MCMC Estimation of Lvy Jump Models Using Stock and Option Prices

40 Pages Posted: 20 May 2011

See all articles by Cindy Yu

Cindy Yu

Iowa State University

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

Date Written: July 2011

Abstract

We examine the performances of several popular Lvy jump models and some of the most sophisticated affine jump-diffusion models in capturing the joint dynamics of stock and option prices. We develop efficient Markov chain Monte Carlo methods for estimating parameters and latent volatility/jump variables of the Lvy jump models using stock and option prices. We show that models with infinite-activity Lvy jumps in returns significantly outperform affine jump-diffusion models with compound Poisson jumps in returns and volatility in capturing both the physical and risk-neutral dynamics of the S&P 500 index. We also find that the variance gamma model of Madan, Carr, and Chang with stochastic volatility has the best performance among all the models we consider.

Keywords: Levy processes, variance gamma model, Markov Chain Monte Carlo, option pricing

Suggested Citation

Yu, Cindy and Li, Haitao and Wells, Martin T., MCMC Estimation of Lvy Jump Models Using Stock and Option Prices (July 2011). Mathematical Finance, Vol. 21, Issue 3, pp. 383-422, 2011, Available at SSRN: https://ssrn.com/abstract=1841235 or http://dx.doi.org/10.1111/j.1467-9965.2010.00439.x

Cindy Yu

Iowa State University ( email )

613 Wallace Road
Ames, IA 50011
United States

Haitao Li

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)

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