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

Authors


Ajay Jasra, Department of Mathematics, 180 Queens Gate, Imperial College London, London, UK.
E-mail: ajay.jasra@ic.ac.uk

Abstract

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.

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