Abstracts

In this paper we consider continuous-time diffusion models driven by fractional Brownian Motion (fBM), with observations obtained at discrete-time instances. As a prototypical scenario we will give emphasis on a a stochastic volatility (SV) model allowing for memory in the volatility increments through an fBM specification. Due to the non-Markovianity of the model and the high-dimensionality of the latent volatility path, estimating posterior expectations is a computationally challenging task. We present novel simulation and re-parameterisation framework based on the Davies and Harte method and use it to construct a Markov chain Monte-Carlo (MCMC) algorithm that allows for computationally efficient parametric Bayesian inference upon application on such models. The algorithm is based on an advanced version of the so-called Hybrid Monte-Carlo (HMC) that allows for increased efficiency when applied on high-dimensional latent variables relevant to the models of interest in this paper. The inferential methodology is examined and illustrated in the SV models, on simulated data as well as real data from the S&P500/VIX time series that may include intra-day data. Contrary to a long range dependence attribute of the SV process (Hurst parameter H > 1/2) many times assumed in the literature, the posterior distribution favours H < 1/2 that points towards medium range dependence.