A single-name CDS is a bilateral contract on a reference entity. The protection buyer pays a running premium on a notional; if a credit event occurs (bankruptcy, failure to pay, and for some entities restructuring, per the ISDA definitions), the protection seller compensates for the loss, in modern practice by cash settlement at an auction-determined recovery price. The buyer is short credit; the seller is long credit, leveraged and unfunded.
The hazard rate. The right primitive is not "probability of default" but the hazard rate λ, the instantaneous conditional default intensity, the rate at which default arrives given survival so far. With constant λ the survival probability is S(t) = e^(−λt) and the probability of default in (t−1, t] is S(t−1) − S(t). This is the right object because a CDS pays only if default happens while the contract is alive, so every cash flow must be survival-weighted.
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How is a CDS priced and quoted?
The two legs.
- Premium leg (per unit of spread, per unit of notional), the risky annuity, universally called RPV01:
RPV01 = Σ Δ × D(t) × S(t) + accrual-on-default, where D(t) is the risk-free discount factor and Δ the accrual fraction. The second term recognises that if default happens mid-period, the buyer still owes the premium accrued since the last payment date; it is conventionally approximated as half a period:Σ 0.5 × Δ × D(t) × (S(t−1) − S(t)). - Protection leg:
LGD × Σ D(t) × (S(t−1) − S(t)), whereLGD = 1 − recovery rate.
The par spread is the running premium that makes the two legs equal at inception: s* = Protection leg PV / RPV01.
Two things fall out permanently. First, the credit triangle: for small λ and a flat curve, s* ≈ λ × LGD. E11.01 taught it as a slide rule; here you can see how good it is, with λ = 2.50% and recovery 40% the triangle predicts 150.00 bp against an exact five-year figure of 149.99 bp. It is excellent at investment grade and degrades as λ rises. Second, and more important, a single spread quote cannot separate λ from recovery. Holding the 5-year spread at 210 bp, the implied hazard is 2.63% at 20% recovery, 3.50% at 40% and 5.25% at 60%. Any claim that "the CDS market is pricing a 16% chance of default" is incomplete without its recovery assumption.
Upfront and the standard coupon. Since the post-2009 "Big Bang" conventions, single-name CDS trade with standardised running coupons (100 bp and 500 bp) plus an upfront reconciling coupon to market spread: Upfront ≈ (s* − standard coupon) × RPV01 × Notional. The buyer pays it when the spread exceeds the coupon and receives it when below. Standardising the coupon is what makes contracts fungible and centrally clearable, the point of the reform.
How do you build a credit curve and mark a CDS?
The credit curve. Bootstrapping a piecewise-constant hazard curve is the FI1.03 discipline in credit: solve the shortest tenor, hold it fixed, solve the next. Worked Example 8 does it for a 3-year quote of 150 bp and a 5-year of 210 bp, and the answer is instructive: λ(0–3y) = 2.50% but λ(3–5y) = 5.32%. A gently sloping spread curve implies a steeply sloping forward hazard curve, exactly as a gently sloping spot curve implies steep forwards.
Marking to market. MTM ≈ (s_now − s_entry) × RPV01_now × Notional, positive for the buyer when spreads widen. Protection bought at 150 bp with the market at 210 bp is worth 60 bp × 4.0865 = 2.4519% of notional: $245,193 on $10m. RPV01 is the position's credit duration and shrinks as spreads widen, which is why deeply stressed credits quote in points upfront rather than in spread.
How does the CDS market work in India?
The India frame (R6). India has a framework for credit derivatives, the RBI's Master Direction (Credit Derivatives, 2022 (read the current version)) permitting single-name CDS on corporate bonds among defined eligible participants. But the market is thin, so an Indian analyst runs the US workflow backwards: rather than reading a hazard rate off a liquid quote, you infer it from the bond's spread over the G-Sec curve. The health warning matters more here than in the US: a bond spread contains a liquidity premium a CDS spread largely does not, so bond-implied hazard rates are biased high. Say the bias out loud, and recognise that IBC-regime recovery assumptions (E11.01) have wide dispersion of their own.