Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo

Abstract. We investigate simulation methodology for Bayesian inference in Lévy‐driven stochastic volatility (SV) models. Typically, Bayesian inference from such models is performed using Markov chain Monte Carlo (MCMC); this is often a challenging task. Sequential Monte Carlo (SMC) samplers are methods that can improve over MCMC; however, there are many user‐set parameters to specify. We develop a fully automated SMC algorithm, which substantially improves over the standard MCMC methods in the literature. To illustrate our methodology, we look at a model comprised of a Heston model with an independent, additive, variance gamma process in the returns equation. The driving gamma process can capture the stylized behaviour of many financial time series and a discretized version, fit in a Bayesian manner, has been found to be very useful for modelling equity data. We demonstrate that it is possible to draw exact inference, in the sense of no time‐discretization error, from the Bayesian SV model.