A Refinement to Ait-Sahalia's (2002) "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach"

This paper provides a closed-form density approximation when the underlying state variable is a one-dimensional diffusion. Building on Aït-Sahalia (2002), we show that our refinement is applicable under a wide class of drift and diffusion functions. In addition, it facilitates the maximum likelihood estimation of discretely sampled diffusion models of short interest-rate or stock volatility with unknown conditional densities. Our interest-rate examples demonstrate that the analytical approximation is sufficiently accurate.