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Rev Fin 1990; 3:393-430
© 1990 the Society for Financial Studies

Article

Simple binomial processes as diffusion approximations in financial models

DB Nelson1 and K Ramaswamy2
1 The University of Chicago, Chicago, USA
2 The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA

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. It is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models. The convergence of the sequence of bond and European option prices from these processes to the corresponding values in the diffusion limit is also demonstrated. Numerical examples from the constant elasticity of variance stock price and the Cox, Ingersoll, and Ross (1985) discount bond price are provided.


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