Jarrow-Turnbull (reduced-form credit)
Quantitative Finance glossary · Probability, Statistics & Linear Algebra
Definition
Reduced-form credit-pricing framework: default time τ is the first jump of an inhomogeneous Poisson process with hazard rate h(t). Risky zero-coupon bond price barP(0,T) = mathbbE^mathbbQ!left[e^-int_0^T r(s),ds,(mathbf1_τ > T + R· mathbf1_τ ≤ T)right]. Under independence of rates and default, factorises into P(0,T)· S(T) plus a recovery term. The canonical alternative to Merton-structural — calibrates directly to CDS market without needing a firm-value model.
Jarrow-Turnbull (reduced-form credit) in plain English
This is the other big school of thought for pricing the risk that a borrower won't pay you back. Rather than modeling the company's assets and asking when they fall below its debts (the "structural" approach), it treats default as a bolt-from-the-blue event that strikes at some random moment, governed by a "hazard rate" — basically the instantaneous odds of default per unit of time, like the chance a lightbulb burns out in the next second. To value a risky bond, you average over all futures: in each one you either survive and collect the full amount, or default early and salvage only a fraction (the recovery R), discounting everything back to today. Its big practical advantage is that this hazard rate can be read straight off market prices of credit insurance (CDS), so you never have to guess the firm's internal balance sheet.
Also called: reduced-form credit
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