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Nonlinear Filtering of Stochastic Differential Equations with Jumps

44 Pages Posted: 15 Oct 2002  

Michael S. Johannes

Columbia Business School - Finance and Economics

Jonathan R Stroud

McDonough School of Business, Georgetown University

Nick Polson

University of Chicago - Booth School of Business

Date Written: October 8, 2002

Abstract

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 verify that our method provides accurate inference. As an application, we apply the methodology 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.

Keywords: Filtering, Stochastic Differential Equations, Jumps, Option Pricing, Volatility

Suggested Citation

Johannes, Michael S. and Stroud, Jonathan R and Polson, Nick, Nonlinear Filtering of Stochastic Differential Equations with Jumps (October 8, 2002). Available at SSRN: https://ssrn.com/abstract=334601 or http://dx.doi.org/10.2139/ssrn.334601

Michael Slater Johannes (Contact Author)

Columbia Business School - Finance and Economics ( email )

3022 Broadway
New York, NY 10027
United States

Jonathan R. Stroud

McDonough School of Business, Georgetown University ( email )

3700 O Street NW
Washington, DC 20057
United States

HOME PAGE: http://jonathanrstroud.com

Nick Polson

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7513 (Phone)
773-702-0458 (Fax)

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