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RFS Advance Access published online on January 12, 2009
Review of Financial Studies, doi:10.1093/rfs/hhn110
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© The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices

Michael S. Johannes
Columbia University

Nicholas G. Polson
University of Chicago

Jonathan R. Stroud
George Washington University

Send correspondence to Michael Johannes, Graduate School of Business, Columbia University, 3022 Broadway, New York, NY 10027; telephone: 212-854-0110; fax: 212-316-9180; E-mail: mj335{at}columbia.edu.

JEL Classification: G11, G12, G17, C11, C13, C15, C51, C52


  Abstract

This paper provides an optimal filtering methodology in discretely observed continuous-time jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines time-discretization schemes with Monte Carlo methods. It is quite general, applying in nonlinear and multivariate jump-diffusion models and models with nonanalytic observation equations. We provide a detailed analysis of the filter's performance, and analyze four applications: disentangling jumps from stochastic volatility, forecasting volatility, comparing models via likelihood ratios, and filtering using option prices and returns.

We thank Mark Broadie for providing option pricing code and Mike Chernov, Neil Shephard, and Mike Pitt, and seminar participants at Cirano/University of Montreal and Columbia University for their comments.


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