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From pricing to rating structured credit products and vice-versa

( Télécharger le fichier original )
par Quentin Lintzer
Université Pierre et Marie Curie - Paris VI - Master 2 2007
  

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s = (1 - R) ·

>n (S0(Ti_1) )

i=1 D(0, Ti) S0(Ti) - 1

(1.1)

 
 

1.2.2 Credit indices

Credit indices are convenient proxys for taking credit exposure on diversified portfolios of single names. They can be sorted by geographical criteria (Europe, Asia, US, Japan, Emerging markets), by industrial sector (e.g. Financials) or by debt riskiness criteria (investment grade, high yield). Among all indices, one shall bear in mind the ones detailed hereafter:

Index name

Debt riskiness

Characteristics

CDX.NA.IG

Investment grade

Diversified portfolio of 125 North American liquid corporate credits

CDX.NA.HY

High Yield

Broad-based portfolio of 100 high yield credits, i.e. sub-investment grade

ITRAXX IG

Investment grade

Diversified portfolio of 125 European liquid corporate credits

ITRAXX XOVER

High Yield

Diversified portfolio of 125 European

high yield credits, i.e. sub-investment grade

 

Similarly to single-name CDS, they are quoted in terms of spread (measured in basis points) over LIBOR/EURIBOR rate. Given that all single-name components are equally weighted in credit indices, an event of default on a single name triggers a proportionate reduction in the notional amount of the index and a lump sum payment from the protection seller to the protection buyer.

1.2.3 Collateralized Synthetic Obligations Basic principles

Collateralized Synthetic Obligations (CSO) are securities issued by a Special Purpose Vehicle (SPV) and backed by a portfolio of credit protection-selling positions taken through several (usually over 100) CDS. The liabilities of the SPV get sliced into several CSO tranches that get hit sequentially in case one or more reference entities within the underlying CDS portfolio default. As a result, the fair premium of any tranche, usually expressed as a spread over 3-month LIBOR/EURIBOR rate, eventually depends on the joint-loss distribution of the underlying CDS portfolio.

CSO tranches can be defined by their attachment and detachment points:

· The attachment point l of the tranche is expressed as a percentage of the investment notional. It is the portfolio loss lower threshold above which the tranche's principal gets hit if one or several reference entities default within the portfolio.

· The detachment point u > l of the tranche is expressed as a percentage of the investment notional. It is the portfolio loss upper threshold above which the tranche's principal gets wiped out after one or several events of default.

CSO tranches are labelled upon their seniority in the capital structure:


· The equity tranche has the lowest attachment point of the structure - 0% - and usually a detachment point below 3%. Hence it is the riskiest tranche of the structure.

· The super senior tranche has the highest attachment point of the structure - usually around 22% - and a detachment point of 100%.

· Mezzanine tranches have an attachment point above the equity's detachment point and a detachment point below the senior's attachment point.

· Senior tranches have an attachment point above the mezzanine's detachment point and a detachment point below the supersenior's attachment point.

Unlike cash Collateralized Debt Obligations (CDO), CSOs are not backed by a portfolio of physical bonds or loans but by a portfolio of CDS contracts. This latter feature allows much more flexibility in structuring tailor-made securities than cash-based CDOs:

· Physical bonds or loans only exist in limited quantity, whereas CDS contracts
can be created as long as two counterparties agree to trade with each other;

· Whenever a cash-CDO is structured, all tranches must be sold to the investors, i.e. the deal must be fully syndicated, unless the CDO-arranging bank wants to keep some risk in it books, whereas CSO tranches can be structured independently because their payoffs can be replicated through model-based offsetting CDS positions.

· Transaction follow-up duties are heavier for cash-CDOs than for CSOs: for instance, loans can be subject to contingent early repayments.

Figure 1.2: Structuring of a single-tranch CSO

CSO tranches on credit indices

As mentioned earlier, the price of a CSO tranche, which is defined by its attachment and detachment points within the capital structure, is a function of the joint-loss distribution of an underlying reference CDS portfolio. This joint-loss distribution function can be modeled in terms of two sets of parametres:

· single-name CDS spreads can be seen as proxies for valuing the default risk of each reference entity;

· cross-asset default risk dependency parametres, i.e. «correlation», that aim at describing the joint default-behaviour of a portfolio of reference entities.

The rationale for setting up a liquid market for tranches with standardized characteristics (attachment and detachment points) and referencing standard CDS portfolios (typically ITRAXX IG or CDX.NA.IG for 3,5,7 and 10 year-maturities) was to make correlation tradable, thereby allowing flexible correlation hedging for structured credit products.

Given that this market for standardized CSO tranches on credit indices aims at pricing correlation only and not default risk on any single name, tranches are quoted in terms of credit spread (measrued in basis points) on a Delta-Exchange basis: in other words, tranches and offsetting CDS positions are traded at the same time so that the resulting exposure of the investor is only to correlation and not to single-name first-order spread risk. Unlike other tranches which are quoted as a full running spread, the equity tranche (0%-3%), which is the riskiest slice of the capital structure, is quoted on a running basis assuming the protection seller on this tranche receives a 5% upfront premium.

Bespoke Collateralized Synthetic Obligations

Bespoke CSOs are tailor-made versions of CSO tranches on credit indices: the underlying CDS portfolio can be customized, as well as the characteristics of the tranche. This range of products offers more flexibility than standard tranches, for it allows the investor to choose his own credit risk profile by playing with the shape of the joint-loss distribution function (bespoke CDS portfolio) and choosing the attachment/detachment points that suit his aversion to risk.

In addition to tailoring the initial underlying CDS portfolio to the investor's needs, investment banks usually propose managed versions of bespoke CSOs that allow the underlying CDS portfolio to be revised later on in the transaction's life: the arranging bank appoints an external credit risk manager whose role is to manage actively the underlying CDS portfolio by making substitutions and weight adjustments among referenced single names.

Options on credit indices and tranches

As the liquidity of credit indices keeps improving, bid-offer spreads decrease and investment banks start proposing swaptions on major credit indices (ITRAXX XOVER, ITRAXX IG, CDX NA IG,...) on standard maturities (roll dates, i.e. 20-Mar, 20- Jun, 20-Sep, 20-Dec) and tenors (3Y,5Y,7Y).

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