Parametric versus Nonparametric Estimation of Diffusion Processes — A Monte Carlo Comparison

In this paper, a Monte Carlo simulation is performed to investigate the finite sample properties of various estimators, based on discretely sampled observations, of the continuous-time Itô diffusion process. The simulation study aims to compare the performance of the nonparametric estimators proposed in Jiang and Knight (1996) with common parametric estimators based on those diffusion processes which have explicit transition density functions. The simulation results show that, with a large sample over a short sampling period, although all the parametric diffusion estimators perform very well, the parametric drift estimators perform very poorly. However, both the nonparametric diffusion and drift estimators perform reasonably well.