Maximum likelihood estimation of diffusions by continuous time Markov chain

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