Credit Default Swaps

• A Credit Default Swap (CDS) is a contract in which the writer offers the buyer protection against a credit event in a reference name for a specified period of time in return for a premium payment.

• Typical CDS cashflows– The contract pays par in return for 100 nominal of debt if the reference

name suffers a credit event before the maturity of the deal.

– The buyer pays a premium quarterly in arrears.

CDS Structure

Protection Buyer

Protection Seller

Quarterly premium in arrears

Protection Buyer

Protection Seller

Defaulted debt of reference name

Par less fraction of premium

Pre-default

Post-default

CDS Example

Protection Buyer

Protection Seller

314.486 bps quarterly in arrears

Protection Buyer

Protection Seller

$1,000,000 plus fraction of premium

Pre-default

Post-default

$1,000,000 ParGMAC

Par Asset Swap Example

Interest Rate Swap

Desk

AS Trading Desk

Investor

Floating Floating payments

+par at maturity

ParFixed

Market

Cash=Bond Dirty PriceFixed CouponCredit Bond

CDS - Asset Swap Hedge

Interest Rate Swap

Desk

AS Trading Desk

Investor/ Protection

Buyer

Floating Floating payments

+par at maturity

ParFixed

Market

Cash=Bond Dirty PriceFixed CouponCredit Bond

Protection Seller

Quarterly premium in arrears and

defaulted debt upon default

Par less fraction of

premium upon default

CDS - Asset Swap Hedge Example

Interest Rate Swap

Desk

AS Trading Desk

Investor/ Protection

Buyer

Market

Protection Seller

$10,000,000 ParGMAC 5 5/8sof 5/15/2009

Floating 3M LIBOR+273.7bps

$10,000,000 initially

Fixed 5.45232% semi-annual

Floating 3M LIBOR+256.8 bps

314.486 bps quarterly in arrears

$10,000,000 less partial premium on default event

$10,000,000 par of GMAC

debt on default event

$9,300,000+$42,187.50=$9,342,187.50

Initial Cashflows

Interest Rate Swap

Desk

AS Trading Desk

Investor/ Protection

Buyer

Market

Protection Seller

$10,000,000 ParGMAC 5 5/8sof 5/15/2009

$9,300,000+$42,187.50=$9,342,187.50

$10,000,000 initially

$719,881

Typical Periodic Cashflows

Interest Rate Swap

Desk

AS Trading Desk

Investor/ Protection

Buyer

Market

Protection Seller

$281,250semi-annually

LIBOR+$68,425 quarterly (approx.

$204,200)

$272,616 semi-annually

LIBOR+$64,200 quarterly (approx.

$200,000)$79,495 quarterly

Cashflows on Default

Interest Rate Swap

Desk

AS Trading Desk

Investor/ Protection

Buyer

Market

Protection Seller

$10,000,000 Pardefaulted

GMAC 5 5/8sof 5/15/2009

$10,000,000 less partial premium

Unwind IR swapUnwind IR swap

$10,000,000 Pardefaulted

GMAC 5 5/8sof 5/15/2009 or similar

Is the Protection Buyer Hedged?

• Upon default, the protection buyer receives $10m from the protection seller and (assuming 40% recovery) delivers defaulted debt worth $4m. At the inception of the contract, the GMAC note was only worth $9.3m. So the buyer receives a net of $6m from the CDS, has really lost only 9.3-4=$5.3m. So the buyer has too much CDS. The correct hedge ratio is given by

• In this case the protection buyer should buy $10m x (.93-.4)/(1-.4)=$8.9m notional CDS to be hedged.

( )

(1 )

bond price RCDS notional bond notional

R

CDS Basis

• A number of factors observed in the market serve to make the price of credit risk that has been established synthetically using credit default swaps to differ from its price as traded in the cash market using asset swaps.

• Identifying such differences gives rise to arbitrage opportunities that may be exploited by basis trading in the cash and derivative markets. This in known as trading the credit default basis and involves either buying the cash bond and buying a CDS on this bond, or selling the cash bond and selling a CDS on the bond.

• The difference between the synthetic credit risk premium and the cash market premium is known as the basis.

CDS Premium – Z-Spread = basis.

CDS Basis

Basis=314.486-291.9=22.586

Interest Rate Swap

Desk

AS Trading Desk

Investor/ Protection

Buyer

Market

Protection Seller

$930,000+$4,218.75=$934,218.75

Floating 3M LIBOR+273.7bps

$1,000,000Fixed 5.45232% semi-annual

Floating 3M LIBOR+256.8 bps

314.486 bps quarterly in arrears

$10,000,000 ParGMAC 5 5/8sof 5/15/2009

Z-Spread=291.9

CDS Basis

• The basis is usually positive, occasionally negative, and arises from a combination of several factors, including– Bond identity: The bondholder is aware of the exact issue that they are

holding in the event of default; however, default swap sellers may receive potentially any bond from a basket of deliverable instruments that rank pari passu with the cash asset. This is the delivery option held by the protection buyer.

– Depending on the precise reference credit, the CDS may be more liquid than the cash bond, resulting in a lower CDS price, or less liquid than the bond, resulting in a higher price.