an introduction to synthetic cdo and its structure
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Synthetic CDO
Himadri Singha (019)
Kumar Vikram (024)
Hozefa Bharmal (078) Group 3
Ritu Agarwal (102)
Subhadip Das (110)
Nikhil Uppal (092)
XLRI Jamshedpur
Basics of Synthetic CDO� This product was introduced where Credit Risk Transfer
was more important
� Credit Risk is transferred by Originator to the Investors by means of CD instruments
� Risk transfer is undertaken by an SPV
� Originator is the “Protection Buyer” and Investors are “Protection Seller”
� Main purpose is to mitigate risk without any asset transfer.
Cash CDO Vs Synthetic CDO
Cash CDO
� Involve a portfolio of cash assets (corporate bonds)
� Ownership of assets is transferred to SPV, issuing the tranches
� SPV bears the operational risk
Synthetic CDO
� Do not own cash assets
� These CDOs gain exposure only to the assets through CDS.
� SPV doesn’t bear the operational risk
Synthetic CDO Structure
Originator
Asset
Asset
Asset
SPV(Protection Seller)
Trustee
High Quality
Asset
Investors
Senior
Mezzanine
Equity
Default
Payment
CDS
Premium
P & I
Proceeds
Coupon
Payment
Waterfall Diagram
Default Payment
Mezzanine Tranche
CDS
Premium
Senior Tranche
Equity
Low Risk
Low Yield
High Risk
High Yield
Types of Synthetic CDO
� Unfunded Synthetic CDO
� Protection seller’s payment obligation is not paid upfront
� Investors are ultimate protection seller.
� Funded Synthetic CDO
� Protection seller’s payment obligation is paid upfront through issuing
CLN
� Proceeds from CLN are invested in Risk Free assets
� Partially Funded Synthetic CDO
Unfunded Synthetic CDOProtection buyer enters into a
CDS with SPV, which in turn,
enters into a CDS with
investors, the ultimate
protection seller
Funded Synthetic CDO
Originator
Asset
Asset
Asset
SPV(Protection Seller)
Trustee
High Quality
Asset
Investors
Senior
Mezzanine
Equity
Default
Payment
CDS
Premium
Coupon
LIBOR +
X bps
Proceeds
From CLN
This is done to “delink” the
credit ratings of the notes
from the rating of the
originator.
Else downgrade of the
originator would downgrade
the issued notes.
Notes equal to 100% of
the value of the ref pool
of assets are issued
Interest payment equal to the yield on
high quality asset + CDS Premium
Partially Funded Synthetic CDO
Originator
Asset
Asset
Asset
Asset
Asset
Asset
SPV(Protection
Seller)
Trustee
High Quality
Asset
Investors
Senior
Mezzanine
Equity
CDS
PremiumCoupon
Libor+
X bps
Pay if default From CLN
Super
Senior
ProtectionUnfunded
Tranche
Funded
Tranche
Proceeds
CDS
Premium
Pay if default
Perceived risk is less
5-10% default risk
SST does not pay purchase
price. Rather SST receives
payments as protection seller
and is liable to pay the originator
if the underlying assets suffer a
loss above specified level.
A typical funding structure
Cash CDO Synthetic CDO
Grade Tranche Size% of
PortfolioTranche Size
% of
Portfolio
Super Senior 43,25,00,000 86.50%
Aaa 43,95,00,000 87.90% 2,00,00,000 4.00%
Aa2 11.500,000 2.30% 12.500,000 2.50%
Baa2 14.000,000 2.80% 15.000,000 3.00%
Equity 3,50,00,000 7.00% 2,00,00,000 4.00%
Total 50,00,00,000 100.00% 50,00,00,000 100.00%
MotivationTypically the reference assets are not actually removed from the sponsoring
firm’s balance sheet. For this reason:
� Synthetic CDOs are easier to execute than cash structures
� the legal documentation and other administrative requirements are less
burdensome
� Synthetic CDO ensures transfer of credit risk of assets not suited for
conventional securitization, while the actual assets are retained on the
balance sheet.
� For example, Bank guarantees, Letter of Credit etc.
� A more efficient way of Credit risk mitigation
� Originator does not have to reduce book size as BS remains unchanged
� The super senior tranche, which prices well below a typical AAA tranche
and which makes up more than 80% of the synthetic CDO, is a major driver
of the economics of the synthetic CDO
Motivation
Cash
Flow CDO
1 billion
dollar
Reference
Portfolio
Senior Tranche (86%)
LIBOR+40bp
Mezzanine (6%)
LIBOR+70bp
Mezzanine (6%)
LIBOR+165bp
Equity (2%)
Synthetic
CDO
1 billion
dollar
Reference
Portfolio
Super Senior Swap(92.5%)
15 bp
Senior (2.5%)
LIBOR+30bp
Mezzanine (3%)
LIBOR+165bp
Equity (2%)
That means if CDO manager can reinvest in collateral pool risk free
asset at, say, (LIBOR-5 bp), it is able to gain from a savings of 20 bp on
each 100 dollar if structure is unfunded
A Considerable Gain
Structure of a CDO TrancheTraditionally, a collateralized debt obligation pool is divided into three
tranches; wherein each tranche behaves as a separate CDO, enabling
the CDO originators to attract multiple investors having varying risk
preferences
1. Senior Tranche or Senior Debt: This is typically highly rated, since
it is ranked on top in terms of priority of payments. However, the
interest rate on investments in this tranche is the lowest due to the
lower risk that accompanies them
2. Mezzanine Tranche: This tranche has moderate returns and
moderate risk
3. Equity Tranche: Investment in this tranche yields the highest
interest rate. This high rate is offered to counter the higher risk on this
tranche. Equity tranche investors are the first to lose funds when loans
in the pool are not repaid
Single Tranche CDOAlso known as ‘tailor made CDOs’, they are customized to
meet the individual investor needs with respect to:
� Portfolio Size
� Asset Classes
� Portfolio diversity and rating
� Portfolio geographical and industrial variation
� Portfolio term to maturity
� Type of collaterals used
� Subordination level
Single Tranche CDO� Single-tranche CDOs represent the vast majority of all new synthetic
CDO issuances.
� The CDO manager sells only a single tranche – usually at the
mezzanine level – of the capital structure to an investor instead of
selling all the tranches at the same time
� The Single Tranche CDO can be issued either directly by the Banks
or via SPVs
Advantages of Single Tranche:
� Single tranche is tailored to the specific investor’s needs
� It is not necessary for the CDO manager to find investors across the
entire capital structure simultaneously
Risk Associated with Synthetic CDO
� Risk of the underlying asset
� Due to the absence of a true sale of the underlying assets,
synthetic CDOs involve the credit risk inherent in the underlying
assets. These assets could be bonds, ABS, MBS, loans etc. The
risk of these assets is generally measured using their credit
rating, historical performances and any other asset specific
information.
� Legal issues associated with the CDO definition
� As there is a conflict of interest between the protection buyer and
the protection seller on the occurrence of a credit event it is of
prime importance that the “trigger events” be clearly defined.
� Counterparty credit risk
� There is a risk of the counterparty’s inability to pay in case of
credit default
Confidentiality & Tax Issues
ConfidentialityGenerally the Protection Buyer cannot share the names of the
Reference Entity with the Protection Seller due to issues of
confidentiality. In order to counter this situation one can nevertheless
� Define general eligibility criteria with which the Reference Obligations
� and Reference Portfolio must comply,
� Appoint the Protection Buyer itself as calculation agent (who determines
whether or not a Credit Event has occurred) and
� Give a supervising role to the Protection Buyer’s external auditors.
Tax IssuesSince the title of the reference Obligations are not transferred to the
Protection Seller, taxation is not a major consideration in the case of a
Synthetic CDO
Moody’s Ratings Framework
� Moody's rating on each rated note represents the expected loss
on the note, which is the difference between the present value
of the expected payments on the note and the present value of
the promised payments under the note, expressed as a
percentage of the present value of the promise
� To evaluate the expected loss, Moody’s incorporates both
quantitative and qualitative analysis
� Moody's expected loss models capture the quantifiable risks
while a legal review of the transaction seeks to ensure that non-
quantifiable risks are mitigated through documentation
provisions
Quantitative Analyses
� The primary source of risk in a synthetic CDO comes from the
reference pool
� Moody’s uses the quantitative analysis to assess the risks
stemming from the reference pool
� The premium payments are excluded from the scope of the
quantitative analysis because the promised premium is large
enough to ensure coverage of the interest payments on the
CDO
� There are two primary methods to model a default risk:
� Binomial Expansion Modeling
� Multiple Binomial Modeling
Binomial Expansion Modeling
� Primarily used for a pool of homogeneous assets
� A model portfolio is created which contains a pool of N diversity
bonds
� Each diversity bond is assumed to have identical characteristics
in terms of par/notional amount, rating, average life, spread and
recovery, and is uncorrelated with every other diversity bond in
the pool
� The number of diversity bonds in the portfolio is equivalent to
Moody's diversity score
Binomial Expansion Modeling
� The losses stemming from the default of each additional diversity
bond in the model portfolio going from zero diversity bond
defaults to N diversity bond defaults is calculated and a
probability assigned to each default scenario
� Calculating this probability-weighted loss for each CDO tranche
generates the expected loss
Multiple Binomial Modeling
� An extension of the Double Binomial Method, used in cases where the
underlying portfolio assets exhibit heterogeneous characteristics -
such as having a clear delineation between low rated and highly rated
assets
� Moody’s divides a pool of reference entities/credits into the most
appropriate number of sub-pools and models the default behavior of
each pool with a separate binomial analysis
� Each diversity bond is assumed to have identical characteristics in
terms of par/notional amount, rating, average life, spread and
recovery, and is uncorrelated with every other diversity bond in the
pool
Multiple Binomial Modeling
The mathematical expression for the multiple binomial-based
expected loss used by Moody’s is as below:
Multiple Binomial Modeling
Factors which warrant the use of the Multiple Binomial Method to quantify
the inherent risks are:
� Portfolio Characteristics
� Most synthetic CDOs have reference entities/credits whose ratings
can vary greatly (typically Aaa down to Baa3 or even Ba3), for a 5-
year synthetic CDO, Moody's idealized default probability can vary
from as little as 0.003% for a Aaa credit to 3.05% for a Baa3 credit
and 11.86% for a Ba3 credit
Multiple Binomial Modeling
� Capital Structure
� Most synthetic CDOs are highly leveraged and are thus sensitive to
fewer defaults than cash flow CDOs .Hence only a small amount of
subordination is necessary to support high ratings. This thin
subordination combined with the relatively small sizes of the rated
tranches generally requires more precision in the calculation of the tail
probability of the loss distribution.
� Structural Features, or Lack Thereof
� Many synthetic CDOs do not have the ability to generate any excess
spread that may be used to offset losses in the reference pool. Hence,
it is even more important to capture the correct loss distribution when
analysing the expected loss of a CDO tranche
Qualitative Analysis
� In case risks inherent in a synthetic CDO are not or cannot be modeled
quantitatively, they would be addressed through the legal
documentation, and hence the importance of Qualitative Analysis
� The important aspects of the qualitative analysis unique to synthetic
CDOs can be grouped into three main categories:
� Trading guidelines for managed synthetic CDOs
� Credit event definitions and their effects on the modeled default
probabilities
� Structural features such as valuation procedures and settlement
mechanisms that affect recovery rate assumptions.
NIG for Synthetic CDO Pricing
� Normal Inverse Gaussian Distribution for Synthetic CDO pricing is an
extension of the popular Large Homogeneous Portfolio (LHP),
approach to CDO pricing
� LHP assumes a flat default correlation structure over the reference
credit portfolio and models defaults using a 1-factor Gaussian copula
� This model leads to an implied correlation skew, as it fails to fit the
prices of different CDO tranches simultaneously
� This is explained by the lack of tail dependence in the Gaussian
copula and a Student t-distribution is proposed
� However, the t-distribution leads to an increase in computation time
and therefore the NIG is proposed
NIG for Synthetic CDO Pricing
� Normal Inverse Gaussian Distribution is a special case of the
generalized hyperbolic distribution
� They are flexible four parameter distribution family that can produce fat
tails and skewness
Properties of NIG
� Normal Inverse Gaussian Distribution is a mixture of the normal and
the inverse Gaussian distributions
� They are flexible four parameter distribution family that can produce
fat tails and skewness
� A non-negative random variable Y has an Inverse Gaussian
distribution with parameters:
Hence
Properties of NIG
� A random variable X follows a Normal Inverse Gaussian Distribution
with parameters
� They density and probability functions are thus:
Properties of NIG
� The main properties of the NIG distribution class are the scaling
property:
� And the closure under convolution for independent random variables X
and Y:
Derivation of Pricing formula using
NIG:� Since M does not depend on a, we set:
� The random variable,
� Is NIG distributed and its parameters are:
Derivation of Pricing formula using
NIG:� Thereafter the 3rd and 4th parameters are restricted to standardize
the distributions of both the factors:
� With
Derivation of Pricing formula using
NIG:� Starting with:
� Then applying the scaling property we get:
� Thereafter applying the convolution property to
Derivation of Pricing formula using
NIG:� Finally, we get:
� The above is the expression for the NIG distribution function and
the density
� Time to market is less compared to a cash deal, with average execution
time typically varies from six to eight weeks based on the structure
compared to three to four months for an equivalent cash deal
� Leads to lower transaction cost as SPV setup cost can be avoided
� Use of credit derivatives offer greater flexibility for risk requirement
� Cost of buying protection is lower and credit protection price is below the
note liability
� Range of reference asset is wider and typically includes bank guarantee,
derivative instruments
� Clients whose loans need not be sold off from the sponsoring agent’s
B/S can be better handled and leads to improved customer relationship
� Credit default swap is cheaper than the underlying cash bond for many
reference names
Advantages
� Three key factors are being considered by analystP
� Default probabilities and cumulative default rates
� Default correlations
� Recovery rates
Default Probability rates
� A number of methods are used to estimate default probabilities like
individual credit ratings and historical probability rates
� Common method is to use average rating of the reference portfolio which
consists of 150 or more reference names
� Rating agencies like Moody’s provide data on the default rates for
different ratings as an average class
Factors to consider during analysis
� Correlations among underlying assets pool is taken into
consideration during analysis
� Because correlation is unobservable, differences of opinion
among market participants as to the correct default
correlation creates trading opportunities
� Diversity score of a CDO plays a part in calculating the
precise correlation value which is used to map the
underlying CDO portfolio into a hypothetical portfolio
consisting of homogeneous assets
� It represents the number of uncorrelated bonds with
identical par value and with the same default probability
Correlations
� Generally analyst constructs a database of recovery rates by industry types and credit ratings used by different agencies
� However, for synthetic CDOs with credit default swap as assets in the portfolio, this factor needs to be ignored
� Analyst performs simulation model to generate scenarios of default and expected returns
� All variables like the number of defaults swap to maturity, recovery rates and timing of defaults etc. are considered as random and thus modeled using stochastic process
� However, actual recovery rates might differ based on the macroeconomic factors
Recovery rates
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