A note on the efficiency of the binomial option pricing model

We discuss the efficiency of the binomial option pricing model for single and multivariate American style options. We demonstrate how the efficiency of lattice techniques such as the binomial model can be analysed in terms of their computational cost. For the case of a single underlying asset the most efficient implementation is the extrapolated jump-back method: that is, to value a series of options with nested discrete sets of early exercise opportunities by jumping across the lattice between the early exercise times and then extrapolating from these values to the limit of a continuous exercise opportunity set. For the multivariate case, the most efficient method depends on the computational cost of the early exercise test. However, for typical problems, the most efficient method is the standard step-back method: that is, performing the early exercise test at each time step.