Estimating Default Probabilities from Market Prices pulled a hazard rate out of a bond's credit spread — useful, but a bond bundles default risk together with interest-rate risk, funding cost, and liquidity, all in one number. What if you want to trade just the default risk, isolated from everything else? That's precisely what a credit default swap (CDS) lets you do: pure, tradeable insurance against one company or country failing to pay its debts, with a price the whole market can watch tick in real time.

The mechanics

A CDS is a bilateral contract between a protection buyer and a protection seller, referencing a specific borrower (the "reference entity") and a notional amount. It runs like an insurance policy:

• The protection buyer pays a periodic premium — the CDS spread, quoted in basis points per year on the notional, usually paid quarterly — for as long as the contract runs, or until a defined credit event (default, bankruptcy, or a missed payment) happens to the reference entity, whichever comes first.
• The protection seller collects that premium and, in exchange, promises to pay the buyer (1 - R) \times \text{notional} if a credit event occurs before maturity — compensating the buyer for exactly the loss a bondholder of that issuer would suffer.

Two "legs" of value change hands over the contract's life: the premium leg (what the buyer pays, contingent on no default yet) and the protection leg (what the seller pays, contingent on default happening). A fairly priced CDS spread is exactly the one that makes the expected present value of those two legs equal at inception — nobody would rationally enter a contract they expect to lose money on.

Pricing: setting the two legs equal

Using the same survival probability S(t) = e^{-\lambda t} from earlier lessons and a risk-free discount factor DF(t) = e^{-rt}, and assuming annual premium payments only while the reference entity has survived:

Here N is the notional and each term S(t_{i-1}) - S(t_i) is the probability of defaulting during year i specifically (this simplified version assumes any default payout arrives at the end of the year it occurs in, and ignores the small accrued-premium adjustment real desks add). Setting premium leg equal to protection leg and solving for the spread c gives the fair CDS spread:

The chart below plots the two curves every term in that formula is built from — survival probability and the discount factor — for a hazard rate and risk-free rate you can move.

Worked example: pricing a 5-year CDS

Notional N = \$10{,}000{,}000, maturity T = 5 years, hazard rate \lambda = 2\%, recovery R = 40\%, risk-free rate r = 3\%, annual payments.

Protection leg = N(1-R)\times 0.0872 = 10{,}000{,}000 \times 0.6 \times 0.0872 \approx \$523{,}000. Premium leg per unit spread = N \times 4.3143 = \$43{,}143{,}000. Setting them equal:

Compare that to the quick approximation from the previous lesson, c \approx \lambda(1-R) = 0.02 \times 0.6 = 1.20\% — remarkably close. That's not a coincidence: a corporate bond's credit spread and the CDS spread on the same reference entity are, in principle, pricing the same default risk, so they should be (and empirically usually are) nearly equal. A trader who spots the two drifting apart is watching the CDS–bond basis — a small, closely-watched arbitrage signal.