An Improved Binomial Lattice Method for Multi-Dimensional Option Problems

We propose an improved binomial lattice approach for valuing complex option problems whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two main ideas: a specific change of time scale as in the log-trasformed binomial approach by Trigeorgis (1991), and a change of basis of the asset span, to trasform them into uncorrelated processes. These features improve the efficiency of the multi-dimensional binomial algorithm. Moreover, the proposed algorithm monotonically converges to the true result and is most suitable to employ Richardson extrapolation for improved accuracy. We present various applications to financial and to real option pricing problems and show the flexibility and improved efficency over existing binomial approaches.