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Quantitative Finance · Glossary

What is Hull–White model?

Also known as: Hull--White model

Definition 7.5 Rates, Credit, XVA and Risk · Chapter 7 — Short-Rate Models

The Hull–White model (1990) is drt=(ϑ(t)−κrt) dt+σ(t) dWtdr_t = (\vartheta(t)-\kappa r_t)\,dt+\sigma(t)\,dW_t with ϑ(t)\vartheta(t) chosen so that the model’s bond prices equal today’s discount factors for every maturity. Equivalently, rt=f(0,t)+xtr_t = f(0,t)+x_t with

dxt=(y(t)−κxt)dt+σ(t) dWt,x0=0,y(t)=∫0te−2κ(t−u)σ(u)2 du.dx_t = \bigl(y(t)-\kappa x_t\bigr)dt+\sigma(t)\,dW_t,\quad x_0=0,\qquad y(t) = \int_0^te^{-2\kappa(t-u)}\sigma(u)^2\,du .
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