MCMC Estimation of Lvy Jump Models Using Stock and Option Prices
40 Pages Posted: 20 May 2011
Date Written: July 2011
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
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