Hazard rate
Quantitative Finance glossary · Quantitative Finance
Definition
Instantaneous conditional default rate per unit time in a reduced-form credit model: h(t) = lim_Δ t to 0 (P(τ in [t, t+Δ t],|,τ > t))/(Δ t). The survival function is S(t) = P(τ > t) = exp!left(-int_0^t h(s),dsright), and the par CDS spread satisfies the credit triangle s ≈ h,(1 - R) — the standard back-of-envelope for inferring market-implied default intensity from CDS quotes. Constant-hazard (exponential default time) is the bootstrap default; piecewise-constant calibration to a CDS curve is the workhorse.
Hazard rate in plain English
The hazard rate answers: 'given a company has survived up to now, how likely is it to default in the very next instant?' Think of a lightbulb that hasn't burned out yet — the hazard rate is its chance of failing in the next second. From it you get the survival probability S(t), the odds the company is still standing at time t, which shrinks the longer and higher the hazard runs. There's a handy back-of-the-envelope shortcut called the credit triangle, s ≈ h,(1-R): the annual cost of insuring the debt (the CDS spread s) roughly equals the default rate h times how much you'd lose if it defaults (with R the fraction you'd recover). Traders run this backwards — from the market price of default insurance, they read off the market's implied chance of default.
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