont'd))
Defaultet Reference Entity has a weighting of 0.80% (=1/125)Protection buyer delivers €80,000 nominal face value of Deliverable Obligations
of the Reference Entity in exchange for €80,000n (=0.80% of €10 MM)Notional amount on which premium is paid reduces by €80,000 to €9,92 MM
resulting in a premim of €44,640Each subsequent credit event will result in a further reduction of the nominal by
€80,000 (=1/125)
Credit Event on a single Reference Entity – Physical Settlement
45bp p.a. = €44,640
DJ DJ iTraxx iTraxx EuropeEurope
Credit risk
Protection sellerProtection sellerProtection buyerProtection buyer
€80,000
€80,000 nominal in bonds/loans
October 7/14, 2004128
Consider an investor buying €10 MM DJ iTraxx Europe Note (CLN) with maturity 09/2009
The investor pays at launch 100 for the Note and receives Euribor+45bp p.a., quarterly
Without Credit Events, the investor continues to receive the coupon on the original notional invested until maturity
At maturity, the Note will redeem at par
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Mechanics Mechanics and Credit and Credit EventsEvents: : FundedFunded CLN Form CLN Form
No Credit Event
InvestorInvestor
DJDJ iTraxxiTraxx EuropeEurope
Credit risk
Par
EURIBOR+CDS spreadIssuerIssuer
October 7/14, 2004129
Credit Event on a single Reference Entity – Cash Settlement
Defaultet Reference Entity has a weighting of 0.80% (=1/125) and final recovery value of 40%
Issuer pays to the investor the Cash Settlement amount of €32,000 =0.80%*€10 MM*40%
Redemption amount of the Note reduces from €10 MM to € 9,92 MM = 99.2%*€10 MM and Coupons of Euribor+45bp are paid on € 9,92 MM subject to any further credit events
InvestorInvestor
DJDJ iTraxxiTraxx EuropeEurope
Credit risk
€32,000
IssuerIssuer EURIBOR+CDS spread
€9,92 MM
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesDJ DJ iTraxx iTraxx Europe Europe Mechanics Mechanics and Credit and Credit EventsEvents: : FundedFunded CLN Form (CLN Form (cont'dcont'd) )
October 7/14, 2004130
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesAppendix: Appendix: Computing the Intrinsic SpreadComputing the Intrinsic Spread
What is the on-market coupon for a CDS on a Credit-Index?We will show that the on-market coupon can be approximated by
- the weighted average of the par CDS spreads of the names in the index
- where the weights are the risky DV01's for each name*
The approximation of the on-market coupon can also be used as a device for a replication of the Credit-Index CDS with single-name CDS on the underlying names.
The on-market coupon is called the intrinsic spread for the Credit-Index CDS.
* The risky DV01 si the change in value of the CDS for a 1bp widening in the spread. When using BLOOMBERGs CDSW the risky DV01 is displayed as 'Sprd DV01'.
October 7/14, 2004131
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesAppendix: Appendix: Computing the Intrinsic Spread Computing the Intrinsic Spread ((cont'dcont'd))
Step 1 (Intrinsic Upfront Payment)
- Use CDSW on each component of the credit index
- then sum up
Step 2 (Market Upfront Payment)
- Use the market convention of modelling the credit index as a single fictitious entity trading at a flat spread curve with recovery 40%:
( ) nameSingleIndexnameSinglenameSingle DVSprdSpreadDealSpreadCDSParpaymentUpfront 01×−=
( )∑∑ ×−=N
nameSingleIndexnameSinglenameSingle DVSprdSpreadDealSpreadCDSParpaymentUpfront 01
( ) EntityFictitiousIndexEntityFictitiousconventionMarket DVSprdSpreadDealSpreadCDSParpaymentUpfront 01×−=
October 7/14, 2004132
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesAppendix: Appendix: Computing the Intrinsic Spread Computing the Intrinsic Spread ((cont'dcont'd))
Step 3 (Intrinsic Spread):
- Equate the upfront payments and back out the intrinsic spread
Step 4 (Approximation of Intrinsic Spread)
- Substitute the Sprd DV01 of the fictitious entity by the average of the index components Sprd DV01's:
( )∑∑ ×−=N
nameSingleIndexnameSingle
N
nameSingle DVSprdSpreadDealSpreadCDSParN
paymentUpfrontN
0111
( ) EntityFictitiousIndexEntityFictitiousconventionMarket DVSprdSpreadDealSpreadCDSParpaymentUpfront 01×−=
∑≈N
nameSingleEntityFictitious DVSprdN
DVSprd 01101
October 7/14, 2004133
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesAppendix: Appendix: Computing the Intrinsic Spread Computing the Intrinsic Spread ((cont'dcont'd))
- The upfront payment equations then become
- and the intrinsic spread can be easily computed as follows:
( )∑∑ ×−=N
nameSingleIndexnameSingle
N
nameSingle DVSprdSpreadDealSpreadCDSParN
paymentUpfrontN
0111
( ) nameSingleIndexEntityFictitious
N
conventionMarket DVSprdSpreadDealSpreadCDSParN
paymentUpfront 011×−= ∑
∑
∑ ×≈ N
nameSingle
N
nameSinglenameSingle
SpreadCDSPar
DVSprdSpreadCDSParspreadIntrinsic
01
October 7/14, 2004134
CDS/CLN on CreditCDS/CLN on Credit--IndicesIndicesAppendix: Appendix: Computing the Intrinsic Spread Computing the Intrinsic Spread ((cont'dcont'd))
Simple average vs intrinsic spread:
In general, the intrinsic spread is lower than the simple average because the higher spreads have lower 'Sprd DV01' and therefore lower weights.
The difference between the simple average and the intrinsic spread is called the intrinsic basis.
N
spreadnameSinglespreadIntrinsic
N
ii
AverageSimple
∑== 1
∑
∑ ×≈ N
nameSingle
N
nameSinglenameSingle
SpreadCDSPar
DVSprdSpreadCDSParspreadIntrinsic
01
spreadIntrinsic AverageSimplespreadIntrinsic<
October 7/14, 2004135
Credit Credit OptionsOptionsCreditCredit--Spread OptionsSpread Options/Warrants/Warrants
CreditCredit--Default Default SwaptionsSwaptions
Credit Options
October 7/14, 2004136
Credit Credit OptionsOptionsOverview Overview
Substantial growth in activity in 2003 - bond and spread options- options on single-name CDS- options on index-linked CDS
Increased liquidity in the CDS market is expected to boost the market for options on CDS
Main growth expected to come from index-linked trades ( DJ iTraxx)
Hedge bond inventory, Volatility TradingBanks
Yield Enhancement, Liability management (Casino's credit spread warrants)
Corporate Issuers
Benchmark Outperformance, Relative Valuation, Yield Enhancement (Covered Call Writing)
Money Managers
Leverage, Debt-Equity Strategies, Relative Valuation, typically Buyers of Volatility
Hedge Funds
Hedge of Liabilities, Yield EnhancementInsurance Companies
ApplicationMarket Participant
October 7/14, 2004137
Credit Credit OptionsOptionsBond and Bond and Spread OptionsSpread Options: Bond : Bond Options Options (Price (Price OptionsOptions))
The Option Buyer pays a premium to the Option Seller for the right (not the obligation) to buy or sell a Reference Asset at a predetermined Strike Price on a predetermined future Expiration Date.
Option Seller
Option Buyer
Premium
Right to purchase the Reference Asset at the Strike Price
Option Seller
Option Buyer
Strike Price
Reference Asset
If the Price > Strike Price The Buyer buys the Reference
Asset at the Strike Price
Option Seller
Option Buyer
If the Price < Strike Price The Buyer does nothing
Expiration Date
Price Option ( Call )
October 7/14, 2004138
Expiration Date
Spread Option ( Call )
Option Buyer
Option Seller
Premium
Right to purchase the Reference Asset at the Strike Spread
Option Buyer
Option Seller
If the Spread > Strike Spread The Buyer does nothing
Option Buyer
Option Seller
Price given Strike Spread
Reference Asset
If the Spread < Strike Spread The Buyer purchases the Reference
Asset at the Strike Spread
The Option Buyer pays a premium to the Option Seller for the right (not the obligation) to buy or sell a Reference Asset at a predetermined Strike Spread on a predetermined future Expiration Date.
Credit Credit OptionsOptionsBond and Bond and Spread OptionsSpread Options: : Spread OptionsSpread Options
October 7/14, 2004139
Credit Credit OptionsOptionsBond and Bond and Spread OptionsSpread Options ApplicationApplication: : Casino's Spread Casino's Spread WarrantsWarrants
Source:
Dresdner Kleinwort Wasserstein
October 7/14, 2004140
Credit Credit OptionsOptionsBond and Bond and Spread OptionsSpread Options ApplicationApplication: : Casino's Spread Casino's Spread Warrants (Warrants (cont'dcont'd))
Source:
Dresdner Kleinwort Wasserstein
October 7/14, 2004141
Credit Credit OptionsOptionsCDS CDS Swaptions Swaptions // OptionsOptions on CDS on CDS
Definition: - Option on Credit Default Swap spread of a credit- Underlying = forward starting CDS (at Option Expiry)- Traded as European options, only exercisable at Expiry Date- 3 to 9 month options on ATM 5 year CDS are most common
Terminology:- Payer: Option to buy protection (short credit risk "put on credit")- Receiver: Option to sell protection (long credit risk "call on credit")- Physically settled (enter into underlying CDS) or cash settled (MtM at option expiry)
What happens if before the Option Expiry there is a Credit Event ?- Payer : Traded with or without knock-out *- Receiver : Credit Event not relevant, since option would be out-of-the-money short before Credit Event
* Knock-out: Exercise is not possible in case of Credit Event in the issuer or guarantor of the CDS Reference Entity. Reason for knock-out is that hedging instruments are eg forward starting CDS that will expire worthless should a default occur prior to expiry date.
October 7/14, 2004142
Expiration Date
Payer CDS Swaption
Option Seller
Option Buyer
MtM of CDS
If the par CDS spread > Strike CDS spread The Seller pays the MtM
of the CDS position to the Buyer
Option Seller
Option Buyer
Payer CDS
If the par CDS spread > Strike CDS spread The Buyer enters a CDS position
at the Strike CDS spread
Option Seller
Option Buyer
If the par CDS spread < Strike CDS spreadThe Buyer does nothing
Option Seller
Option Buyer
Premium
Right to buy Protection at the Strike CDS Spread
Cash Settlement Physical Settlement
Credit Credit OptionsOptionsCDSCDS SwaptionsSwaptions // OptionsOptions on CDS: Payeron CDS: Payer
October 7/14, 2004143
Expiration Date
Receiver CDS Swaption
Option Seller
Option Buyer
MtM of CDS
If the par CDS spread < Strike CDS spread The Seller pays the MtM
of the CDS position to the Buyer
Option Seller
Option Buyer
Payer CDS
If the par CDS spread < Strike CDS spread The Buyer enters a CDS position
at the Strike CDS spread
Option Seller
Option Buyer
If the par CDS spread > Strike CDS spreadThe Buyer does nothing
Option Seller
Option Buyer
Premium
Right to sell Protection at the Strike CDS Spread
Cash Settlement Physical Settlement
Credit Credit OptionsOptionsCDSCDS SwaptionsSwaptions // OptionsOptions on CDS: Receiveron CDS: Receiver
October 7/14, 2004144
Options on iTraxx Main Series 1 6 Aug 8:51 am
Sep 04 Expirystrike ---> 40 42.5 45 47.5 50tenor v bid/ask delta bid/ask delta bid/ask delta bid/ask delta bid/ask delta
Payer 18 / 21 -81% 10 / 14 -62% 4 / 8 -42% 1 / 5 -25% 0 / 3 -14%Receiver 1 / 5 19% 5 / 9 37% 11 / 15 58% 19 / 23 75% 30 / 33 86%
Dec 04 Expirystrike ---> 40 42.5 45 47.5 50tenor v bid/ask delta bid/ask delta bid/ask delta bid/ask delta bid/ask delta
Payer 29 / 35 -80% 22 / 28 -70% 16 / 22 -59% 11 / 18 -49% 8 / 14 -39%Receiver 3 / 8 20% 6 / 12 30% 11 / 17 41% 17 / 24 51% 25 / 31 61%
All exchanging spot delta at 42.5Options don't KO on defaultPrices in cents of notional, payable upfrontPayers are options to buy protection (=pay fixed)Receivers are options to sell protection (=receive fixed)A positive delta means buyer of option buys CDS in the exchangeA negative delta means buyer of option sells CDS in the exchange
Closest strike to:ATM spot
ATM forward
Credit Credit OptionsOptionsCDS CDS SwaptionsSwaptions on on iTraxx iTraxx
Example: If you buy €100 MM @ strike 45 Dec04 Payer, you pay €220,000 upfront and you have the right to buy 5 years protection on DJ iTraxx Europe @ 45 on Dec 22, 2004
October 7/14, 2004145
Correlation ProductsCorrelation ProductsFirstFirst--toto--Default (Default (FtDFtD) CDS) CDS
TranchedTranched CreditCredit--Index Index ProductsProducts((Tranched Tranched DJ DJ iTraxxiTraxx))
Correlation Products
October 7/14, 2004146
Correlation ProductsCorrelation ProductsFtDFtD CDS: CDS: MechanicsMechanics
FtD basket CDS are simple products allowing investors to take advantage of both
- their views on default probability of companies- the correlation between those defaults
The protection buyer in a FtD CDS is protected against only the first defaultTypical basket consists of 5-6 reference entitiesSimilar to single-name CDS
Reference EntityReference Entity
Reference EntityReference Entity
Reference EntityReference EntityReference EntityReference Entity
Reference EntityReference Entity
Protection sellerProtection sellerProtection buyerProtection buyerCDS spread
Credit risk
No Credit Event
October 7/14, 2004147
Correlation ProductsCorrelation ProductsFtDFtD CDS: CDS: MechanicsMechanics ((cont'dcont'd))
Credit Event: First Reference Entity DefaultAfter first Credit Event the FtD CDS is terminatedThe protection buyer delivers a Deliverable Obligation of the defaulted
Reference EntityThe protection seller pays par
Reference EntityReference Entity
Reference EntityReference Entity
Reference EntityReference EntityReference EntityReference Entity
Defaulted Reference EntityDefaulted Reference Entity
Protection buyerProtection buyer Protection sellerProtection seller
100
ConvertibleConvertibleLoanLoan
BondBondCTD BondCTD Bond
October 7/14, 2004148
Correlation ProductsCorrelation ProductsFtDFtD CDS: CDS: RulesRules--ofof--thumbthumb
Upper bound (0% default correlation):- An FtD CDS offers only partial protection against the first defaulting Reference Entity,- therefore the sum of the individual premiums should define an upper bound to the FtD CDS premium:
- When the correlation between defaults is 0%, the FtD CDS premium corresponds to the sum of the individual CDS premiums
∑< SpreadCDSnameSingleSpreadCDSFtD
Lower bound (100% default correlation):- Assuming the correlation between the defaults is 100%, the riskiest credit in the basket will always be the first to default,- therefore the maximum of the individual CDS premiums defines a
lower bound for the FtD CDS premium:
SpreadCDSFtDSpreadCDSnameSingleMaximal <
October 7/14, 2004149
Correlation ProductsCorrelation ProductsFtDFtD CDS: CDS: RulesRules--ofof--thumb thumb ((cont'dcont'd))
Basic relationship Spread-Correlation:
Market FtD CDS Spreads:- Range typically from 60% to 80% of total spread
October 7/14, 2004150
Correlation ProductsCorrelation ProductsFtDFtD CDS: JPM Standard CDS: JPM Standard FtD BasketsFtD Baskets
JPMorgan introduced 'standard' FtD Baskets Basket composition is rules-based and draws on the DJ iTraxx subindices
October 7/14, 2004151
Correlation ProductsCorrelation ProductsFtDFtD CDS: JPM Standard CDS: JPM Standard FtD Baskets FtD Baskets ((cont'dcont'd))
FtD Implied Spread and Underlying CDS levels:
October 7/14, 2004152
Correlation ProductsCorrelation ProductsFtDFtD CDS: JPM Standard CDS: JPM Standard FtD Baskets FtD Baskets ((cont'dcont'd))
FtD Implied Spread and Underlying CDS levels:
Sample Market Quotes
October 7/14, 2004153
Correlation ProductsCorrelation ProductsTranched Tranched DJ DJ iTraxxiTraxx: : Description Description
DJ tranched iTraxx is a synthetic CDO on a static portfolioThe portfolio of Reference Entities corresponds to the DJ iTraxx Reference
EntitiesTranches:
- Equity Tranche bears the first 3% of losses of the static portfolio- Second-Loss Tranche bears the second 3% of losses- ...
3%, 6%, 9%, 12%, 22% are called attachement/detachement points or lower/upper subordination levels
DJ DJ iTraxx iTraxx EuropeEurope
Portfolio of 125Portfolio of 125
Credit Default Credit Default Swaps Swaps
1212--22% Tranche22% Tranche
99--12% Tranche12% Tranche
66--9% Tranche9% Tranche
33--6% Tranche6% Tranche
00--3% Tranche3% Tranche
Contractually tranched
First-loss Tranche
Equity Tranche
October 7/14, 2004154
Correlation ProductsCorrelation ProductsTranched Tranched DJ DJ iTraxxiTraxx: : Mechanics for Equity Mechanics for Equity TrancheTranche
Consider an investor selling protection for €10 MM on the Equity Tranche with maturity 09/2009
Assume that the DJ tranched iTraxx 0-3% Tranche trades at 500bpThe periodic premium received by the investor is €500,000 (=5% of €10 MM)
Without Credit Events, the investor continues to receive the premium on the original notional until maturity
No Credit Event
InvestorInvestor
DJDJ iTraxxiTraxx EuropeEurope
Credit risk
(First 3% of Losses)
€500,000Protection buyerProtection buyer
October 7/14, 2004155
Credit Event: One Reference Entity defaults @ 40% RecoveryThe 60% loss on the Reference Entity translates into a 0.48% (=60%/125) loss
on the 125-name portfolioThe investor would lose the entire notional for a loss of 3%A loss of 0.48% corresponds therefore to a 16% (=0.48%/3%) loss of notionalThe investor pays €1.6 MM (=16% of €10 MM) to the protection buyerThe new notional is €8.4 MM(= €10 MM - €1.6 MM)The investor receives 500bp on €8.4 MM contingent on any further credit event
For a vanilla Credit-Index CDS the payment of the investor would be €48,000 and the new notional would be €9,92 MM (for a much lower premium !)
Correlation ProductsCorrelation ProductsTranched Tranched DJ DJ iTraxxiTraxx: : Mechanics for Equity Mechanics for Equity Tranche (Tranche (cont'dcont'd))
InvestorInvestor
DJDJ iTraxxiTraxx EuropeEurope€1,6 MM
Protection buyerProtection buyer€420,000
Credit risk
(First 3% of Losses)
October 7/14, 2004156
Credit Event: 7 Reference Entities default each @ 40% RecoveryThe total loss on the Reference Entities (420%) translates into a 3.36%
(=420%/125) loss on the 125-name portfolioThe investor would lose the entire notional for a loss of 3%A loss of 3.36% corresponds therefore the loss of the full notionalThe investor pays €10 MM to the protection buyerThe protection buyer stops paying the spreadThe loss portion exceeding 3% (0.36%) triggers settlement cashflows for
buyers and sellers of the 3-6% tranche
Correlation ProductsCorrelation ProductsTranched Tranched DJ DJ iTraxxiTraxx: : Mechanics for Equity Mechanics for Equity Tranche (Tranche (cont'dcont'd))
InvestorInvestor
DJDJ iTraxxiTraxx EuropeEurope€10 MM
Protection buyerProtection buyer
October 7/14, 2004157
Correlation ProductsCorrelation ProductsTranched Tranched DJ DJ iTraxxiTraxx: Sample Market : Sample Market QuotesQuotes
October 7/14, 2004158
Outlook...Outlook...
Total Return Total Return Swaps Swaps
(TRS)(TRS)
Equity Equity Default Default SwapsSwaps
(EDS)(EDS)
ConstantConstant--Maturity Maturity CDSCDS
(CMCDS)(CMCDS)
Digital Default CDSDigital Default CDS
(DDS)(DDS) Recovery Recovery SwapsSwaps
(RCDS)(RCDS)
Spread Spread CDSCDS
(SCDS)(SCDS)
................
Outlook...
October 7/14, 2004159
• The J.P. Morgan Guide to Credit Derivatives, JPMorgan / RISK, 2000• Credit Derivatives and Structured Credit, Bowler T and Tierney J.F., Deutsche Bank, August 2000• Credit Derivatives Explained, O'Kane D, Lehman Brothers, March 2001• Global Credit Derivatives: Risk Management or Risk?, Special Report FitchRatings, March 2003• Kreditderivate: Implikationen für die Kreditmärkte, Effenberger D, Deutsche Bank, June 2003• Global Credit Derivatives: A Qualified Success, Special Report, FitchRatings, September 2003• Credit Derivatives: A Case of Mixed Signals?, Credit Market Research, FitchRatings, December 2003• Kreditderivate: Wirkung auf die Stabilität der Finanzmärkte, Effenberger D, Deutsche Bank, April 2004• The Lehman Brothers Guide to Exotic Credit Derivatives, Lehman Brothers, 2004• Corporate use of credit derivatives: next stop in risk management, Morgan Stanley / RISK, May 2004• Credit Derivatives: An Overview of Market Participants & Activity, Benison T, JPMorgan, 2004
ReferencesReferencesGeneralGeneral
October 7/14, 2004160
• Credit Risk Modelling and Credit Derivatives, Schönbucher P J, Dissertation, Bonn 2000• Valuing Credit Default Swaps I: No Counterparty Default Risk, Hull J C and White A, The Journal of Derivatives, Fall 2000• Credit: The Complete Guide to Pricing, Hedging and Risk Management, Arvanitis A and Gregory J, RISK Books, 2001• Price and probability, Martin R, Thompson K and Browne C, RISK, January 2001• Credit Swap Valuation, Duffie D, Financial Analysts Journal 55(1), 1999, reprinted in Credit 2001•Valuing Default Swaps Under Market and Credit Risk Correlation, Jarrow R A and Yildirim Y,The Journal of Fixed Income, March 2002• Credit Derivatives Pricing Models, Schönbucher P.J., John Wiley & Sons, June 2003
References References TheoreticalTheoretical
October 7/14, 2004161
• Asset Swaps, Tim Frost, JPMorgan, December 1995• Railtrack and SAirGroup, Harvey R and Adams J, JPMorgan, October 2001• Unwind valuation of Credit Default Swaps, Goldman Sachs, December 2001• Fundamentals of the Default Swap Market, Corey J and Poprik B, Deutsche Bank, December2001• Credit Linked Notes – The Mechanics, Palmer A et al, JPMorgan, August 2002• Understanding the basis, Van den Bok A, ABN AMRO, January 2003• Fitch Examines Effect of 2003 Credit Derivatives Definitions, Special Report, FitchRatings, March 2003• Introduction to Credit Derivatives, Mettler B, JPMorgan Credit Derivatives Conference, 2004• Credit Derivatives Pricing and Research, Beinstein E, JPMorgan Credit Derivatives Conference, 2004• Credit Derivatives Documentation, Thompson D, JPMorgan Credit Derivatives Conference, 2004• Bond spreads as a proxy for credit default swap spreads, Davies M and Pugachevsky D, Bear Stearns / RISK, 2004
References References SingleSingle--name name CDS/CLNCDS/CLN
October 7/14, 2004162
• Dow Jones TRAC-X, Mettler B, JPMorgan Credit Derivatives Conference, 2004• Introducing DJ iTraxx Europe Series 1, Due J et al, JPMorgan, June 2004• Dow Jones iTraxx CDS Indices Europe, www.iboxx.com, June 2004• Computing Intrinsic Spreads of Portfolio Credit Default Swaps, Baheti P and Naldi M, Lehman Brothers, July 2004• Pricing and hedging credit default swaps on indices, Davies M and Pugachevsky D, Bear Stearns / RISK, 2004• Basic CDS Index Analytics, Derivatives Week, June 2004
References References Credit Index CDS/CLNCredit Index CDS/CLN
October 7/14, 2004163
• Corporate Bond Options, Kakodkar A and Francis C, Merrill Lynch, June 2003• An Introduction to Credit Options, Spinner A, Derivatives Week, May 2004• Credit option trading comes of age, Macaskill J, RISK, May 2004• Credit spread warrants, Park S, Dresdner Kleinwort Wasserstein, 2004• Index Monitor: Credit Spread Warrants, Stangl G and Schon C, Dresdner Kleinwort Wasserstein, May 2004• Credit Options Primer, Lehman Brothers, June 2004• Bets on for credit spread warrants, RISK, July 2004• Covered Credit Spread Warrants, Introducing credit options to corporate bond investors, Nevstad H, Dresdner Keinwort Wasserstein, July 2004
References References Credit Credit OptionsOptions
October 7/14, 2004164
• First to Default Basket Swaps, Tierney J.F., Deutsche Bank, February 2002• Introducing Dow Jones Tranched TRAC-X, McGinty L et al, JPMorgan, November 2003• Introduction to Correlation Products, Mazur B and Mettler B, JPMorgan Credit DerivativesConference, 2004• Credit Correlation: A Guide, McGinty et al, JPMorgan, March 2004• Introducing Base Correlations, McGinty et al, JPMorgan, March 2004• A Model for Base Correlation Calculation, McGinty L and Ahluwalia R, JPMorgan, May 2004• Introducing Standard First to Default Baskets, McGinty L, Harris M and Due J, JPMorgan, July2004• A Model for First to Default Implied Correlation Calculation, McGinty L et al, JPMorgan, July2004• The Bank of America Guide to Advanced Correlation Products, Bank of America, 2004
References References Correlation ProductsCorrelation Products