A lattice approach for pricing of multivariate contingent claims

The lattice approach developed by Boyle, Evnine and Gibbs (BEG) is hitherto one of the most appealing, when it comes to pricing multivariate contingent claims. The BEG approach has, however, some problems, two of the major ones being that the method can lead to negative jump probabilities and has a slow rate of convergence. In this paper, a lattice approach (the NEK approach) is developed which avoids both of the aforementioned problems of the BEG approach. It is shown that the NEK approach has a very fast rate of convergence. The results are accurate enough for most needs with as few as ten time steps, and the results are astonishingly accurate with twenty time steps. Moreover, the NEK approach is simple and easy to understand, and also easy to implement. The latter property follows from the fact that all jump probabilities are equal and that the formulas for the jump sizes are extremely simple.