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Hull White Model is a Type that represents a short rate that follows a single-factor stochastic process r according to the SDE:
dr = (θ - αr)dt + σdw
where w is a Wiener process, α and σ are constants and θ is a deterministic function of the time t
It follows that the short rate follows a gaussian process with a mean reverting stochastic drift, a fact that results in being normally distributed. Web reference available