Simple Binomial Processes as Diffusion Approximations in Financial Models (Reprint 003)

Daniel B. Nelson and Krishna Ramaswamy (krishna@wharton.upenn.edu)

Rodney L. White Center for Financial Research Working Papers from Wharton School Rodney L. White Center for Financial Research

Abstract: A binomial approximation to a diffusion is defined as computationally simple if the number of nodes grows at most linearly in the number of time intervals. This paper shows how to construct computationally simple binomial processes which converge weakly to commonly employed diffusions in financial models. It also demonstrates the convergence of the sequence of bond and European option prices from these processes to the corresponding values in the diffusion limit. Numerical examples from the Constant Elasticity of Variance stock price and the Cox, Ingersoll, and Ross discount bond price are provided.

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