Incorporating Higher Moments into Value at Risk Estimation

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 the standard normal distribution with time-varying higher moments. We allow the first four moments of the GCE to depend on past information, which leads to a more accurate approximation of the tails of the distribution. The results unambiguously show that our GCE-based VaR forecasts provide accurate and robust estimates of the realised VaR, outperforming those generated by the constant-higher-moments models