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The similarity of our approach lies in the use of Euler numerical scheme, using discretely sampled data and maximum likelihood estimation, but the main difference is that in our proposal does not need any numerical optimization because it is possible to obtain a closed formula for the estimators.
Lo, 1988, "Maximum-Likelihood-Estimation of Generalized Ito Processes with Discretely Sampled Data", Econometric Theory, 4:231-247
Brandt and Santa-Clara develop a new econometric method for estimating the parameters of a diffusion from discretely sampled data. Compared with existing estimators of continuous time models, their method is particularly effective for multivariate diffusions, is very transparent and adaptive, and inherits all the desirable asymptotic properties of the unattainable maximum likelihood estimator.
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