Nonlinear Filtering of Stochastic Differential Equations with Jumps

Michael S. Johannes, Nick Polson, Jonathan R. Stroud
2002 Social Science Research Network  
In this paper, we develop an approach for filtering state variables in the setting of continuous-time jump-diffusion models. Our method computes the filtering distribution of latent state variables conditional only on discretely observed observations in a manner consistent with the underlying continuous-time process. The algorithm is a combination of particle filtering methods and the "filling-in-the-missing-data" estimators which have recently become popular. We provide simulation evidence to
more » ... erify that our method provides accurate inference. As an application, we apply the methodolgy to the multivariate jump models in Duffie, Pan and Singleton (2000) using daily S&P 500 returns from 1980-2000 and we investigate option pricing implications. * Johannes is at the
doi:10.2139/ssrn.334601 fatcat:rfej2t4qajg6ll7leofnhcgkxe