This research unit (Verona) has the following objectives:
1. We aim at developing a faster MCMC algorithm (in terms of CPU
time) for the simulation of the full conditional densities.
Firsts results in this direction, with an independence chain
hybrid MCMC algorithm (Metropolis-Hastings nested in a single-move
Gibbs sampler) instead of the previous slower Adaptive Rejection
Sampling, seem encouraging. Several methodological issue are
still to be considered when dealing with GED or Skew-GED errors
as we do.
2. In the bayesian approach we follow it is
natural to consider the issue of volatility forecasting for an
arbitrary number of steps ahead. In this settings of volatility
forecasting, our purpose is to obtain the predictive distribution
of future volatilities, given the available sample of asset
returns. This approach is useful in the context option
(derivatives) pricing where information on the volatility of the
underlying asset is required.
3. We aim at an extension of
our previous analysis to the case of non-zero correlation between
the return shock and the volatility shock. This correlation is
often introduced in the analysis to take into account th
''leverage'' effect, i.e. the observed empirical relevant negative
correlation between the volatility shock and the return shock.
This development should, in the first place, consider the
multivariate Skew-Normal distribution and then should be extended
to distributions with fatter tails.