Abstract

http://ssrn.com/abstract=334601
 
 

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Nonlinear Filtering of Stochastic Differential Equations with Jumps


Michael S. Johannes


Columbia Business School - Finance and Economics

Jonathan R. Stroud


University of Pennsylvania - Statistics Department

Nick Polson


University of Chicago - Booth School of Business

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.

Number of Pages in PDF File: 44

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

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Date posted: October 15, 2002  

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: http://ssrn.com/abstract=334601 or http://dx.doi.org/10.2139/ssrn.334601

Contact Information

Michael Slater Johannes (Contact Author)
Columbia Business School - Finance and Economics ( email )
3022 Broadway
New York, NY 10027
United States

Jonathan R. Stroud
University of Pennsylvania - Statistics Department ( email )
Wharton School
Philadelphia, PA 19104
United States
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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