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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