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This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, using a version of Bayes’ rule for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. An application to daily stock market returns over 1953–1996 reveals substantial divergences from estimates based on the Efficient Methods of Moments (EMM) methodology; in particular, more substantial and time-varying jump risk. The implications for pricing stock index options are examined.