# Credit Default Swaps

A credit default swap (CDS) is a contract that gives the buyer of the contract a right to receive compensation from the seller of the contract in the event of default of a third party. The buyer of the contract is typically a bondholder who is looking to transfer his credit exposure to another party. The seller is typically a bank which earns from the premiums it receives from the buyer.

Each CDS has a notional amount and it requires the buyer to pay a premium called CDS spread. Because the periodic premium rates are standardized, the buyer may also be required to pay an amount at the time 0 of the CDS seller. This amount is called upfront premium.

The seller of the CDS pays the buyer an amount equal to the loss incurred by the buyer on occurrence of a credit event. The credit event is binary in nature, i.e. it occurs, or it doesn’t. Typical credit events include (a) a filing for bankruptcy by the third party on whose bond the CDS was issued, (b) any failure by the third party to pay interest on its bonds and (c) any restructuring of the debt.

## Formula

When it is established that a credit event has occurred, the amount paid by the CDS seller to the buyer is calculated using the following formula:

$$\text{Payout Amount}=\text{N}\times \text{Payout Ratio}=\text{N}\times(\text{1}\ -\ \text{Recovery Rate})$$

Where N is the notional amount and payout ratio is the loss incurred by a bondholder as a percentage of the bond’s par value. It equals 1 minus the recovery rate, which is the percentage of amount owed which is recovered by a bondholder during the bankruptcy proceedings.

During the life of the CDS, the profit (loss) that accrues to the buyer (seller) of the CDS can be approximated as follows:

$$\text{Profit to buyer of CDS}=\Delta \text{CDS}\ \times \text{N}\times \text{D}$$

ΔCDS is the basis point change in credit spread, N is the notional amount and D is the duration of the bond.

It follows that if the default spread increases over the life of the CDS, the buyer gains and if the spread shrinks the seller gains.

## Example

A bank has loaned $40 million to a company for 5 years requiring periodic interest payments equal to LIBOR + 2.2%. The bank’s policy requires all loans to be backed by a credit default swap on the principal amount of loans made. In this case, the bank can buy a CDS with a notional amount of$40 million. The CDS costs 2%. The bank must pay an amount equal to 2% of the notional amount to the CDS seller each year. Annual premium amounts to $800,000 (2% ×$40 million).

If the borrower defaults on the final principal payment and the bank collects only 50% of its principal back, it can claim the differential from the seller of the CDS. The amount he will receive from the CDS sell is approximately equal to $20 million ($40 million × (1 – 50%)). If the borrower doesn’t default on the final principal amount, the bank doesn’t receive anything.