Binomial Approximation in Financial Models: Computational Simplicity and Convergence

This paper explores the potential of transformation and other schemes in constructing a sequence of simple binomial processes that weakly converges to the desired diffusion limit. Convergence results are established for valuing both European and American contingent claims when the underlying asset prices are approximated by simple binomial processes. We also demonstrate how to construct reflecting and absorbing binomial processes to approximate diffusions with boundaries. Numerical examples show that the proposed simple approximations not only converge, but also give more accurate results than existing methods, such as that of Nelson and Ramaswamy (1990), especially for longer maturities.