The majority of stylized facts of financial time series and several Value-at-Risk measures are modeled via univariate or multivariate GARCH processes. It is not rare that advanced GARCH models fail to converge for computational reasons, and a usual parsimonious approach is the GJR-GARCH model....

We elaborate on a new distributional scheme resulting from the generalized Pearson distribution with application to financial modelling. As case studies we consider the major historical indices daily returns, DJIA, NASDAQ composite, FTSE100, CAC40, DAX and S&P500, as well as, high-frequency...