RFS Advance Access originally published online on January 12, 2009
Review of Financial Studies 2009 22(7):2759-2799; doi:10.1093/rfs/hhn110
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Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices
Columbia University
University of Chicago
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: C11, C13, C15, C51, C52, G11, G12, G17
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Abstract |
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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.