Hull-White model
Quantitative Finance glossary · Quantitative Finance
Definition
Time-inhomogeneous extension of Vasicek that exactly calibrates to the initial yield curve via a time-varying mean: dr_t = (θ(t) - a,r_t),dt + σ,dW_t, with θ(t) chosen so the model reproduces P(0,T) for all T. Affine term structure: P(t,T) = A(t,T),e^-B(t,T),r_t. Trinomial-tree (Hull-White-1996) and PDE implementations are standard; the one-factor restriction is its key limitation for non-parallel curve moves, motivating two-factor G2++ and HJM.
Hull-White model in plain English
Interest-rate models need to agree with today's actual market rates before you trust them on anything fancier. The Hull-White model does this by taking a simple model where rates drift back toward a long-run level and giving that target level a time-varying dial, θ(t), tuned so the model exactly reproduces every bond price observed today. Think of tuning a guitar string by string until the whole instrument matches a reference pitch perfectly. Once calibrated, it prices bonds and options with clean formulas and standard tree/grid methods. Its main weakness is that it has just one source of randomness, so it can't capture the curve twisting (short rates rising while long rates fall) — which is why richer two-factor models exist.
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