We propose new systematic tail risk measures constructed using two different approaches. The first extends the canonical downside beta and co-moment measures, while the second is based on the sensitivity of stock returns to innovations in market crash risk. Both tail risk measures are associated...

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 new simple approach to estimation of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting...

Multidimensional Value at Risk (MVaR) generalises VaR in a natural way as the intersection of univariate VaRs. We reduce the dimensionality of MVaRs which allows for adapting the techniques and applications developed for VaR to MVaR. As an illustration, we employ VaR forecasting and evaluation...

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation...

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...

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...

We propose two simple evaluation methods for time-varying density forecasts of continuous higher-dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation...