An Analytical Implementation of the Hull and White Model

Abstract

One of the most parsimonious models of interest rate behavior is the “extended Vasicek” model of Hull and White. It has only one stochastic factor, but has the flexibility to match the initial term structure in the market, making it arbitrage-free. To build the market term structure into a trinomial valuation lattice, Hull and White's implementation of the model involves a search process at each date plus forward induction. In this article, Grant and Vora show how this process may be streamlined considerably by using an analytic solution rather than a search at each date.