This paper considers ML estimation of a diffusion process observed discretely. Since the exact loglikelihood is generally not available, it must be approximated. We review the most efficient approaches in the literature, and point to some drawbacks. We propose to approximate the loglikelihood using the EIS strategy (Richard and Zhang, 1998), and detail its implementation for univariate homogeneous processes. Some Monte Carlo experiments evaluate its performance against an alternative IS strategy (Durham and Gallant, 2002), showing that EIS is at least equivalent, if not superior, while allowing a greater flexibility needed when examining more complicated models
