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The author develops a simple, discrete time model to value options when the underlying process follows a jump diffusion process. Multivariate jumps are superimposed on the binomial model of J. C. Cox, S. A. Ross, and M. Rubinstein (1979) to obtain a model with a limiting jump diffusion process. This model incorporates the early exercise feature of American options as well as arbitrary jump distributions. It yields an efficient computational procedure that can be implemented in practice. As an application of the model, the author illustrates some characteristics of the early exercise boundary of American options with certain types of jump distributions.