Synthetic CDO

Table of Contents

A synthetic CDO sells protection on the losses of a credit basket, limited to a tranche. ORE models it with the trade type SyntheticCDO and a CdoData block. This note records the domain grounding, as ORE documents it in its product catalogue.

1. Identifiers

What a trader books it as, and what to grep for. The codes are the trade type catalogue's, which is what the database enforces.

Field Value
Full name Synthetic CDO
Short name Synthetic CDO
ORE Studio product code SyntheticCDO
Asset class credit
Family none; see below
ORE trade data node none; the payload is not a per-type node
ORE documentation syntheticcdo.tex

2. Summary

A synthetic collateralised debt obligation (CDO) is a basket credit derivative. The protection seller receives a premium and covers the portfolio losses of a tranche. The tranche runs from an attachment point to a detachment point. Losses below the attachment point fall on the protection buyer. Losses above the detachment point fall outside the contract. The basket can follow an index such as CDX or iTraxx, or name bespoke constituents.

3. Detail

3.1. What it is

ORE defines the product as follows:

A synthetic CDO is a basket credit derivative, where the protection seller receives a premium cash flow in exchange for providing (notional) protection against portfolio losses due to defaults in a specific tranche characterized by the attachment point A and detachment point D.

Source: ORE User Guide, Products catalogue, syntheticcdo.tex.

3.2. In plain terms

A synthetic CDO is a slice of the credit risk of a group of borrowers. The seller of the slice covers the losses that fall inside it. Losses below the slice belong to the buyer. Losses above it belong to no one in this contract. The slice pays a premium for that exposure.

3.3. How it works in ORE

The trade uses a CdoData block. The AttachmentPoint is the fraction of portfolio loss where protection starts. The DetachmentPoint is the fraction where it stops. The Qualifier names the credit index that defines the default and base correlation curves used for pricing. A bespoke basket sets the Qualifier to the index that matches it most closely and names its own constituents in a BasketData sub-node. A fixed LegData holds the premium leg. The protection mechanics follow the credit family conventions, with settlement, accrual, and upfront terms.

3.4. Mathematical notes

The portfolio loss given default sums the loss of each defaulted asset. ORE states the loss of one asset as the notional reduced by the recovery: LGD equals (1 minus recovery) times notional. The tranche absorbs the portfolio loss between its two points. The premium pays on the tranche notional, which shrinks as losses consume the tranche.

3.5. What moves its value (static sensitivities)

  • The credit curves of the basket constituents. They drive the loss distribution.
  • The base correlation surface. It prices the tranche between its points.
  • The discount curve of the premium currency.
  • The attachment and detachment points. They set the risk window.
  • The composition and weights of the basket.

A seller of a senior tranche gains when defaults stay below the attachment point. A seller of an equity tranche carries the first losses.

3.6. How the profile ages (dynamic sensitivities)

Defaults reduce the basket and the outstanding tranche notional. Each loss inside the tranche is settled and deducted from the attachment base. The remaining premium pays on the reduced notional. Near maturity, the loss window narrows to the remaining life. At maturity the contract stops with the surviving basket and the residual tranche.

3.7. Why a customer would want it

An investor buys a tranche to take a chosen slice of portfolio credit risk, from first-loss to senior. A bank sells tranches to transfer the risk of its loan book. The product tunes risk and return precisely. In ORE Studio a customer books synthetic CDO to value them and run sensitivities on the ORE engine.

3.8. Example

ORE's catalogue shows a mezzanine tranche of an index: 

<CdoData>
  <Qualifier>RED:2I65BRHH6</Qualifier>
  <AttachmentPoint>0.12</AttachmentPoint>
  <DetachmentPoint>0.22</DetachmentPoint>
  <ProtectionStart>20140425</ProtectionStart>
  <UpfrontDate/>
  <UpfrontFee/>
  <SettlesAccrual>Y</SettlesAccrual>
  <ProtectionPaymentTime>atDefault</ProtectionPaymentTime>
  <LegData>
    <LegType>Fixed</LegType>
    <Payer>true</Payer>
    ...
  </LegData>
  <BasketData>
    ...
  </BasketData>
</CdoData>

Source: ORE User Guide, Products catalogue, syntheticcdo.tex, listing CDO Data (leg and basket abbreviated).

The tranche covers portfolio losses between 12 and 22 percent. The family basis is the Credit Default Swap, applied to the basket. The Index Credit Default Swap is the untranched form of the same protection.

4. See also

Emacs 29.3 (Org mode 9.6.15)