1
Introduction to Credit Default Swaps
A Credit Default Swap (CDS) is a credit derivative that allows investors to transfer credit risk without transferring the underlying asset. It functions as insurance against the default of a specific borrower or reference entity.
Basic CDS Structure
In a CDS transaction, there are two parties:
- Protection Buyer: Pays periodic premiums and receives protection against credit events
- Protection Seller: Receives premiums and compensates the buyer if a credit event occurs
CDS Premium Calculation Formula
CDS Premium = (CDS Spread × Notional Amount × Days in Period) / 360
Where:
CDS Spread = Annual spread in basis points
Notional Amount = Protected principal amount
Days in Period = Days in payment period
360 = Day count convention
CDS Premium = (CDS Spread × Notional Amount × Days in Period) / 360
Where:
CDS Spread = Annual spread in basis points
Notional Amount = Protected principal amount
Days in Period = Days in payment period
360 = Day count convention
Key CDS Terms
- Reference Entity: The borrower whose credit risk is being transferred
- Reference Obligation: The specific debt instrument covered by the CDS
- Notional Amount: The face value of protection purchased
- Maturity: The length of protection (commonly 1, 3, 5, or 10 years)
- CDS Spread: The annual premium expressed in basis points
2
Credit Events and Settlement
Credit events trigger the protection payment in a CDS. The International Swaps and Derivatives Association (ISDA) standardizes the definition of credit events.
Standard Credit Events
| Credit Event | Description | Threshold |
|---|---|---|
| Failure to Pay | Missed payment after grace period | $1 million (typically) |
| Bankruptcy | Formal insolvency proceedings | No threshold |
| Restructuring | Material changes to debt terms | $10 million (typically) |
| Obligation Acceleration | Debt becomes immediately due | $10 million (typically) |
| Obligation Default | Cross-default on other obligations | $10 million (typically) |
| Repudiation/Moratorium | Rejection of debt obligations | $10 million (typically) |
Settlement Methods
When a credit event occurs, the CDS can be settled in two ways:
Physical vs. Cash Settlement
Physical Settlement:
- Protection buyer delivers reference obligation to protection seller
- Protection seller pays full notional amount
- More common in early CDS contracts
- Protection seller pays (Notional × (1 - Recovery Rate))
- Recovery rate determined through auction process
- More efficient and widely used today
CDS Cash Settlement Formula
Cash Settlement Payment =
Notional Amount × (100% − Recovery Rate)
Where:
Notional Amount = Protected principal
Recovery Rate = % of face value recovered after default
100% − Recovery Rate = Loss given default (LGD)
Cash Settlement Payment =
Notional Amount × (100% − Recovery Rate)
Where:
Notional Amount = Protected principal
Recovery Rate = % of face value recovered after default
100% − Recovery Rate = Loss given default (LGD)
3
CDS Pricing and Valuation
CDS pricing involves determining the fair value of the periodic premium payments in exchange for default protection. The CDS spread reflects the market's assessment of credit risk.
Basic Pricing Framework
The CDS spread should theoretically equal the credit spread of the reference entity's bonds, adjusted for differences in recovery rates and liquidity.
CDS Spread Approximation Formula
CDS Spread ≈
Credit Spread × (1 − Recovery Rate) / (1 − Bond Recovery Rate)
Where:
CDS Spread = Credit default swap spread
Credit Spread = Bond yield spread over risk-free rate
Recovery Rate = Expected recovery on CDS
Bond Recovery Rate = Expected recovery on bond
CDS Spread ≈
Credit Spread × (1 − Recovery Rate) / (1 − Bond Recovery Rate)
Where:
CDS Spread = Credit default swap spread
Credit Spread = Bond yield spread over risk-free rate
Recovery Rate = Expected recovery on CDS
Bond Recovery Rate = Expected recovery on bond
Present Value Approach
The fair CDS spread equates the present value of premium payments to the present value of expected loss payments:
| Component | Formula | Description |
|---|---|---|
| Premium Leg PV | Spread × Σ[Survival Prob × Discount Factor × Time] | Present value of premium payments |
| Protection Leg PV | LGD × Σ[Default Prob × Discount Factor] | Present value of protection payments |
| Fair Spread | Protection Leg PV / Premium Leg PV | CDS spread that makes PV = 0 |
Example: CDS Valuation
A 5-year CDS with:
Expected Loss = $10M × 2% × (1 - 40%) = $120,000 per year
The CDS spread would be determined to make the present value of premiums equal to the present value of expected losses.
- Notional: $10 million
- Annual default probability: 2%
- Recovery rate: 40%
- Risk-free rate: 3%
Expected Loss = $10M × 2% × (1 - 40%) = $120,000 per year
The CDS spread would be determined to make the present value of premiums equal to the present value of expected losses.
CDS-Bond Basis
The CDS-bond basis is the difference between the CDS spread and the credit spread of the reference entity's bond. A positive basis suggests the CDS is expensive relative to the bond, while a negative basis suggests the opposite.
Basis = CDS Spread - Bond Credit Spread
Basis = CDS Spread - Bond Credit Spread
4
CDS Applications and Strategies
Credit default swaps serve multiple purposes in financial markets, from risk management to speculation and arbitrage.
Hedging Applications
| Strategy | Objective | Implementation | Risk Considerations |
|---|---|---|---|
| Credit Protection | Hedge bond portfolio | Buy CDS on holdings | Basis risk, counterparty risk |
| Portfolio Hedge | Reduce overall credit exposure | Buy index CDS | Imperfect correlation |
| Regulatory Capital | Reduce capital requirements | Transfer credit risk | Regulatory recognition |
Trading and Speculation
CDS can be used to take directional views on credit risk without owning the underlying bonds:
- Long Credit Risk: Sell CDS to earn premiums when expecting credit improvement
- Short Credit Risk: Buy CDS when expecting credit deterioration
- Relative Value: Trade spread differences between entities or maturities
- Curve Trading: Exploit term structure inefficiencies
Basis Trade Strategy
When CDS spreads are wide relative to bond spreads:
- Buy the bond (long credit exposure)
- Buy CDS protection (hedge credit risk)
- Profit from basis convergence
- Carry positive spread differential
Synthetic Instruments
CDS enable creation of synthetic credit exposure:
- Synthetic Long Bond: Sell CDS + Buy risk-free bond
- Synthetic Short Bond: Buy CDS + Short risk-free bond
- Total Return Swaps: Exchange total returns for funding costs
5
CDS Indices and Tranches
CDS indices provide exposure to baskets of credits, while tranched products offer leveraged exposure to specific loss levels.
Major CDS Indices
| Index | Region | Sector | Constituents |
|---|---|---|---|
| CDX.NA.IG | North America | Investment Grade | 125 names |
| CDX.NA.HY | North America | High Yield | 100 names |
| iTraxx Europe | Europe | Investment Grade | 125 names |
| iTraxx Crossover | Europe | Sub-Investment Grade | 75 names |
Index Tranches
Tranched CDS products divide the credit risk of an index into different loss layers, providing leveraged exposure to specific risk levels.
Standard Index Tranches
For a typical CDS index:
- 0-3% Tranche (First Loss): Highest risk, highest spread
- 3-7% Tranche: Mezzanine risk
- 7-10% Tranche: Senior mezzanine risk
- 10-15% Tranche: Senior risk
- 15-30% Tranche: Super senior risk
Tranche Risk Characteristics
- Subordinate Tranches: High sensitivity to default correlation
- Senior Tranches: Low sensitivity to individual defaults
- Correlation Risk: Changes in default correlation affect tranche values differently
- Leverage Effect: Small portfolio losses create large tranche losses
6
Risks and Regulatory Considerations
While CDS provide valuable risk management tools, they also introduce specific risks and regulatory challenges.
Key Risks in CDS Trading
Counterparty Risk
The protection buyer faces the risk that the protection seller may default, especially when protection is most needed during market stress. This risk has led to increased use of central clearing.
| Risk Type | Description | Mitigation |
|---|---|---|
| Counterparty Risk | Protection seller may default | Central clearing, collateral |
| Basis Risk | CDS and bond spreads diverge | Close monitoring, basis trades |
| Liquidity Risk | Difficulty unwinding positions | Trade liquid names/indices |
| Legal Risk | Disputes over credit events | Standard ISDA documentation |
| Model Risk | Valuation model errors | Multiple models, benchmarking |
Regulatory Developments
Post-financial crisis regulations have significantly changed the CDS landscape:
- Central Clearing: Mandatory clearing for standardized CDS
- Trade Reporting: Transaction reporting to trade repositories
- Capital Requirements: Increased capital charges for CDS exposures
- Margin Requirements: Initial and variation margin for non-cleared trades
- Position Limits: Restrictions on speculative positions in some jurisdictions
Market Impact of Regulation
Regulatory changes have led to:
- Increased standardization of CDS contracts
- Greater market transparency
- Higher trading costs due to margin and capital requirements
- Concentration of trading in dealer banks and large institutions