Credit Default Swap (CDS) Calculator

CDS Mechanics and the Role of the Spread: In a standard CDS contract, the protection buyer pays a running spread — expressed in basis points per annum on the notional — until either a credit event (default, restructuring, bankruptcy) or the contract's maturity. In return, the protection seller compensates the buyer for the loss given default (LGD), which equals the notional multiplied by one minus the recovery rate. The spread is set so that the present value of premium payments equals the present value of the expected contingent payment at inception, making the contract zero-NPV at initiation.

Hazard Rate and Default Probability: Under the risk-neutral framework, the CDS spread is directly linked to the hazard rate (\(\lambda\)), the instantaneous conditional probability of default per unit time, through the relationship \(s \approx \lambda \times (1-R)\), where R is the recovery rate. Rearranging gives \(\lambda = s / (1-R)\). The cumulative default probability over the contract tenor T is then \(P(\text{default}) = 1 - e^{-\lambda T}\). These are risk-neutral (market-implied) quantities calibrated to observed spreads, not necessarily physical default frequencies.

Mark-to-Market Valuation: Once a CDS is entered, changes in the market spread alter its fair value. A protection buyer profits when spreads widen (credit deteriorates) because the protection they locked in at a lower spread becomes more valuable. The simplified MTM formula used here is \((s_{\text{market}} - s_{\text{contract}}) \times N \times D \times T_{\text{remaining}}\), where D is the discount factor over the remaining life. Positive MTM for the buyer indicates an in-the-money position. Full production models use a risky annuity (the sum of risk-adjusted discount factors across payment dates) rather than a simple flat approximation, but this formula provides an accurate first-order estimate for standard contracts.

Model Simplifications: This calculator uses a constant flat hazard rate, which assumes a time-homogeneous Poisson default process. In practice, term structure models (e.g., bootstrapped hazard curves) allow the hazard rate to vary over different maturities. The MTM approximation uses a flat discount factor rather than integrating across each payment date's survival probability — full ISDA model implementations are more precise but require iterative numerical methods.

Recovery Rate Uncertainty: The recovery rate is treated as a fixed, known constant here. In reality, recovery rates are highly uncertain and vary across seniority, industry, and economic cycle. The standard ISDA CDS model typically assumes a 40% recovery for senior unsecured debt as a convention, but realized recoveries have ranged from near zero to over 80%.

Counterparty and Basis Risk: CDS contracts carry counterparty credit risk — if the protection seller itself defaults, the hedge fails. Post-2008 reforms pushed standardized CDS to central clearing (CCPs) to mitigate this. Additionally, the CDS-bond basis (difference between CDS-implied spread and bond spread) means hedging with CDS does not perfectly offset bond price risk. This calculator does not model collateral posting, upfront payments used in standard ISDA contracts since 2009, or accrued premium calculations on default.

Accrued Premium on Default: ISDA standard contracts also include an accrued premium from the last payment date to the credit event date. This is omitted here for simplicity but can amount to one full quarterly payment in the worst case.