Lean Trees—A General Approach for Improving Performance of Lattice Models for Option Pricing

Abstract

The well-known binomial and trinomial tree models for option pricing are examined from the point of view of numerical efficiency. Common lattices use a large part of time resources for calculations which are almost irrelevant for the solution. To avoid this waste of resources, the tree is reduced to a “lean” form which yields the same order of convergence, but with a reduction of numerical effort. In numerical tests it is shown that the proposed method leads to a significant improvement in real calculation time without loss of accuracy for a broad class of derivatives.