Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices
Michael S. Johannes, Nicholas G. Polson, Jonathan R. Stroud
Columbia University, University of Chicago, and George Washington University
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 non-analytic observations
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.
The manuscript is available in PDF format.