VAR and Es for Linear Portfolios with Mixture of Generalized Laplace Distributions Risk Factors

In this paper, we propose an explicit estimation of Value-at-Risk (VaR) and Expected Shortfall (ES) for Linear Portfolios when the risk factors change with a conditional convex mixture of generalized Laplace distributions with a time-varying kurtosis. We therefore introduce the dynamics Delta-GLDVaR, Delta-GLD-ES, Delta-MGLD-VaR and Delta-MGLD-ES estimation, by using conditional correlation multivariate GARCH. Note also that, the GLD impose less restrictive assumptions during estimation that should improve the precision of the VaR and ES through the time-varying shape and fat tails of the risk factors in relation with the historical sample data. We also suggested some areas of application such as Credit Risk, portfolio optimization etc