Hull-White model

Hull-White model

In financial mathematics, the Hull-White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. It is relatively straight-forward to translate the mathematical description of the evolution of future interest rates onto a tree or lattice and so interest rate derivatives such as bermudan swaptions can be valued in the model.

The first Hull-White model was described by John Hull and Alan White in 1990. The model is still popular in the market today.

The model

One-factor model

The model is a short-rate model. In general, it has dynamics

:dr(t) = ( heta(t) - alpha(t) r(t)),dt + sigma(t), dW(t),!

There is a degree of ambiguity amongst practitioners about exactly which parameters in the model are time-dependent on what name to apply to the model in each case.The most commonly accepted hierarchy has

:θ constant - the Vasicek model:θ has t dependence - the Hull-White model:θ and α also time-dependent - the extended Vasicek model

Two-factor model

The two-factor Hull-White model
pages= pp. 657–658
chapter= Interest Rate Derivatives: Models of the Short Rate
quote=


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