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In this paper we present a novel method for estimating the parameters of aparametric diffusion processes. Our approach is based on a closed-form MaximumLikelihood estimator for an approximating Continuous Time Markov Chain (CTMC)of the diffusion process. Unlike typical time discretization approaches, suchas psuedo-likelihood approximations with Shoji-Ozaki or Kessler's method, theCTMC approximation introduces no time-discretization error during parameterestimation, and is thus well-suited for typical econometric situations withinfrequently sampled data. Due to the structure of the CTMC, we are able toobtain closed-form approximations for the sample likelihood which hold forgeneral univariate diffusions.  Comparisons of the state-discretization approach with approximate MLE(time-discretization) and Exact MLE (when applicable) demonstrate favorableperformance of the CMTC estimator. Simulated examples are provided in additionto real data experiments with FX rates and constant maturity interest rates.

Maximum Likelihood Estimation of Diffusions by Continuous Time Markov Chain