Index Credit Default Swap

ORE defines the input form as follows:

An index credit default swap (trade type IndexCreditDefaultSwap) is set up using an IndexCreditDefaultSwapData block

Source: ORE User Guide, Products catalogue, indexcds.tex. The block also includes LegData and BasketData trade component sub-nodes.

An index CDS is insurance on a whole group of borrowers at once. One premium covers the basket. If one borrower defaults, the seller pays that borrower's loss. The premium base and the protection base shrink as defaults happen.

The LegData sub-node is a fixed leg and holds the recurring premium. Payer true means the trade buys protection. Payer false means it sells protection. The notional on the fixed leg is the unfactored notional, which excludes any defaults. ORE contrasts it with two other notions. The trade date notional is reduced by defaults between series inception and the trade date. The current notional, also called the factored notional, is reduced by defaults up to the current evaluation date.

The BasketData sub-node is optional. It specifies the constituent reference entities of the index and is intended for non-standard indices that need a bespoke basket. When it is omitted, the index constituents come from the CreditCurveId element in the trade data.

The premium leg is a risky annuity on the unfactored notional. The protection leg pays the loss of each defaulted constituent, the notional minus its recovery, from the factored base. The mechanics follow the single-name Credit Default Swap, applied name by name to the basket.

• The index credit curve. It prices the basket and its defaults. A spread widening raises the value of bought protection.
• The discount curve of the premium currency.
• The composition of the index. Constituent weights and recoveries shape the loss distribution.
• The premium and any upfront fee. They fix the running cost.

A protection buyer gains when the index worsens. A seller gains when it improves.

Each default of a constituent settles its loss and reduces the factored notional. The running premium keeps paying on the unfactored base. The protection window shortens as the trade runs. Near maturity, only near-term defaults matter. At maturity the trade stops with the surviving basket.

A bank hedges a portfolio of credit exposures with one index trade instead of many single-name CDS. An investor sells protection on an index to earn the portfolio premium. The product prices and trades more cheaply than a bespoke basket. In ORE Studio a customer books index CDS to value them and run sensitivities on the ORE engine.

ORE's catalogue shows an index trade with its basket:

<IndexCreditDefaultSwapData>
  <CreditCurveId>RED:2I65BRHH6</CreditCurveId>
  <SettlesAccrual>Y</SettlesAccrual>
  <ProtectionPaymentTime>atDefault</ProtectionPaymentTime>
  <ProtectionStart>20160206</ProtectionStart>
  <UpfrontDate>20160208</UpfrontDate>
  <UpfrontFee>0.0</UpfrontFee>
  <LegData>
    <LegType>Fixed</LegType>
    <Payer>false</Payer>
    ...
  </LegData>
  <BasketData>
    <Name>
      <IssuerId>CPTY_1</IssuerId>
      <CreditCurveId>RED:</CreditCurveId>
      <Notional>100000.0</Notional>
      <Currency>USD</Currency>
    </Name>
    ...
  </BasketData>
</IndexCreditDefaultSwapData>

Source: ORE User Guide, Products catalogue, indexcds.tex, listing Index CreditDefaultSwap Data (constituents abbreviated).

The single-name form is the Credit Default Swap. The Index Credit Default Swap Option trades the right to enter this contract.