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Maximum Likelihood Estimation of Latent Affine Processes

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  • David S. Bates

Abstract

This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. The equivalent of Bayes' rule is derived for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. Likelihood functions can consequently be evaluated directly by Fourier inversion. An application to daily stock returns over 1953-96 reveals substantial divergences from EMM-based estimates: in particular, more substantial and time-varying jump risk.

Suggested Citation

  • David S. Bates, 2003. "Maximum Likelihood Estimation of Latent Affine Processes," NBER Working Papers 9673, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:9673
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    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003.
    2. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    3. Pezzo, Rosanna & Uberti, Mariacristina, 2006. "Approaches to forecasting volatility: Models and their performances for emerging equity markets," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 556-565.
    4. Cyrus Ramezani & Yong Zeng, 2007. "Maximum likelihood estimation of the double exponential jump-diffusion process," Annals of Finance, Springer, vol. 3(4), pages 487-507, October.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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