Review and Announcement

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Review and Announcement

• Default facts, rating, models
• Examples with structural models
• Proposal due Thursday

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MFIN 7011 Credit RiskSummer, 2008Dragon Tang

• Lecture 9
• Credit Derivatives
• Tuesday, July 22, 2008
• Readings
• Duffie and Singleton Chapter 8
• Graveline and Kokalari (2006)

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Credit Derivatives

• Objectives
• Usefulness of credit derivatives
• Different types of credit derivatives
• Spread option pricing

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How Citigroup Survived in Enron Case

• Enrons two largest creditors Citigroup and J.P.
  Morgan Chase
• Citigroup lent about 5.0 billion to Enron
• J.P. Morgan Chase lent 2.6 billion to Enron
• However, J.P. Morgan Chase was hit harder than
  Citi!
• Citigroup created protection (insurance) on its
  Enron exposure good use of credit derivatives!
• J.P. Morgan Chase bought insurance (through
  surety bonds), insurer requested a 400 million
  discharge for being defrauded
• Caveat Legal losses for helping Enron to raise
  money
• Citi 2.0 billion for class action 120 million
  to SEC, 25 million to NY
• J.P. Morgan Chase 2.2 billion for class action
  135 million to SEC 25 million to NY

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Caveat Citigroup and Enron (Yosemite Example)

• Citigroup helped Enron to disguise its debt as
  trade through commodity prepay transactions
• Citi helped Yosemite (a special purpose entity
  for Enron) raised 800m from investors at 8.25,
  transferred the money to Delta (a SPE of Citi),
  which then paid Enron for oil in the future,
  Enron then paid Citi for oil in the future and
  Citi paid Delta for oil in the future, circular
  cancellation resulting in Delta returning money
  to Yosemite, Enron then paid Yosemite at least
  8.25
• Similarly, Mahonia case for J.P. Morgan Chase
• Such transactions were reasons Citi and Morgan
  were fined

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Citigroup Enron Credit Derivative

• The credit derivative used by Citigroup was
  Credit Linked Notes (CLN) on Enron
• Citi sold CLNs to investors
• Those CLN has fixed maturity, coupon, and
  principal
• However, if Enron went bankruptcy before CLN
  maturity, investors would receive Enron bonds
  instead of their principal
• Citi benefited from
• Transferring exposure to Enron default to
  investors
• Paying low coupon rate (7.37) on CLNs (possibly
  due to Citis information advantage) instead of
  8.07
• Caveat Investors could sue Citi for insider
  trading?
• (In my opinion) Citis Enron CLNs (infamously)
  marked a milestone in the development of credit
  derivatives market

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Credit Derivatives Cure for Credit Risk

• Credit risk is a disease affecting economic
  growth
• E.g., largest four banks in China carried about
  300 billion non-performing loans (NPL) in 2004.
  By 2006, NPL in China dropped to 160 billion
• One way to eliminate credit risk Not lend any
  money!
• Another more realistic way pay first, service
  later
• Better yet sell credit risk to somebody who
  loves it
• Credit risk transfer (CRT) facilitates the
  separation of credit risk from other parts of the
  cash flow
• Biggest financial innovation in the last two
  decades
• Credit derivatives tools to manage credit risk
• Credit risk of one single entity transfer it
  from seller to buyer
• Credit risk of a pool of entities repackage and
  re-distribute credit risk

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Usefulness of Credit Derivatives

• Separate the management of credit risk from the
  asset with which that risk is associated
• The Reference Entity, whose credit risk is being
  transferred, need neither be party to nor aware
  of a credit derivative transaction. This
  confidentiality enables banks and corporate
  treasurers to manage their credit risks
  discreetly without interfering with important
  customer relationships
• Credit derivatives are the first mechanism via
  which short sales of credit instruments can be
  executed with any reasonable liquidity and
  without the risk of a short squeeze. The
  alternative for banks would have to short sell
  their loan which is more or less impossible.
• Credit derivatives are off-balance sheet
  instruments. The more costly the balance sheet,
  the greater the appeal of an off-balance-sheet
  alternative.

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Growth of Credit Derivatives Markets (1996-2008
est., in Billions)
First credit derivative was created by JP Morgan
in 1995.
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Participants of Credit Derivatives Markets

• Most lucrative financial market currently, All
  big players (institutional investors), biggest
  players are Deutsche Bank, Morgan Stanley,
  Goldman Sachs, and J.P. Morgan Chase
• Commercial Banks hedging credit exposure (may
  also trade/speculate to take advantage of better
  information)
• Securities houses 2/3 trading 1/3 hedging
• Insurance companies provide insurance against
  credit risk and collect premium
• Hedge funds speculating
• Mutual funds, pension funds, corporations,
  governments
• Mostly Over-the-counter (OTC) contracts, started
  listing on Chicago Mercantile Exchange in 2007

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Participants of Credit Derivatives Markets
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Types of Credit Derivatives

• Total return swap With a total return swap, an
  asset owner transfers the total return of a
  specific asset (with credit exposure), such as a
  bond or trade receivables, to a counterpart in
  exchange for a fee
• The underlying asset is not transferred
• Similar to interest rate swap
• Credit default swap (CDS) one party pays the
  other a periodic fee in exchange for loss in
  credit events (more details to come)
• Credit linked notes (CLN) a debt note CDS
• Credit spread options protection against changes
  in credit spreads
• Collateralized debt obligations (CDO) claims to
  a pool of credit products in different seniority
  tranches (more details to come)
• Credit can be on loan, bond, mortgage etc.
• Reallocating credit risk to equating supply and
  demand for credit products (e.g., AAA has high
  demand but low supply, CDO can create more
  AAA-like securities)
• CDS Indices and CDS options

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Types of Credit Derivatives by Market Share
More than half of underlying assets for credit
derivatives are rated A/BBB.
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Total Rate of Return Swaps (TRORS)

• TRORS is a form of financing
• TRORS allows an investor to enjoy the cash flow
  without actually owning the security
• At the end of the TRORS, the TROR receiver pays
  any decline in price to the TROR payer and gets
  the increase in price from the TROR payer
• He pays a regular floating rate payment on a
  periodic basis
• TRORS are off-balance sheet transactions, the
  highest volume and the most popular sector of the
  credit derivative market
• Low-cost borrowers with large global balance
  sheet are naturally advantaged as payers in TRORS

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TRORS
TROR
Payer of TROR
Receiver of TROR
LIBOR Spread
TROR
Reference Asset
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TRORS

• Total return Coupons (final value original
  value)
• Reference Asset Bond, Loan, Index, Equity,
  Commodity
• TROR Receiver is long both price and default risk
  of the reference asset.
• Receivers of TROR are often referred to as
  investors
• TROR Payer is the legal owner of the reference
  asset
• TRORS usually terminates in the event of default
• Receiver make the net payment of the price
  depreciation
• Or, receiver takes delivery of the reference
  asset and pay the original price to the payer

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Motivation of Receiver

• The compelling reason to become a receiver of
  TRORS is leverage
• No initial cash payment is required cash flows
  are usually paid on a net basis
• Hedge funds are eager to be TROR receivers
• Hedge funds and other lesser credits usually have
  to deposit collateral

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Exercise

• Three investors want to receive the total rate of
  return of a given asset.
• The asset is a BB- bond with a coupon of LIBOR
  150 bps, with the current yield 8.30
• LIBOR is currently at 5.80
• Two of the investors are hedge funds and must pay
  a funding cost of LIBOR 100. The third investor
  is a mutual fund, which pays cash for the
  investment. The first hedge funds has to put up
  5 up front collateral, the second deposits 10.
  The collateral earns LIBOR flat.
• Calculate the net return rate for the three
  investors

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Motivation of Payer

• Creates a hedge for price risk and default risk
  of the reference asset
• Effectively creates a short position of the
  reference asset, without legally shorting it
• Accounting/Tax Reasons Can defer unrecognized
  loss in a bond position, without risking further
  losses
• This does not work under the US tax regime
  paying the TROR on an asset will be evaluated as
  a true sale

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Creating Synthetic Assets

• A financial institution can short credits even in
  maturities for which no reference asset exists
• The return of the underlying asset can have a cap
  or a floor
• Mismatch maturity TRORS has shorter maturity
  than the reference asset
• Investor of TRORS bears price risk
• Not the same as the tranched asset swap asset
  swap package which can be put back to the seller
  provided the reference bonds are not in default
  so the seller is immunized from the default risk
  but not the market-price risk or
  credit-spread-widening risk if the put is
  exercised.

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Funding Arbitrage
A- Bank
AA Bank
Funding LIBOR30bps
TROR
TROR
Funding LIBOR-15bps
BBB Asset LIBOR65bps
BBB Asset LIBOR65bps
Net Spread 35bps
Net Spread 80bps
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Funding Arbitrage
TROR
AA Bank
A- Bank
LIBOR 15bps
TROR
LIBOR - 15bps
BBB Asset LIBOR65bps
Net Spread 30bps (Collateralized loan)
Net Spread 50bps
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Funding Arbitrage

• Benefits to the AA bank
• hedge market and credit risk of the BBB asset
• reduce the capital charge of the transaction if
  A- bank and BBB asset are independent, then the
  implied rating on the effective credit risk to
  the AA bank is A
• Benefits to the A- bank
• lock in a favorable financing rate 15bps
  reduction
• No need to put up any economic capital
• A leveraged off-balance sheet transaction
• It works because of the difference in the funding
  costs of the two institutions

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Funding Arbitrage
A- Bank
AA Bank
Funding LIBOR15bps
TROR
Off Balance Sheet BBB Rated 100 BIS Asset 50bps
Synthetic A Rated 20 BIS Asset 30bps Net
Coupon
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Balance Sheet Management

• The capital market desk of a bank is in the
  business to issue bonds. Sometimes, it ends up
  not being able to sell off all the bonds it
  underwrites.
• One way to offload the bonds from the balance
  sheet is to sell them to a conduit of another
  bank. The conduit purchases the bonds funded with
  a commercial paper program.
• The conduit does not want to take the risk of the
  bonds, therefore it pays the TROR on the bonds to
  the internal derivatives desk. The derivatives
  desk then passes the risk by paying the TROR on
  the bonds to a subsidiary of the original bank
• End effect The asset is legally off loaded from
  the balance sheet, but the risk remains with the
  originating bank.

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Balance Sheet Management
Bonds
LIBOR X
Bank As CMD
Bank Bs Conduit
CP Markets
10 millions
10 millions
TROR on 10 million bonds
LIBOR X 10 bps
TROR on 10 million bonds
Bank Bs Derivatives Desk
Bank As Subsidiary
LIBOR X 15 bps
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Credit Linked Notes (CLN)

• The most basic CLN consists of a bond, issued by
  a well-rated borrower, packaged with a credit
  default swap on a less credit worthy risk
• SPV organizer does not bear credit risk of
  borrower investors can be separated into
  different tranches (first tranche absorbs initial
  default losses)

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Why Credit-Linked Notes?

• There is no need for an ISDA master agreement or
  confirmation simple documentation
• Investor who are not authorized to do derivatives
  or off-balance sheet transactions can participate
• Credit lines to the investor, the hedge provider,
  are not used. This is particularly valuable for
  very long dated or leveraged transactions
• It doesnt matter that the investor is providing
  a hedge and is highly correlated with the
  reference credit, as the issuer gets par up front
• The credit quality of the investor is irrelevant

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Four Major Structure Types of CLNs

• Principal-protected notes
• Receive the credit rating of the issuer
• The investor risks loss of coupon income in the
  event of default of a different reference credit
• Boosted coupon notes
• Receive the credit rating of the issuer
• The principal payment is linked to the default
  event and default value of a different reference
  credit, with underlying credit risk of a
  lower-rated credit
• Boosted coupon notes
• Receive the credit rating of the issuer
• The principal payment is linked to the default
  event of a different reference credit(s)
• the principal payment may have levered risk or
  even risk of loss of the entire principal amount
  in the event of a default of the reference
  credit(s)
• Reduced coupon notes
• Receive the credit rating of the issuer
• The principal repayment is face amount
• The termination payment is enhanced by the loss
  in the event of default of a reference asset

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CDS Indices

• Benchmark indices for overall credit market
  condition
• North America and emerging markets Dow Jones CDX
• CDX.NA.IG 125 most liquid investment grade
  individual CDS average, updated every half year
• CDX.NA.HY 100 most liquid high yield individual
  CDS average, updated every half year
• Europe and Asia iTraxx
• iTraxx Europe 125 most liquid European
  individual CDS
• iTraxx CJ 50 most liquid Japanese individual CDS
• Each index has different tranches
• 0-3 tranche absorbs the first 3 of losses
  similarly for 3-7 7-10 10-15 15-30
  tranches

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Pricing Derivatives

• The dynamic of the underlying asset
• The payoff of the derivative
• Then, the price of the derivative

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Risks in Underlying Assets

• Interest risk
• Default risk
• Recovery risk
• Spread risk (changes of the rating)
• Liquidity risk

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Spread Models

• Spread models do not break down the spread into
  default risk and recovery risk components
• It is easier to directly model the spread itself
• This approach is ideal in modeling credit spread
  options

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Spread Models

• The spread is assumed to follow
• where s is the spread, k is the rate of mean
  reversion, ? is the long run mean of the spread,
  s is the volatility coefficient, and dz is the
  Wiener increment.
• In the simplest case, the model assumes that
  interest rates are constant, which is a
  reasonable assumption to make when the spread
  option has short maturity

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Spread Option Pricing

• European spread option pricing
• where R is an appropriate discount rate, K is
  the threshold spread or exercise price, and f(sT)
  is the probability function

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A One-Factor Spread Model

• Two-period model with each period equal to one
  year
• Term structure of riskless rate r0.08,0.09
• Term structure of spread rate s0.010,0.015
• Then
• Term structure of risk rate rs 0.09,0.105
• The price of a risk zero coupon bond of maturity
  two yeas (face value 100)
• 81.8984 100/(10.105)2
• The riskless forward rate
• f12 1.092/1.08 1 0.1001

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A One-Factor Spread Model

• A simple discrete binomial representation of the
  model
• In order to undertake pricing without violation
  of arbitrage, under a risk-neutral regime, it is
  necessary to risk-adjust the stochastic process
  above by modifying its drift term by adding ?
• s(t) can take one of two values (with equal
  probability)

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A One-Factor Spread Model

• Assumptions
• s(0)0.010
• k0.2
• ?0.02
• s0.03
• With equal risk-neutral probability(0.5)

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A One-Factor Spread Model

• The price of a 2-year risky zero

81.8984 100/(10.105)2
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A One-Factor Spread Model

• Then
• ? 0.0081
• Spread call option (K0.02)
• Face Value(0.0231-0.02)0.5/1.08

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Extensions

• Extend these models to multi-periods
• Incorporate an additional factor
• Make the interest rate stochastic and correlated
  with the credit spread

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Counterparty Risk

• Many contracts are traded over-the-counter
  between default-prone parties
• Each side of the contract is thus exposed to the
  counterparty risk of the other party

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Credit Risk of Derivatives

• Unilateral default risk
• European option
• The option writer may default on his obligations
• The default risk of the option holder is
  manifestly not relevant
• Bilateral default risk
• Defaultable swaps
• Swap agreements between two default-prone
  entities
• Note a defaultable swap should not be confused
  with a default swap, which is a credit
  derivative, a form of insurance against the
  reference risk

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Summary

• Brief introduction of credit derivatives
• Usefulness
• Types
• Spread option pricing
• Next Credit Default Swaps (CDS)