An Improved Binomial Lattice Method for Multi-Dimensional Options

We propose a binomial lattice approach for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two simple ideas: a log-transformation of the underlying processes, which is step by step consistent with the continuous--time diffusions, as proposed by Trigeorgis (1991), and a change of basis of the asset span, to transform asset prices into uncorrelated processes. We apply an additional transformation to approximate drift-less dynamics. Even if these features are simple and straightforward to implement, we show that they significantly improve the efficiency of the multi-dimensional binomial algorithm. We provide a thorough test of efficiency compared to most popular binomial and trinomial lattice approaches for multi--dimensional diffusions. Although the order of convergence is the same for all lattice approaches, the proposed method shows improved efficiency.