  Several studies explore inferences based on stochastic volatility (SV)
models, taking into account the stylized facts of return data. The common
problem is that the latent parameters of many volatility models are
high-dimensional and analytically intractable, which means inferences require
approximations using, for example, the Markov Chain Monte Carlo or Laplace
methods. Some SV models are expressed as a linear Gaussian state-space model
that leads to a marginal likelihood, reducing the dimensionality of the
problem. Others are not linearized, and the latent parameters are integrated
out. However, these present a quite restrictive evolution equation. Thus, we
propose a Bayesian GED-Gamma SV model with a direct marginal likelihood that is
a product of the generalized Student's t-distributions in which the latent
states are related across time through a stationary Gaussian evolution
equation. Then, an approximation is made for the prior distribution of
log-precision/volatility, without the need for model linearization. This also
allows for the computation of the marginal likelihood function, where the
high-dimensional latent states are integrated out and easily sampled in blocks
using a smoothing procedure. In addition, extensions of our GED-Gamma model are
easily made to incorporate skew heavy-tailed distributions. We use the Bayesian
estimator for the inference of static parameters, and perform a simulation
study on several properties of the estimator. Our results show that the
proposed model can be reasonably estimated. Furthermore, we provide case
studies of a Brazilian asset and the pound/dollar exchange rate to show the
performance of our approach in terms of fit and prediction.
  Keywords: SV model, New sequential and smoothing procedures, Generalized
Student's t-distribution, Non-Gaussian errors, Heavy tails, Skewness
