Dynamic density forecasts for multivariate asset returns

We propose a simple and flexible framework for forecasting the joint density of asset returns. The multinormal distribution is augmented with a polynomial in (time‐varying) non‐central co‐moments of assets. We estimate the coefficients of the polynomial via the method of moments for a carefully selected set of co‐moments. In an extensive empirical study, we compare the proposed model with a range of other models widely used in the literature. Employing a recently proposed as well as standard techniques to evaluate multivariate forecasts, we conclude that the augmented joint density provides highly accurate forecasts of the ‘negative tail’ of the joint distribution. Copyright © 2010 John Wiley & Sons, Ltd.     

Incorporating higher moments into value‐at‐risk forecasting

Value‐at‐risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a simple approach to forecasting of a portfolio VaR. We employ the Gram‐Charlier expansion (GCE) augmenting the standard normal distribution with the first four moments, which are allowed to vary over time. In an extensive empirical study, we compare the GCE approach to other models of VaR forecasting and conclude that it provides accurate and robust estimates of the realized VaR. In spite of its simplicity, on our dataset GCE outperforms other estimates that are generated by both constant and time‐varying higher‐moments models. Copyright © 2009 John Wiley & Sons, Ltd.