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 to O(n^(3/2) log n) (where n is the number of time steps). Two instances of this Lean Tree Model are presented: a binomial one for pricing American put options and a trinomial one with largest possible generality to be used for a wide class of derivatives. In numerical tests it is shown that the proposed method leads to a significant improvement in real calculation time without loss of accuracy.