Simulated nonparametric estimation of continuous time models of asset prices and returns

This paper introduces a new parameter estimator of dynamic models in which the state is a multidimensional, continuous-time, partially observed Markov process. The estimator minimizes appropriate distances between nonparametric joint (and/or conditional) densities of sample data and nonparametric joint (and/or conditional) densities estimated from data simulated out of the model of interest. Sample data and model-simulated data are smoothed with the same kernel. This makes the estimator: 1) consistent independently of the amount of smoothing; and 2) asymptotically root-T normal when the smoothing parameter goes to zero at a reasonably mild rate. When the underlying state is observable, the estimator displays the same asymptotic efficiency properties as the maximum-likelihood estimator. In the partially observed case, we derive conditions under which efficient estimators can be implemented with the help of auxiliary prediction functions suggested by standard asset pricing theories. The method is flexible, fast to implement and possesses finite sample properties that are well approximated by the asymptotic theory.