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RFS Advance Access originally published online on February 17, 2006
Review of Financial Studies 2006 19(3):909-965; doi:10.1093/rfs/hhj022
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© The Author 2006. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org.

Maximum Likelihood Estimation of Latent Affine Processes

David S. Bates
University of Iowa

Address correspondence to David S. Bates, Henry B. Tippie College of Business, University of Iowa, Iowa City, IA 52242-1000, or e-mail: david-bates{at}uiowa.edu.

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.


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