The project in its core aims at novel extension of the recent studies on econometrics volatility models to account, on the one hand, for dynamics, and for more general than Gaussian noise distributions on the other. The research stems from and creates bridges between recent developments, both in econometrics and in stochastic modelling. The attempt is to combine these two areas of research to obtain accurate models for analyzing dependence and risk contagion in global financial markets and identify attributes which affect this dependence. Our models provide both computational efficiency resulting from the Markovian structure of the fields, and flexible distributional modelling facilitated by the extension beyond Gaussianity as offered by the generalized skewed Laplace laws. The main focus is on random models that are pertinent to econometrics modelling and potentially effective in dynamical extensions. This would involve model fitting, statistical inference, prediction and reconstruction for the underlying stochastic models.