MCMC Methods for Continuous-Time Financial Econometrics

96 Pages Posted: 27 Dec 2003  

Michael S. Johannes

Columbia Business School - Finance and Economics

Nick Polson

University of Chicago - Booth School of Business

Date Written: December 22, 2003

Abstract

This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuous-time asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these high-dimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the Clifford-Hammersley theorem, the Gibbs sampler, the Metropolis-Hastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuous-time asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regime-switching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.

Suggested Citation

Johannes, Michael S. and Polson, Nick, MCMC Methods for Continuous-Time Financial Econometrics (December 22, 2003). Available at SSRN: https://ssrn.com/abstract=480461 or http://dx.doi.org/10.2139/ssrn.480461

Michael Slater Johannes (Contact Author)

Columbia Business School - Finance and Economics ( email )

3022 Broadway
New York, NY 10027
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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