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MCMC ESTIMATION OF LÉVY JUMP MODELS USING STOCK AND OPTION PRICES
Author(s) -
Yu Cindy L.,
Li Haitao,
Wells Martin T.
Publication year - 2011
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00439.x
Subject(s) - jump diffusion , jump , markov chain monte carlo , stochastic volatility , econometrics , volatility (finance) , mathematics , affine transformation , stock (firearms) , economics , poisson distribution , monte carlo method , statistics , physics , mechanical engineering , quantum mechanics , pure mathematics , engineering
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.