We are often worried when we lend money to someone. There is always a chance that the borrower might default before we receive our money back. We might require the borrower to pay us a portion of the money with interest. However there is always an uncertainty that the borrow might not pay all of the payments in full.
Credit default swap (CDS) was introduced to protect the lender in case the borrower defaults. CDS is one of the most famous and widely used financial contracts.
This article outlines what CDS is, its usages along with the formula that is used to price CDS.
Please read FinTechExplained disclaimer.
Let’s understand how CDS works from a simple example mentioned below.
Scenario: You lend money to Party Z
Let’s assume you lend money to your friend. Call him Party Z
Party Z invests in different markets and borrows money from a range of sources to support his business. You are worried that the Party Z might not give you your money back and he might default on his payments.
To save yourself from unexpected loss, you ask Party Z to pay a portion of the money on periodic basis with high interest. This enables you to get more money back in return in shorter time. This is the price that the Party Z is paying by borrowing money from you.
Party Z in this example is the reference entity.
You can enter into a CDS contract to protect yourself from the risk that party Z might default. CDS contract is between you and another party, let’s call him Party X. Party X insures the money you lent Party Z. Party X is now selling the insurance and requires you to pay premium periodically in return of offering you the protection. Now you have reduced the credit risk of Party Z.
What Is A CDS Contract?
CDS is a financial contract between the buyer and seller of the insurance contract to protect against the credit losses related to a reference entity such as Party Z in the example above.
CDS contract enables you to buy insurance to protect from the risk that the counterparty might default. The counterparty is known as Reference Entity and this risk is known as credit risk.
This diagram illustrates what CDS contract is:
Seller of the CDS contract receives premium payments periodically. In case of any loss, the seller will pay the required compensation. Occasionally, only a portion of the amount is insured.
CDS contracts gained popularity in 1999.
Any loss that occurs due to the reference entity is known as credit event.
CDS Is Insurance Contract
It’s the same concept as buying phone insurance. If you are worried that your phone might break or gets lost then you buy phone insurance to protect yourself against the risks. The insurer receives payments periodically and offers protection.
Just like insurance contracts, there are two sides of CDS contracts.
- Buyer: One who buys the CDS (insurance) contract. Buyer pays payments on timely basis e.g. monthly to the seller of the CDS contract. Buyer receives compensation if a loss occurs.
- Seller: One who sells CDS contract. Seller pays compensation if a loss occurs. This loss is known as credit event. Seller receives timely payments from the buyer.
CDS contract protects you from the credit event that your counterparty might default. The contract is terminated after the credit event occurs.
If a loss does not occur then the contract terminates without any payments.
As a consequence, there are a number of attributes of a CDS contract, including:
- Notional: Amount you are insuring. This is the money buyer lent to the reference entity or what the CDS buyer thinks the contract with the reference entity is worth. It can also be a portion of the amount that that the buyer wants to insure.
- Start And Maturity Dates: This is the date when the contract expires. Until this date, the buyer will pay payments to the seller of the CDS contract.
- Payment Frequency: This is the payment frequency and could be monthly, quarterly, annually etc.
- Reference Obligation: This is the entity the buyer is protecting against.
- Premium Payments: This is the amount of money the buyer needs to pay to the seller of the CDS contract.
- Default Probability: Likely-hood of the reference entity defaulting. It is expressed in percentage.
- Recovery Rate: This is the probability of getting money back once the counterparty defaults.
- Pay Or Receive: Indicating whether you are paying or receiving periodic payments.
How Do We Price A CDS?
This section outlines the calculation to calculate price of a CDS contract that the buyer of the CDS contract has to pay to enter into a CDS contract.
CDS is very similar to an interest rate swap. If you want to read about interest rate swap in detail then have a look at my article:
There are two legs of the CDS contract:
- Premium Leg: The buyer pays periodic premium payments to the seller of the CDS contract. Each premium payment is known as the premium cashflow.
- Fixed leg: This is the amount that the buyer receives when a credit event occurs.
The price of a CDS contract is therefore the difference between the present value of premium and fixed leg. It is likely that the payments might not be paid therefore the fixed leg needs to take probability of default into account.
The protection leg needs to take the recovery rate into account when calculating present value of the cashflows.
CDS Pricing Formula:
- Fixed Leg: Sum Of Present Value Of ((Survival Probability) x Annual Premium) + Sum Of Present Values Of (Difference Of From Current And Last Survival) x Annual Premium)
- Premium Leg: (1-Recovery Rate) x Sum Of Present Values Of (Difference Of From Current And Last Survival Probability)
Survival probability is calculated from the transition matrix. It is not in scope of this article.
This article outlined what CDS is, its usages along with the formula that is used to price CDS.
If you want to know about counterparty risk in general then please have a look at my article:
Hope it helps.