MCMC Estimation of L evy Jump Models Using Stock and Option Prices

Abstract

We examine the performances of several popular L evy jump models and some of the most sophisticated a ne jump-di usion models in capturing the joint dynamics of stock and option prices. We develop e cient MCMC methods for estimating parameters and latent volatility/jump variables of the L evy jump models using stock and option prices. We show that models with in nite-activity L evy jumps in returns signi cantly outperform a ne jump-di usion 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 nd that the variance gamma model of Madan, Carr, and Chang (1998) with stochastic volatility has the best performance among all the models we consider. aLi is from the Stephen M. Ross School of Business, University of Michigan, Ann Arbor, MI 48109; E-mail: htli@umich.edu; phone: (734) 615-5475. bWells is from the Department of Biological Statistics and Computational Biology and the Department of Social Statistics, Cornell University, Ithaca, NY 14853; E-mail: mtw1@cornell.edu; phone: (607) 255-4388; he gratefully acknowledges the support of NSF Grant DMS 02-04252. cYu is from the Department of Statistics, Iowa State University, Ames, IA 50011; E-mail: cindyyu@iastate.edu; phone: (515) 294-3319. We thank Yacine A t-Sahalia for providing the data used in this study. We thank Yacine A t-Sahalia, Antje Berndt, Peter Carr, Francois Derrien, Bjorn Eraker, Wayne Fuller, John Hull, Raymond Kan, Bob Jarrow, George Jiang, John Maheu, Nour Meddahi, Tom McCurdy, Ray Renken, Sidney Resnick, Ernst Schaumburg, Neil Shephard, George Tauchen, Liuren Wu, the associate editor, two anonymous referees, and seminar participants at Cornell University, Hong Kong University of Science and Technology, Iowa State University, Virginia Commonwealth University, the University of Arizona, the University of Toronto, and the 17th Derivatives Conference at FDIC for helpful comments. We are responsible for any remaining

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Cite this paper

@inproceedings{Li2008MCMCEO, title={MCMC Estimation of L evy Jump Models Using Stock and Option Prices}, author={Haitao Li and Martin T. Wells and Cindy L. Yuc and Antje Berndt and Peter Carr and Francois Derrien and Bjorn Eraker and Wayne Fuller and John C. Hull and Raymond Kan}, year={2008} }