  This paper presents a tractable sufficient condition for the consistency of
maximum likelihood estimators (MLEs) in partially observed diffusion models,
stated in terms of stationary distribution of the associated fully observed
diffusion, under the assumption that the set of unknown parameter values is
finite. This sufficient condition is then verified in the context of a latent
price model of market microstructure, yielding consistency of maximum
likelihood estimators of the unknown parameters in this model. Finally, we
compute the latter estimators using historical financial data taken from the
NASDAQ exchange.
