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

Ajay Jasra, David A. Stephens, Arnaud Doucet, Theodoros Tsagaris

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

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. © 2010 Board of the Foundation of the Scandinavian Journal of Statistics.
Original languageEnglish (US)
JournalScandinavian Journal of Statistics
Volume38
Issue number1
DOIs
StatePublished - Mar 1 2011
Externally publishedYes

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