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 bps quarterly in arrears Protection Buyer Protection Seller $1,000,000 plus fraction of premium Pre-default Post-default $1,000,000 Par GMAC

Par Asset Swap Example Interest Rate Swap Desk AS Trading Desk Investor FloatingFloating payments +par at maturity ParFixed Market Cash=Bond Dirty Price Fixed Coupon Credit Bond

CDS - Asset Swap Hedge Interest Rate Swap Desk AS Trading Desk Investor/ Protection Buyer FloatingFloating payments +par at maturity ParFixed Market Cash=Bond Dirty Price Fixed Coupon Credit 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 Par GMAC 5 5/8s of 5/15/2009 Floating 3M LIBOR+273.7bps $10,000,000 initially Fixed % semi-annual Floating 3M LIBOR bps 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 Par GMAC 5 5/8s of 5/15/2009 $9,300,000+$42,187.50=$9,342, $10,000,000 initially $719,881

Typical Periodic Cashflows Interest Rate Swap Desk AS Trading Desk Investor/ Protection Buyer Market Protection Seller $281,250 semi-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 Par defaulted GMAC 5 5/8s of 5/15/2009 $10,000,000 less partial premium Unwind IR swap $10,000,000 Par defaulted GMAC 5 5/8s of 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.

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= = Interest Rate Swap Desk AS Trading Desk Investor/ Protection Buyer Market Protection Seller $930,000+$4,218.75=$934, Floating 3M LIBOR+273.7bps $1,000,000 Fixed % semi-annual Floating 3M LIBOR bps bps quarterly in arrears $10,000,000 Par GMAC 5 5/8s of 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.