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RFS Advance Access originally published online on September 20, 2006
Review of Financial Studies 2008 21(5):2345-2378; doi:10.1093/rfs/hhl036
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© The Author 2006. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A Bayesian Analysis of Return Dynamics with Lévy Jumps

Haitao Li
University of Michigan

Martin T. Wells
Cornell University

Cindy L. Yu
Iowa State University

Address correspondence to Haitao Li, University of Michigan, Stephen M. Ross School of Business, Ann Arbor, MI 48109, or e-mail: htli{at}umich.edu

JEL Classification: G12, C11, C15, C32


  Abstract

We have developed Bayesian Markov chain Monte Carlo (MCMC) methods for inferences of continuous-time models with stochastic volatility and infinite-activity Lévy jumps using discretely sampled data. Simulation studies show that (i) our methods provide accurate joint identification of diffusion, stochastic volatility, and Lévy jumps, and (ii) the affine jump-diffusion (AJD) models fail to adequately approximate the behavior of infinite-activity jumps. In particular, the AJD models fail to capture the "infinitely many" small Lévy jumps, which are too big for Brownian motion to model and too small for compound Poisson process to capture. Empirical studies show that infinite-activity Lévy jumps are essential for modeling the S&P 500 index returns.

We would like to thank Torben Andersen and Luca Benzoni for their help in the early stage of this study. We thank Yacine Ait-Sahalia, Antje Berndt, Peter Carr, Bjorn Eraker, Bob Jarrow, Nour Meddahi, Ray Renken, Sidney Resnick, Ernst Schaumburg, Neil Shephard, George Tauchen, Liuren Wu, an anonymous referee, and seminar participants at Cornell University, the 2004 CIREQ/CIRANO financial econometrics conference, the 2004 International Chinese Statistical Association Applied Statistics Symposium, and the 2004 Institute of Mathematical Statistics Annual Meeting/6th Bernoulli World Congress for helpful comments. Martin Wells gratefully acknowledges the support of NSF Grant DMS 02-04252. We are responsible for any remaining errors.


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