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