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 straightforward 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 C. Hull and Alan White in 1990. The model is still popular in the market today.
The model is a short-rate model. In general, it has dynamics
There is a degree of ambiguity amongst practitioners about exactly which parameters in the model are time-dependent or what name to apply to the model in each case. The most commonly accepted hierarchy has
The two-factor Hull–White model (Hull 2006:657–658) contains an additional disturbance term whose mean reverts to zero, and is of the form:
where has an initial value of 0 and follows the process:
For the rest of this article we assume only has t-dependence. Neglecting the stochastic term for a moment, notice that the change in r is negative if r is currently "large" (greater than θ(t)/α) and positive if the current value is small. That is, the stochastic process is a mean-reverting Ornstein–Uhlenbeck process.
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