Numerical modeling of bond options: implementing the Hull-White trinomial tree

Abstract

The Hull-White model is a single-factor, arbitrage-free approach to modeling the term structure of interest rates. It models the term structure by describing the evolution of the short rate, or the instantaneous rate of interest. Implementing this model results in a trinomial pricing tree that can be used to price complex interest rate derivatives such as options on swaps and bonds. The difficulty of this model lies in its relative complexity and multi-stage implementation. The model's advantage over similar models is its calculation speed. We do not develop a new method but rather explain the original implementation of the algorithm behind the Hull-White interest rate model using MATLAB programming code. We will first explain the generalized Hull-White model. We will then run the Hull-White model using market data to price a four-year bond option(put) on a nine-year zero-coupon bond.