Evergreen Trees: The Likelihood Ratio Method for Binomial and Trinomial Trees

Despite their age, binomial and trinomial trees are still used extensively in the financial industry to price securities with early exercise features such as American equity options and callable bonds. This technique is related to the fully explicit finite difference method used to numerically solve partial differential equations. The purpose of this article is to present an alternative mathematical derivation for binomial and trinomial trees using the path integral formalism. Recasting the tree in this light admits an extremely efficient, accurate, and novel method to calculate deltas by using the likelihood ratio method.