← Search

A Bayesian Analysis of Return Dynamics with Lévy Jumps

Haitao Li¹; Martin T. Wells²; Cindy Yu³

¹ University of Michigan–Ann Arbor · ² Cornell University · ³ Iowa State University

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.

DOI

10.1093/rfs/hhl036

Volume

21 (5)

Pages

2345-2378

Language

en

Export

BibTeX

Sources

openalex crossref