Approximate maximum likelihood estimation for one‐dimensional diffusions observed on a fine grid

We consider a one-dimensional stochastic differential equation that is observed on fine grid of equally spaced time points. A novel approach for approximating the transition density presented, which based an Itô-Taylor expansion sample path, combined with application so-called ϵ -expansion. The resulting approximation economical respect to number terms needed achieve given level accuracy in high-frequency sampling framework. This method leads closed-form approximate likelihood function from maximum estimator may be calculated numerically. detailed theoretical analysis proposed provided and it shown compares favorably Gaussian likelihood-based does excellent job exact, but usually intractable, estimator. Numerical simulations indicate exact our tend close, latter performs very well relative other methods literature speed, accuracy, ease implementation.