Simple Binomial Processes as Diffusion Approximations in Financial Models

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.The seminal work of Merton (1969) and Black and Scholes (1973) paved the way for the use of continuous-time models in finance. The usefulness of the underlying mathematical techniques has never been in doubt: the pricing of options and other contingent claims has relied heavily on these techniques. When Sharpe (1978) developed the binomial approach, the option pricing model became accessible to a much We thank

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