Building recombining trinomial trees for time-homogeneous diffusion processes

Abstract

Time-homogeneous diffusion processes are widely applied in finance and economics to model the values of assets. Two classic examples can be referred to in Black and Scholes (1973) and Cox et al. (1985). The applications include investment decisions and pricing derivatives. Due to mathematical tractability, approximation methods such as the Monte Carlo simulation and the lattice approximation are required in the applications. In this paper, we present a simple method to construct a recombining trinomial tree to approximate a time-homogeneous diffusion process in distribution. As an important application of lattice approximation is pricing derivatives, we also offer several numerical examples of pricing derivatives to examine our method of constructing recombining trinomial trees.