Algorithms behind Term Structure Models of Interest Rates II: The Hull-White Trinomial Tree of Interest Rates

Abstract

In this article we implement the trinomial tree of the Hull-White model, which can be easily extended to allow different assumptions about the dynamics of the short rate process. We present the Mathematical algorithm for the extended Vasicek and the Black-Karasinski model. Whenever negative interest rates are generated with a positive probability, we make use of alternative branching processes, which guarantee the positivity of interest rates. Finally we show how to price simple options such as caplets, and compare the convergence of trinomial trees with different geometries.