Unbiased Parameter Inference for a Class of Partially Observed Lévy-Process Models

Abstract

We consider the problem of static Bayesian inference for partially observed Lévy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the time-discretization of the afore-mentioned Lévy process. The unbiased method is exceptionally amenable to parallel implementation and can be computationally efficient relative to competing approaches. We implement the method on S &P 500 log-return daily data and compare it to some Markov chain Monte Carlo (MCMC) algorithms.