Credit Derivatives

1
Credit Derivatives
2
Credit Derivatives

• Credit Derivatives and Its Growth
• Credit Default Swaps (CDS)
• Binary Credit Default Swaps
• Total Return Swaps
• CDS Forwards
• CDS Options
• Collateralized Debt Obligations (CDO)
• Synthetic CDOs

3
Credit Derivatives

• A credit derivative is a bilateral contract that
  isolates specific aspects of credit risk from an
  underlying instrument and transfers the risk
  between the two parties
• Allows replication, hedging and transfer of
  credit risk
• Demand created by
• Specific types of credit risk can be added to a
  portfolio without acquiring the credit asset
  itself
• Credit risks of instruments can be managed
• Broader range of investors can deal in credit
• Regulatory capital arbitrage

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Credit Derivatives

• Financial contracts with a payout linked to
• Loan or bond values
• Default or credit events
• Credit spreads
• Credit ratings
• With cash settlement or delivery of the relevant
  underlying
• asset or portfolio, if appropriate
• On single name, baskets, indices
• Delivery as notes or OTC contracts
• Delivery as swaps or options

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Credit Derivatives

• 1992 First use of the phrase credit derivative
  by ISDA
• 1993-5 Market does not take off
• SP refuse to rate credit derivative products
• Doubt among practitioners whether credit
  derivative deals that had
• been done would be completed
• 1996 Vast range of applications for credit
  derivatives realised
• 1997 First synthetic securitisation (JP Morgans
  Bistro deal)
• 1999 ISDA issued series of definitions,
  including credit events, obligations and
  settlement (physical or cash). By end of year,
  84 of structures were based on these definitions
• 1999- Period of sharp growth in credit
  derivative market

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Credit Derivatives
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Credit Derivatives

• First generation
• Total return swap
• Credit default swap
• Default digital
• Spread options
• Second generation
• Floating rate asset derivatives
• Fixed coupon asset derivatives
• Rating option
• Bankruptcy swap
• Third generation exotics

8
Credit Derivatives

• Total Return Swaps
• Party A pays any total positive returns on the
  underlying asset (including interest and capital
  appreciation)
• Party B pays a funding payment (LIBOR margin)
  and any capital depreciation
• Party A transfers all the credit risk of the
  underlying asset to Party B without the selling
  the asset

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Credit Derivatives

• Credit Default Swaps
• Party A pays a fee of x basis points until
  default or maturity
• Party B pays an agreed notional amount upon
  credit event
• (relative to an underlying reference loan or
  security)
• Party A can take cost of swap into account in
  pricing the
• loan and remove credit default risk of perhaps a
  valued
• customer

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Credit Derivatives

• Credit Spread Derivatives
• Credit spread is primarily used as compensation
  for the
• possibility of default
• Two general formats of credit spread
• Absolute spread the credit spread relative to
  a benchmark that is
• regarded as default risk free
• Relative spread the spread between two
  credit-risky assets
• Forwards and options on the credit spread
• Call options give the purchaser the right to
  buy the spread
• Seller benefits from a decreasing spread
• Allows the trading of credit spreads as an
  isolated variable
• without being exposed to interest rate risk

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Credit Derivatives

• Credit Linked Notes
• Credit derivative embedded in a fixed-income
  security
• Structure of a credit-default note (where the
  embedded derivative is a credit-default swap)
• Both total return swaps (total rate of return
  credit-linked notes) and credit-spread forwards
  (credit-spread notes) are also often used as the
  embedded derivative

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Credit Derivatives

• Credit Events
• According to ISDA, credit events are
• Bankruptcy
• Obligation acceleration
• Obligation default
• Failure to pay
• Repudiation/Moratorium
• Restructuring
• Bankruptcy swap same structure but only pays
  out upon bankruptcy wasoffered by
  EnronCredit.com
• Rating option same structure but event that
  triggers payment is an upgrade or downgrade by a
  rating agency
• Can be extended to portfolios
• First to default pays out when one credit in a
  protected portfolio defaults
• m to default swap

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Credit Derivatives

• Breakdown of Credit Derivatives in 2000

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Credit Derivatives

• Applications of Credit Derivatives
• 1. Transfer credit risk of valued customer to
  another institution
• Dynamic management of credit risk
• Gain exposure to restricted markets
• Yield enhancement
• Regulatory capital arbitrage

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Credit Derivatives

• Applications of Credit Derivatives
• 2. Gain Exposure to Restricted Markets / Yield
  Enhancement
• Fund wants high yield investment
• Emerging markets
• Problem of investment restrictions
• Typical cannot invest below BBB grade debt

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Credit Derivatives

• Applications of Credit Derivatives
• 2. Gain Exposure to Restricted Markets / Yield
  Enhancement

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Credit Derivatives

• Applications of Credit Derivatives
• 3. Regulatory Capital Arbitrage
• OECD Banks A and B compete to give a loan of 10m
  to Company X
• Risk-weighting is 100 since counterparty is a
  corporate
• Regulatory capital is therefore 800,000
• Banks must raise 9.2m from third-parties

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Credit Derivatives

• Applications of Credit Derivatives
• 3. Regulatory Capital Arbitrage

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Credit Derivatives

• Applications of Credit Derivatives
• 3. Regulatory Capital Arbitrage
• Banks now co-operate by entering into a credit
  default swap
• Bank As counterparty is now an OECD bank (Bank
  B) risk-weighting 20
• Regulatory capital is therefore 160,000
• Must raise 9.84m from third-parties
• Bank Bs counterparty remains Company X and so
  must still hold 800,000 of regulatory capital

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Credit Derivatives

• Applications of Credit Derivatives
• 3. Regulatory Capital Arbitrage

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Credit Derivatives

• Applications of Credit Derivatives
• 3. Regulatory Capital Arbitrage
• Bank As income is reduced as it is now paying a
  credit
• default swap fee of x basis points per annum
• Bank As return on capital (net income /
  regulatory capital)
• increases under the credit default swap
  arrangement for
• values for x lt 60bp
• Bank Bs net income (and thus return on
  capital) increases for values for x gt 33bp
• If feasible then regulatory capital arbitrage
  can occur and the return on capital for both
  banks can increase by entering a credit default
  swap with each other

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Credit Default Swap

• The most popular credit derivative.
• The market started to grow fast in the late
  1990s. By 2003 notional principal totaled 3
  trillion.
• Credit derivatives are contracts where the payoff
  depends on the creditworthiness of one or more
  companies or countries.
• Buyer of the instrument acquires protection from
  the seller against a default (credit event) by a
  particular company or country (the reference
  entity).

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Credit Default Swap

• The buyer of the insurance obtains the right to
  sell bonds issued by the company for their face
  value when a credit event occurs.
• The total face value of the bonds that can be
  sold is known as the credit default swaps
  notional principal.
• The buyer of the CDS makes periodic payments to
  the seller until the end of the life of the CDS
  or until a credit event occurs. These payments
  are typically made in arrears every quarter,
  every half year, or every year.
• The settlement in the event of a default involves
  either physical delivery of the bonds or a cash
  payment.

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Credit Default Swap (cont)

• 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 for life of contract or until default
• If there is a default, the buyer has the right to
  sell bonds with a face value of 100 million
  issued by company X for 100 million (Several
  bonds are typically deliverable)

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Credit Default Swap (cont)
90 bps per year
Default Protection Buyer, A
Default Protection Seller, B
Payoff if there is a default by reference
entity100(1-R)
Recovery rate, R, is the ratio of the value of
the bond issued by reference entity immediately
after default to the face value of the bond
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Credit Default Swap (cont)

• Suppose payments are made quarterly in the
  example just considered. What are the cash flows
  if there is a default after 3 years and 1 month
  and recovery rate is 40?

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Details of Contractual Agreement

• THE BUYER OF THE CDS MAKES PERIODIC PAYMENTS
  UNTIL THE END OF THE LIFE OF THE CDS OR UNTIL A
  CREDIT EVENT OCCURS (IN ARREARS)
• SETTLEMENT OCCURS _at_ DEFAULT BY PHYSICAL DELIVERY
  OF BONDS /OR CASH PAYMENT

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Example

• Say a 5 yr CDS begins on 3/1/04
• Assume a notional principle of 100 Million and
  the buyer agrees to pay 90 basis points annually
  for protection against default by the entity
• If there is no default the insurer gets pmts of
  900K/yr

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Example

• If the contract specifies physical settlement,
  the buyer has the right to sell bonds issued by
  the reference entity with a face value of 100m
  for 100m.
• If the contract requires cash settlement, an
  independent calculation agent will poll dealers
  to determine the mid-market value of the cheapest
  bonds a pre-designated number of days after the
  credit event. Suppose this bond is worth 35 per
  100 of face value, the cash payoff would be 65m.

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Example

• The payments from the buyer of protection to
  seller of protection cease when there is a credit
  event. But, since payments are in arrears, there
  is a final accrual payoff payment.
• For the example, the buyer would be required to
  pay the seller the amount of the annual payment
  accrued between March 1, 2007, and June 1, 2007
  (approximately 225,000).

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CDS SPREAD

• The total amount paid per year, as a percent of
  the notional principal, to by protection is the
  CDS spread.
• A market maker on CDS might bid 250 basis points
  and offer 260 basis points. This means that the
  market maker is prepared to buy protection by
  paying 250 basis points per year and to sell
  protection for 260 basis points per year.

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Recovery Rate (R)

• R Bond FV p. default
• The recovery rate for a bond is normally defined
  as the bonds value immediately after a default
  as a of Face Value
• PAY-OFF
• the amount of cash given in settlement
• L(1-R) where LNotional Principle

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CDSs and Bond Yields

• A CDS can be used to hedge a position in a
  corporate bond.
• Suppose an investor buys a 5 yr, 7 yield
  corporate bond for its FV with CDS spread 2/yr
  (the value of the CDS), and, AT THE SAME TIME,
  buys protection against the issuer of the bond in
  a 5yr CDS
• The CDS effectively converts the corporate bond
  into a risk-free bond()

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CDSs and Bond Yields

• A CDS can be used to hedge a position in a
  corporate bond.
• Suppose that an investor buys a 5-yr corporate
  bond yielding 7 per year for its face value and
  at the same time enters into a 5-yr CDS to buy
  protection again the issuer of the bond
  defaulting. Suppose that the CDS spread is 2
  per annum.
• The effect of the CDS is to convert the corporate
  bond to a risk-free bond. If the bond issuer
  doesnt default, investor earns 5/yr.
• IF Default, investor earns 5/yr to date of
  default, can swap the defaulted bonds for FV and
  can reinvest the FV _at_ risk free rates for the
  remainder of the 5 years.

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CDS Spreads

• Spread n-year corporate bond par yield n-year
  risk-free yield
• IF CDS Spread was markedly less than this, the
  investor can earn more than the risk-free rate by
  buying the corporate bond and buying protection.
• IF CDS Spread was markedly greater than this, the
  investor could borrow _at_ less than the risk-free
  rate by shorting the corporate bond and selling
  CDS protection.

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Valuation of Credit Default Swap

• Mid-market CDS spreads (the ave. of the bid and
  offer CDS spreads quoted by brokers) are in
  practice calculated from default probability
  estimates
• HOW IT WORKS 5 part process
• Determining Unconditional default and survival
  probabilities
• Calculate the PV of expected pmts
• Calculate the PV of expected payoff
• Calculate the PV of accrual payment
• Set PMTPAYOFF and solve for S, the mid-market
  spread

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Valuation of Credit Default Swap

• Initial unconditional default probability is a
  nominally determined rate for the first year.
• Succeeding conditional default probability are
  derived for the initial unconditional default
  probability and preceding conditional
  probabilities.
• Working Assumptions
• Default always occurs in the middle of the year
• CDS pmts made once/year _at_ the end of the year
• CDS payments are made at a rate of S per year
• Notional principle 1

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Valuation of Credit Default Swap

• Suppose the probability of a reference entity
  defaulting during a year condition on no earlier
  default 2 Base year default probability
• Then you can extrapolate the following
  probability values
• yr Default Prob. Survival Prob.
• 1 0.0200 0.9800(1-.02)
• 2 0.0196(.02.98) 0.9604(.98.98)
• 3 0.0192 (.02.9604) 0.9412(.98.98.98)
• 4 0.0188 0.9224
• 5 0.0184 0.9039

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Valuation of Credit Default Swap

• year Surv. Prob Exptd Pmt Disc. Factor PV
  of Exptd Pmt
• 1 .9800 .9800S .9512 .9322S
• 2 .9604 .9604S .9048 .8690S
• 3 .9412 .9412S .8607 .8101S
• 4 .9224 .9224S .8187 .7552S
• 5 .9039 .9039S .7788 .7040S
• TOTAL 4.0704S
• .9412Se-.053 .8101S

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Valuation of Credit Default Swap

• Calculation of the PV of Expected Payoff
  Notional Principle1
• Yr Def. Prob. RR E PO Disc Factor PVEPO
• .5 .0200 .4 .0120 .9753 .0117
• 1.5 .0196 .4 .0118 .9277 .0109
• 2.5 .0192 .4 .0115 .8825 .0102
• 3.5 .0188 .4 .0113 .8395 .0095
• 4.5 .0184 .4 .0111 .7985 .0088 TOTAL
  .0511
• .0192 X .6 X 1 .0115 .0115e-.052.5.0102

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Valuation of Credit Default Swap

• Calculation of PV of accrual pmt
• Yr Def. Prob. Expd A/Pay DF PVEAP
• .5 .0200 .0100S .9753 .0097S
• 1.5 .0196 .0098S .9277 .0091S
• 2.5 .0192 .0096S .8825 .0085S
• 3.5 .0188 .0094S .8395 .0079S
• 4.5 .0184 .0092S .7895 .0074S
• TOTAL .0426S
• a .0192 probability of final accrual pmt
  half-way through 3rd year. Accrual payment .5S,
  so .0192 X .5S .0096Se-.05 2.5.0085S

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Valuation of Credit Default Swap

• Putting it all together and solving for the
  Spread (S)
• PV of Expected pmts 4.0704S
• PV of Accrual pmt 0.0426S
• PV of TOTAL pmts 4.1130S
• PV of TOTAL payoffs .0511
• Set pmts to payoffs and solve for S
• 4.1130S.0511 S.0124
• Mid-market Spread (S) should be 0.124 times the
  principal or 124 basis points per year

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Compute the Value of a CDS

• Probabilities are known, use CDS spreads (As
  discussed earlier)
• Probabilities are unknown, but mid-market CDS
  spreads are known
• Two-step procedure
• Estimate the risk-neutral default probabilities
• Estimate the recovery rate

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Estimation of default probabilities
Why risk-neutral default probabilities instead of
historical data probabilities?(actuarial
default) Actuarial default does not consider
systematic risk faced by whole economy, so it is
usually lower than risk-neutral default
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Estimation of default probabilities (continued)

• How to determine risk-neutral probabilities
• The prices of bonds issued by the reference
  entity provide the main source of data for the
  estimation.
• If we assume that the only reason a corporate
  bond sells for less than a similar Treasury bond
  is the possibility of default, then
• Value of treasury bond-value of corporate bond
  present value of cost of defaults

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Estimation of default probabilities (continued)
Example 5-year zero-coupon Treasury bond with a
face value 100 yields 5 and a similar 5-year
zero-coupon bond issued by a corporation yields
5.5. (Both rates are expressed with continuous
compounding) The value of Treasury bond is
100e-.055 77.8801 The value of
corporate bond is 100e-.0555 75.957 The PV
of the cost of default is
77.8801-75.9572 1.9229
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Estimation of default probabilities (continued)
Let P denotes the probability of default during
the 5-year life of the bond. If we assume there
are no recoveries in the event of default, the
impact of a default is to create a loss of 100 at
the end of the five years. The expected rate of
defaults in a risk-neutral world is 100p and the
present value of the expected loss is
100pe(-0.055) then 100pe(-0.055)1
.9229, get p2.47
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Estimation of Expected Recovery Rate

• The valuation requires estimates of the amount
  claimed by bondholders in the event of a default
  and the expected recovery rate.
• If recovery rate is non-zero, it is necessary to
  make an assumption about the amount the
  bondholders will claim in the event of default.
• The claim can be assumed to equal to face value
  of the bond plus accrued interest. The market
  value of the reference obligation just after
  default is the recovery rate times the sum of its
  face value and accrued interest. So the payoff
  from CDS is
• L-RL1A(t) L1-R-A(t)
• Where L is the notional principal R is the
  recovery rate
• A (t) is the accrued interest on the
  reference obligation at time t as a percent of
  its face value

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Binary Credit Default Swaps

• Same structure as a regular credit default swap
  except the payoff is a fixed dollar amount.
• First calculate the present value of expected
  payment (in terms of s)
• Second calculate the present value of expected
  payoff
• Finally calculate the present value of accrual
  payment (in terms of s)
• Then Present value of payments (in terms of s)
  expected value of expected payoff

EXCEL
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Total Return Swaps

• Swap where one party agrees to pay the other the
  "total return" of a defined underlying asset,
  usually in return for receiving a stream of LIBOR
  based cash flows.
• This is not a common type of Credit Derivative.
• Most commonly used with equity indices, single
  stocks, bonds and defined portfolios of loans,
  mortgages and leases.
• It is a mechanism to accept the economic benefits
  of asset ownership without utilizing the balance
  sheet.

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Total (Rate of) Return Swaps

• Is a financial contract designed to transfer
  credit risk between parties.( TR Payer and TR
  Receiver)
• Payments between the parties to a TR Swap are
  based upon changes in the market valuation of a
  specific credit instrument.
• The payer pays to the receiver the total return
  of an specified Asset
• The change-in-value payment is equal to any
  appreciation (positive) or depreciation
  (negative) in the market value of the Reference
  Obligation.
• TR Return Swaps are often used as financing tool.

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• Total (Rate of) Return Swaps (Cont)

The payer pays the cash flow on an investment in
10 million 5 Corp Bond. The receiver pays the
cash flows on a 10 million Bond that pays LIBOR
plus 25 bp.
POSITION As It borrows money _at_ LIBOR 25 bp
POSITION Retain the Asset. Faces less risk
TOTAL RETURN ON AN ASSET
TOTAL RETURN RECEIVER
TOTAL RETURN PAYER (bank)
LIBOR 25 BASIS POINT
TR
ASSET
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Examples of Total Return Swaps

• Loan Swap
• Assume Bank BBB has a 5 yr fixed rate 5.5 loan
  to Company AAA
• This loan is an asset on Banks balance sheet.
• An investor seeking investment diversification,
  may enter on a Total Return Swap with Bank
  BBB
• In this transaction the investor is entitle to
  the total returns of the loan, including interest
  and any default shortfall.
• In return the bank will receive LIBOR plus 55 bp
  to compensate for the use of its balance sheet.

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Examples of Total Return Swaps

• Equity Index Swap
• Investor willing to match the performance of SP
  500.
• He can buy ETF stocks or SP 500 stocks.
• OR
• Total Return Swap based upon the SP500 index for
  2 Years.
• Every 6 months the investor would receive the
  total return of the index and pay LIBOR plus
  30bp.
• No management costs, and he doesnt have to fund
  the position in stocks. ( Off Balance Sheet )

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Total Return Swaps Motivation

• The Receiver
• To take advantage of Leverage.
• No initial cash payment.
• No upfront collateral is required.
• The Payer
• Creates a hedge for both price and default risk.
• Lock in a return and take a negative view on its
  own asset.
• Defer loss without risking even more losses.

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CDS Forwards

• Forward Is the obligation to buy or sell a
  particular credit default swap in the future.
• Example
• Forward contract to sell 3 years protection on
  Delta Airlines Credit for 290 bp starting next
  year.
• If the company defaults during next year the
  banks obligation ceases.

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CDS Options

• Is an option to buy or sell a particular credit
  default swap in
• the future.
• Example
• An investor may negotiate the right to buy 3
  years protection
• on Delta Airlines Credit for 290 bp starting
  next year.
• If one year from now the CDS tuns out to be more
  than 290bp
• Then the call will be exercised.
• Conversely an investor may negotiate the right
  to sell the same
• Protection (Put Option)

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Collateralized Debt Obligations

• A way of creating securities with widely
  different risk characteristics from a portfolio
  of debt instruments.
• Assets, called collateral, usually comprise loans
  or debt instruments.
• Investors bear the credit risk of the collateral.
• CDO provides a way of creating high quality debt
  from average quality debt.

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Collateralized Debt Obligations

• Multiple tranches of securities are issued by the
  CDO, offering investors various maturity and
  credit risk characteristics
• Tranches are categorized as senior, mezzanine,
  and subordinated/equity, according to their
  degree of credit risk.
• If there are defaults of the CDOs or the CDOs
  collateral otherwise underperforms, scheduled
  payments to senior tranches take precedence over
  those of mezzanine tranches, while scheduled
  payments to mezzanine tranches take precedence
  over those to subordinated/equity tranches.

60
Collateralized Debt Obligations

• Senior and mezzanine tranches are typically
  rated.
• The ratings reflect both the credit quality of
  underlying collateral as well as how much
  protection a given tranche is afforded by
  tranches that are subordinate to it.
• Senior tranches receive ratings of A to AAA.
• Mezzanine tranches receive ratings of B to BBB.

61
Collateralized Debt Obligations

• A CDO has a sponsoring organization, which
  establishes a special purpose vehicle to hold
  collateral and issue securities.
• Sponsors can include banks, other FIs or
  investment managers.
• The creator of the CDO normally retains the
  subordinate tranche and sells the remaining
  tranches in the market.

62

• In its simplest form, a CDO is a debt
  security issued by a special purpose vehicle and
  backed by a diversified loan or bond portfolio

Special Purpose Vehicle
Assets Liabilities
US100 million US100
million
Portfolio of loans, bonds, or CDs either
purchased in secondary market or from balance
sheet of a commercial bank.
Senior tranche US70 million
Mezzanine US20 million
Subordinated US10 million
63
Synthetic CDO

• The creator of the CDO sells a portfolio of
  credit default swaps to third parties.
• It then passes on the default risk to the
  synthetic CDOs tranche holders.
• Synthetic deals can be created in greater size
  than cash deals, and avoid the currency and
  interest rate risk of most cash based CDOs.

64
Typical Synthetic CDO Structure
SPV (protection seller)
Investors (end-seller of Protection)
Highly rated securities (collateral)
Funds
Funds
Risk-free Cash Flow
CDOs (tranched)
Portfolio CDS Premium
Portfolio CDS Settlement following credit
events
Protection Buyer
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Alternative Structure

• An alternative structure for a synthetic CDO (or
  a cash CDO) is where the first tranche agrees to
  absorb losses from the first X of companies that
  default (as opposed to the first X of losses).
• The second tranche agrees to absorb the losses
  from the next Y of defaulting companies, and so
  on.

66
4 Good Reasons for CDO Business

• Spread arbitrage opportunities
• Regulatory capital relief
• Funding
• Economic risk transfer