Credit Derivatives

1
Credit Derivatives
By A. V. Vedpuriswar
February 8, 2009
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Historical perspective on credit derivatives

• Traditionally, credit risk has differentiated
  commercial banks from investment banks.
• Commercial banks are in the credit risk
  business.
• Investment banks are in the market risk
  business.
• Investment banks are not comfortable with
  holding anything for a long time.
• Commercial banks on the other hand use their
  huge balance sheets and ability to take credit
  risk to gain more business.
• Commercial banks have also enjoyed the advantage
  of no mark-to-market accounting, unlike
  investment banks.

3
Historical perspective on credit markets

• Investment banks wanted to enter credit
  markets.
• Till the advent of credit derivatives, the only
  way to deal with credit risk was to sell it.
• But selling a loan required the permission of
  the borrower.
• This might hamper the relationship.
• How could banks transfer the credit risk without
  actually selling the loan?

4
Innovations from Bankers Trust (1)

• The first innovation was the total return swap.
• A bank wanted to accommodate a client without
  increasing credit risk.
• The bank entered into a swap with Bankers Trust.
• BT got the interest on the loan and capital
  gain.
• BT had to pay in case of capital loss.
• BT paid a funding cost to the bank.
• Loan was held on the banks balance sheet
  without assuming credit risk.

5
Innovations from Bankers Trust (2)

• Japanese banks had sold options to BT.
• These options were now deep in the money.
• BT faced a lot of credit risk vis a vis the
  banks.
• Japanese banks were not doing well.
• BT sold investors a five year bond.
• It was linked to a portfolio of five Japanese
  banks, each rated A.

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Innovations from Bankers Trust (2) cont..

• The bonds paid a relatively high rate of
  interest.
• But if any of the banks defaulted on its
  obligations, the investors suffered losses and
  did not get their investments back.
• Instead they got bonds issued by the defaulting
  bank.
• The bonds delivered had a face value equal to
  the initial investment.
• This came to be called the first-to-default,
  basket.

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The emergence of Credit Default Swaps

• CDS emerged out of the need for credit
  protection.
• Protection buyer pays counterparty a fee.
• The investor agrees to indemnify the bank
  against losses in case of default.
• Compensation is payable in case of default.
• CDS is effectively an insurance against
  bankruptcy.

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What is a CDS?

• Is it an insurance?
• Is it a swap?
• Is it a forward?
• It is actually an option.
• Bought by the protection buyer.
• Sold by the protection seller.
• The strike price is the par value of the
  reference asset.
• The option can only be exercised in case of a
  credit event.

9
CDS vs Insurance

• Only licensed players can sell insurance.
• CDS is an unregulated business.
• The CDS is a bet between two people on whether
  the borrower will pay up.
• It has little to do directly with the loan.
• Imagine buying insurance on a house we do not
  own!

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The Basics of CDS

• Pay off is linked to credit events.
• Insurance is provided against default by a
  particular company, known as the reference
  entity.
• Buyer makes periodic payments to seller until the
  end of the life of the CDS or until a credit
  event.
• In the event of a default, settlement takes place
  by physical delivery of bonds or cash payment.
• CDS spread is the total amount paid per year as a
  percent of the notional principal.
• The CDS spread should be roughly equal to the
  excess of the par yield of a corporate bond over
  the par yield of a risk free bond. If this is not
  so, arbitrage is possible.

11
Who is the reference entity?

• The reference entity lies at the heart of a CDS.
• But identifying the entity is not always easy.
• In 2000, UBS bought protection on Armstrong
  World Industries from Deutsche Bank.
• AWI was restructured and sold to Armstrong
  Holding
• UBS claimed the reference entity was bankrupt.
• Deutsche Bank refused to pay up.
• Eventually, the dispute was settled out of
  court.

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Credit events

• Credit events can be of various types
• - Failure to pay
• - Bankruptcy
• - Moratorium
• - Repudiation
• - Restructuring

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How much will be paid?

• There are two mechanisms
• - Cash settlement
• - Delivery
• The key is in establishing the market price of
  the bond after default.
• But a market may not exist for these bonds.

14
Cheapest to deliver bond

• Usually, a number of different bonds can be
  delivered in the event of a default.
• When a default happens, the protection buyer can
  review alternative deliverable bonds.
• The cheapest bond can be delivered.

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Credit Indices

• CDX (USA)
• Traxx (Europe)

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Valuation of CDS

• Present value of expected payments for protection
  seller is equated with the pay off in case of a
  default.
• Default probabilities have to be estimated.
• Recovery rate also has to be estimated.
• The exception is a binary CDS, where the pay off
  in case of a default is independent of recovery
  rate.

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Related instruments

• A forward CDS is the obligation to buy or sell a
  particular CDS on a particular reference entity
  at a particular future time, T.
• If the reference entity defaults, before time, T,
  the forward contract cases to exist.
• A CDS option is an option to buy or sell a
  particular CDS on a particular reference entity
  at a particular time, T.
• A basket CDS involves a number of reference
  entities.
• An add up basket CDS provides a pay off when any
  of the reference entities default.

18
Related instruments

• A first to default CDS provides a pay off only
  when the first default occurs.
• A second to default CDS provides a pay off only
  when the second default occurs.
• An nth default CDS provides a pay off only when
  the nth default occurs.

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Total return swap

• This is a swap of the total return of the asset
  against a contracted pre fixed return.
• The protection buyer is not only concerned with
  losses in case of a credit event but also in case
  of mark to market losses.
• Usually, mark to market losses continue for
  sometime before defaults start.
• By total returns we mean actual earnings from the
  reference asset and the actual appreciation or
  depreciation in price.
• The protection seller guarantees a pre fixed
  spread.
• The protection buyer passes on actual
  collections and variations in prices to the
  protection seller.

20
Credit linked notes

• CLNs convert credit derivatives into bond form.
• The protection buyer issues notes/bonds with an
  embedded credit derivative.
• The protection seller buys the CLNs.
• In case of credit events, the amount due is
  appropriated and only the balance is given to the
  protection seller.
• The CLN carries a coupon which represents the
  interest on the funding and the credit risk
  premium on the protection sold.

21
Credit spread option

• It is a call or put option on an asset
  exercisable, based on a certain spread.
• The holder of the option is the protection buyer.
• If the spread of a particular bond exceeds a
  spread over LIBOR ( the strike spread), the
  protection buyer can exercise the option.
• An option to put an asset is an option to call a
  pre determined spread.
• An option to call an asset is an option to put a
  pre determined spread.
• Credit spread options are not based only on
  credit default.
• Spreads can be related to various factors besides
  credit events.

22
Collateralised Debt Obligations

• A CDO is a way of creating securities with widely
  different risk characteristics from a portfolio
  of debt instruments.
• These tranches are called equity, mezzanine
  (subordinated) and senior trenches respectively.
• The creator of the CDO normally retains the
  equity tranche and sells the remaining tranches
  in the market.
• Senior note holders take a hit only when losses
  on the equity/mezzanine trenches cross pre
  specified limits.

23
Synthetic CDO

• Credit is transferred but not the loan itself.
• Bank keeps the loans on its books.
• Enters into a CDS on the loans with the SPV.
• SPV receives fees.
• In turn, SPV offers credit protection.
• SPV raises money as in a normal CDO.
• But the money is parked in government bonds.
• The bonds are pledged to cover any payments that
  the SPV may have to make to the bank under the
  CDS if any entity defaults.
• Synthetic securitisation avoids the need to get
  the clients consent.

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Problem

• The total notional amount of a set of corporate
  bonds is 1,000,000. The duration is 4. The
  bonds are selling at par. The current bond yield
  is 8 while the T Bill yield is 6. Credit spread
  put options are available with a strike spread of
  3. They will mature in 90 days. On the day of
  expiry of the options, the bond price has dropped
  to 93. The bond yield is 10. The T bill yield
  remains unchanged. How will an investor in the
  corporate bonds benefit by buying the option?

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• Spread on the date of maturity 10-6 4
• Since this is more than 3, the option will be
  exercised.
• Payoff (1, 000, 000 ) (4)( .04-.03)
  40,000
• Loss on the face value of the bond
• 1,000,000(.07) 70,000.
• The net loss is 70,000 40,000 30,000.

26
Problem

• The notional principal of a credit spread put
  option is 1,000,000. The yield is 9 while the
  duration is 3.57. T bill yield is 7. The option
  has a strike spread of 3. On the date of
  maturity, the bonds are yielding 13.79 and
  trading at 860,000. What is the payoff?

27

• Loss on the bond principal
• 1,000,000 860,000 140,000.
• Gain on the put
• (13.79- 7 - 3)(.01)(3.57)(1,000,000)
  135,303
• Net loss
• 140,000 - 135,303 4697

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Problem

• The notional principal in a credit spread
  forward contract is 1,000,000. The spread
  agreed to at the beginning of the contract is 3.
  The duration of the bonds is 4. If the spread
  increases to 4, what will be the implications
  for the buyer?

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• The loss for the buyer (1,000,000)(4)(.04 -.03)
  40,000.
• This is the gain for the seller.

30

• The notional principal in a credit spread
  forward contract is 3,000,000. The spread
  agreed to at the beginning of the contract is
  4.3. The duration of the bonds is 3.6. If the
  spread increases to 6.86 on the date of maturity
  , what will be the implications for the buyer?

31

• The spread widens. So the buyer incurs a loss.
• Loss for the buyer
• (3,000,000)(0.0686-0.0430)(3.6) 276,480
• This is a gain for the seller.

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Problem

• Suppose the probability of a reference entity
  defaulting during a year, conditional on no
  earlier default is 2. Assume the risk free
  LIBOR rate is 5. The recovery rate, in case of
  a default is 40. Assume the notional principal
  is 1 and the payment for protection, s is made
  every year at the end of the year. Assume
  defaults happen midway during the year. If the
  maturity of the swap is 5 years, how will you
  price the credit default swap.

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Solution

• 4.0705 s is the amount of payment made to
  receive credit protection.

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Solution Cont..

• Now we calculate the present value of the
  amounts that cannot be recovered. The defaults
  happen in the middle of the year. So the
  recovery also happens in the middle of the year.

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35
Solution Cont..

• Now we calculate the accrual amount in the event
  of a default.

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Solution Cont..

• So to break even,
• 4.0705s .0426 s .0511
• s .0124
• So the quote must be 124 basis points per year
  (124 basis points 1.24 0.124)

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Problem

• A enters into a 4 year credit default swap with B
  to hedge a 500 million bond. The probability of
  default is 3, recovery 30 in the event of
  default and the risk free rate is 6 compounded
  continuously. The premium is paid annually.
  Defaults happen only mid way during a year. What
  is the CDS spread?

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Solution

• Let the CDS spread be s.
• Premium payable every year (500(s)
• Present value of premium payment (no default)

• Present value (500s) (3.2068) 1603.4s

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Solution (Cont..)

• Present value of premium payment (default)

• Present value 25.55s

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Solution (Cont..)

• Present value of compensation receivable (in case
  of default)

• Present value (.1022) (500) (.70) 35.77
• To break even, we can write 1603.4s
  25.55s 35.77
• or s .02196
• 2.20 220 basis points