A Refinement to Aït‐Sahalia's (2002) “Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed‐Form Approximation Approach”*

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Abstract
This paper provides a closed-form density approximation when the underlying state variable is a one-dimensional diffusion. Building on Ait-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

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