A credit default swap has a simple economic purpose — the protection buyer pays a periodic premium (the CDS spread) and the protection seller pays face value minus recovery in the event of a credit event. But the mechanics of how that spread is derived, how the trade is marked to market, and how it relates to the underlying bond market require a precise framework to understand.
The Basic Structure: Premium Leg vs Protection Leg
A CDS has two legs:
- Premium leg: The protection buyer pays the agreed CDS spread (in basis points per annum) on the notional amount, quarterly in arrears, until maturity or until a credit event occurs. If a credit event occurs mid-period, an accrued premium payment is also owed for the days since the last coupon.
- Protection leg: The protection seller agrees to pay (1 − Recovery Rate) × Notional if a credit event occurs during the life of the CDS.
At inception, the CDS has zero value: the present value of the premium leg equals the present value of the expected protection payment. The CDS spread is the rate that achieves this balance.
The ISDA Standard Model and Upfront vs Running Spread
Before 2009, CDS were quoted as a running spread — the annualised premium paid quarterly. The five-year CDS on Company X might be "150bp running," meaning the buyer pays 150bp × notional / 4 each quarter.
After 2009, the CDS market adopted the ISDA standard model ("Big Bang" and "Small Bang" protocols), which standardised coupon rates at 100bp or 500bp per annum (for investment-grade and high-yield, respectively). Now, instead of quoting a running spread, CDS are quoted as an upfront payment — the present value difference between the standardised coupon and the market spread. If the market CDS spread is 200bp but the coupon is 100bp, the buyer must pay an upfront amount to compensate the seller for the below-market coupon they will receive.
The ISDA standard model converts between quoted spread and upfront using a standardised set of assumptions about recovery rate (40% for senior unsecured), interest rate discounting, and default timing conventions. Bloomberg and Markit provide calculators implementing this model. The quoted spread (or "par spread") is the hypothetical running spread that would make the CDS worth zero — useful for comparison across names regardless of coupon convention.
Hazard Rates and the Survival Curve
CDS pricing relies on a hazard rate (or default intensity) — the instantaneous probability of default per unit time. If a company has a constant hazard rate of λ per year, the probability of surviving to time t is:
Survival Probability(t) = e^(−λt)
The probability of defaulting between time t and t+dt is λ × Survival Probability(t) × dt. The hazard rate can be approximated from the CDS spread as:
λ ≈ CDS Spread / (1 − Recovery Rate)
For a 150bp CDS spread and 40% assumed recovery, the implied hazard rate is approximately 150 / (1 − 0.40) = 250bp per year, or a 2.5% annual default probability.
Bootstrapping the CDS Curve
CDS are quoted at standard maturities: 1Y, 2Y, 3Y, 4Y, 5Y, 7Y, 10Y. Each point on the curve implies a hazard rate for the corresponding period. The CDS curve is bootstrapped from shortest to longest maturity: the 1Y CDS implies a 1Y hazard rate; the 2Y CDS (combined with the 1Y hazard rate) implies the incremental hazard rate for year 2; and so on. This bootstrapping produces a term structure of survival probabilities — the credit curve — analogous to the yield curve in rates markets.
A flat CDS curve (5Y spread = 10Y spread) implies the market assigns the same average default probability per year regardless of maturity. An upward-sloping curve implies higher near-term default probability declining over time (common for stressed credits). A downward-sloping or inverted curve implies high near-term default risk — typically a signal of imminent stress.
Mark-to-Market and CDS Duration
After a CDS is entered, it will gain or lose value as the issuer's credit spread moves. The sensitivity of a CDS's value to a 1bp change in the CDS spread is called the CDS duration (or spread DV01 / CS01). For a five-year CDS with a notional of $10 million, the CS01 might be approximately $4,600 per basis point — meaning if the issuer's CDS spread widens by 10bp, the mark-to-market gain for a protection buyer is approximately $46,000.
The CDS duration is analogous to bond modified duration and is approximately equal to the RPV01 (risky present value of a basis point annuity) — the present value of receiving 1bp per year for the remaining life of the CDS, discounted by both the risk-free rate and the survival probability.
CDS Spread vs Bond Spread: The Basis
In theory, the CDS spread of a company should equal the spread of its floating-rate bonds over the risk-free rate — both represent compensation for the same default risk. In practice, the two diverge due to:
- Cheapest-to-deliver optionality: CDS protection buyers can deliver the cheapest deliverable bond on default, making CDS more valuable (tighter) than bonds.
- Funding and repo: Cash bond investors must fund their positions; CDS buyers do not — creating a funding advantage for CDS at times of stress.
- Structural differences: CDS may cover restructuring events that don't affect bond prices; some bond covenants differ from CDS deliverable obligations.
- Supply and demand: Index roll demand, regulatory hedging flows, and technical positioning all create basis.
The CDS-bond basis is the CDS spread minus the asset swap spread of the corresponding bond. A negative basis (bond asset swap spread wider than CDS) suggests the bond is cheap relative to CDS — a potential convergence trade.