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