A Bayesian Analysis of Return Dynamics with Lévy Jumps

Posted: 19 Sep 2008

See all articles by Haitao Li

Haitao Li

University of Michigan - Stephen M. Ross School of Business; Cheung Kong Graduate School of Business; Cheung Kong Graduate School of Business

Martin T. Wells

Cornell University - Law School

Cindy Yu

Iowa State University

Date Written: September 2008

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.

Keywords: G12, C11, C15, C32

Suggested Citation

Li, Haitao and Wells, Martin T. and Yu, Cindy, A Bayesian Analysis of Return Dynamics with Lévy Jumps (September 2008). The Review of Financial Studies, Vol. 21, Issue 5, pp. 2345-2378, 2008, Available at SSRN: https://ssrn.com/abstract=1270458 or http://dx.doi.org/hhl036

Haitao Li (Contact Author)

University of Michigan - Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
734-615-5475 (Phone)

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Martin T. Wells

Cornell University - Law School ( email )

Comstock Hall
Ithaca, NY 14853
United States
607-255-8801 (Phone)

Cindy Yu

Iowa State University ( email )

613 Wallace Road
Ames, IA 50011
United States

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