A Bayesian Analysis of Return Dynamics with Lévy Jumps
University of Michigan - Stephen M. Ross School of Business; Cheung Kong Graduate School of Business
Martin T. Wells
Cornell University - School of Law
Iowa State University
The Review of Financial Studies, Vol. 21, Issue 5, pp. 2345-2378, 2008
We have developed Bayesian Markov chain Monte Carlo (MCMC) methods for inferences of continuous-time models with stochastic volatility and infinite-activity Lévy jumps using discretely sampled data. Simulation studies show that (i) our methods provide accurate joint identification of diffusion, stochastic volatility, and Lévy jumps, and (ii) the affine jump-diffusion (AJD) models fail to adequately approximate the behavior of infinite-activity jumps. In particular, the AJD models fail to capture the “infinitely many” small Lévy jumps, which are too big for Brownian motion to model and too small for compound Poisson process to capture. Empirical studies show that infinite-activity Lévy jumps are essential for modeling the S&P 500 index returns.
Keywords: G12, C11, C15, C32Accepted Paper Series
Date posted: September 19, 2008
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