Hybrid MSV-MGARCH Models - General Remarks and the GMSF-SBEKK Specification

Abstract

The first so-called hybrid MSV-MGARCH models were characterized by
the conditional covariance matrix that was a product of a univariate latent
process and a matrix with a simple MGARCH structure (Engle’s DCC or scalar
BEKK). The aim was to parsimoniously describe volatility of a large group
of assets. The proposed hybrid models, similarly as pure MSV specifications
(and other models based on latent processes), required the Bayesian approach
equipped with efficient MCMC simulation tools. The numerical effort has
payed – the hybrid models seem particularly useful due to their good fit
and ability to jointly cope with large portfolios. In particular, the simplest
hybrid, now called the MSF-SBEKK model, has been successfully used in
many applications. However, one latent process may be insufficient in the case
of a highly heterogeneous portfolio. Thus, in this study we discuss a general
hybrid MSV-MGARCH model structure, showing its basic characteristics
that explain greater flexibility of such hybrid structure with respect to the
corresponding MGARCH class. From the empirical perspective, we advocate
the GMSF-SBEKK specification, which uses as many latent processes as there
are relatively homogeneous groups of assets. We present full Bayesian inference
for such models, with the use of an efficient MCMC simulation strategy. The
approach is used to jointly model volatility on very different markets. Joint
modelling is formally compared to individual modelling of volatility on each
market.