MCMC ESTIMATION OF LÉVY JUMP MODELS USING STOCK AND OPTION PRICES

Authors


  • Martin Wells gratefully acknowledges the support of NSF Grant DMS 02-04252. We thank Yacine Aït-Sahalia for providing the data used in this study. We thank Yacine Aït-Sahalia, Antje Berndt, Peter Carr, Francois Derrien, Jefferson Duarte, Bjorn Eraker, Wayne Fuller, John Hull, Raymond Kan, Bob Jarrow, George Jiang, Dilip Madan (the editor), 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, Rice 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 errors.

Address correspondence to Cindy L. Yu, Department of Statistics, Iowa State University, Ames, IA 50010; e-mail: cindyyu@iastate.edu.

Abstract

We examine the performances of several popular Lévy 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 Lévy jump models using stock and option prices. We show that models with infinite-activity Lévy 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.

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